SCALE-UP OF BIOREACTORS
A SCALE-DOWN APPROACH
SCALE-UP OF BIOREACTORS
A SCALE-DOWN APPROACH
Proefschrift ter v e r k r i j g i n g v a n d e g r a a d v a n d o c t o r in d e t e c h n i s c h e w e t e n s c h a p p e n a a n d e T e c h n i s c h e H o g e s c h o o l Delft, o p g e z a g v a n d e R e c t o r M a g n i f i c u s , p r o f . i r . B . P . T h . V e l t m a n , in het o p e n b a a r te v e r d e d i g e n t e n o v e r s t a a n v a n het C o l l e g e v a n D e k a n e n o p 20 m a a r t 1984 te 16.00 u u r d o o rNicolaas Marius Gerard Oosterhuis, g e b o r e n te Z a a n d i j k ,
Dtt proefschrift is goedgekeurd door de p r o m o t o r
Prof.dr.ir. N.W.F. Kossen
'Ei' mompelde hij, 'ik ben verbaasd over de grove wijze waar-op men hier is waar-opgetreden. Het is duidelijk dat men zich meer heeft bezig gehouden met de vraag: wat is daar aan de hand?, dan met de kwestie: wat kunnen we er mee doen? Maar dat noemt men nu eenmaal wetenschap . . .1
Voorwoord
Het boekje dat hier voor u ligt is het resultaat van ongeveer drie en een half jaar werk. Daar-aan hebben veel mensen hun bijdrage geleverd.
Ook is door verschillende instanties financiële steun verleend. Z o werd het onderzoek ge-steund door de Stichting voor de Technische Wetenschappen (projectnummer D S T 1 1 . 0 1 1 3 ) .
Mijn dank gaat in de eerste plaats uit naar mijn promotor, professor dr.ir. N.W.F. Kossen. Beste N i c o , je kritische kijk op en steun en begeleiding tijdens het onderzoek waren zeer waardevol.
De metingen op produktieschaal zijn mogelijk gemaakt door de interesse en steun van Avebe (Ter Apelkanaal). Zonder de inzet, het enthousiasme en zonder de geboden faciliteiten bij dit bedrijf zou een groot deel van dit onderzoek niet mogelijk zijn geweest.
Een belangrijke bijdrage aan het onderzoek werd geleverd door A k z o Corporate Research (Arnhem), waarvoor mijn dank dan ook bijzonder groot is.
Het vele praktische werk dat uiteindelijk tot dit boekje heeft geleid is mede uitgevoerd door een enthousiaste groep studenten: Peter van der Ham, Niek Groesbeek, Johan Boelee, Els Schenk, A n t o n Sweere en Peter Olivier. Hun bijdrage en persoonlijke inzet waren erg waar-devol.
Het is niet mogelijk om iedereen te bedanken die op welke wijze dan ook een actieve bijdra-ge heeft bijdra-geleverd aan de totstandkoming van dit proefschrift. T o c h wil ik een poging wabijdra-gen. Mijn dank gaat uit naar: drs. W.C. Bus, drs K . F . Gotlieb, C o r Mellema, Jos Meibefg, P. Nijssen, Herman Poker, Nanne P o p k e n , T o n V l o t , Piet de Vries, wachtchefs en produktiepersoneel gluconaat fabriek (Avebe, Ter Apelkanaal, Veendam en F o x h o l ) ;
Jan van Barneveld, Leo de Meulmeester, Hans Pragt, W i m S m i t , dr. C. K o o i j , dr. A . Opschoor ( A k z o Corporate Research, A r n h e m ) ;
Wiebe Olijve, ir. E. H. Houwink (Organon Int., Oss);
ir. G . A . M . Kerstjens, dr. A . J . H . Noliet ( A k z o Chemie, Amersfoort, Deventer);
José van Dijk, A d de Graaf, Bart Kerkdijk, Nico Kossen, Karei L u y b e n , Cor Ras, (vakgroep Bioprocestechnologie, Technische Hogeschool Delft);
A . L . van Maarseveen, prof. J . M . S m i t h , Marijn Warmoeskerken (Vakgroep Fysische Techno-logie, Technische Hogeschool Delft);
Werkplaats 'gebouw voor Analytische Scheikunde' en de werkplaats 'afd. Fysische Techno-logie' (Technische Hogeschool Delft);
Henny Appels-den Ridder, Kees Koerts, directie Suiker Unie, huisdrukkerij Suiker Unie (Suiker Unie, Breda, Roosendaal);
Birgitta Marijnissen en vele anderen.
A C K N O W L E D G E M E N T
These investigations were supported (in part) by the Netherlands Foundation for Technical Research (STW), future Technical Science Branche/Division of the Netherlands Organization for the Advancement of Pure Research (ZWO).
This thesis has been carried out within the Biotechnological Laboratory of the Delft Univers-ity of Technology.
Postal address: Laboratory of Biotechnology, Department of Chemical Technology, Delft University of Technology, Julianalaan 6 7 , 2628 B C Delft, The Netherlands.
Present authors' address: Suiker Unie Research, Microbiological and Biotechnological De-partment, Oostelijke Havendijk 15, 4704 R A Roosendaal, The Netherlands.
Contents
Chapter 1 Introduction
1.1. General 13
1.2. Scale-up problems 14
1.3. Scale-up methods in use 16 1.3.1. Fundamental method 16 1.3.2. Semi-fundamental method 16 1.3.3. Dimensional and regime analysis 16
1.3.4 Rules of thumb 17
1.4. Scale-up based on constant operating variables 17 1.4.1. Scale-up based on constant power/volume 17
1.4.2. Scale-up based on constant k j a 18 1.4.3. Scale-up based on constant tip speed 19
1.4.4. Equal mixing times 19 1.4.5. Combination of different operating variables 20
1.4.6. Comparison of the scale-up criteria 20
1.5. Environmental approach 21
1.6. Scale-down approach 21 1.6.1. Introduction 21 1.6.2. The microbial model system 23
1.6.3. Production scale reactor 24
1.7. Regime analysis 25 1.7.1. Time constants for transport phenomena 25
1.7.1.1. Oxygen transfer 25 1.7.1.2. Circulation time 25 1.7.1.3. Gas residence time 25 1.7.1.4. Oxygen transfer from an individual gas bubble 25
1.7.1.5. Heat transfer 26 1.7.2. Time constants for conversion 26
1.7.2.1. Oxygen consumption 26 1.7.2.2. Time constant for substrate utilization 27
1.7.2.3. Time constant for growth 27 1.7.2.4. Time constant for heat production 27
1.7.3. Conclusions 28
Chapter 2 Power input measurements in a production scale bioreactor
2.1. Introduction 32
2.2. Experimental procedure 32 2.2.1. Equipment 32 2.2.2. Procedure for the measurement of the power consumption 33
2.3. Results and discussion 34 2.3.1. Ungassed power input 34 2.3.2. Gassed power input 34
2.4. Conclusions 37
2.5. References 38
Chapter 3 Estimation of the gas holdup in different scale stirred tank bioreactors
3.1. Introduction 39
3.2. Correlations from literature 39
3.3. Derivation of a holdup correlation 41
3.4. Materials and methods 42 3.4.1. Reactors 42 3.4.2. Holdup measurement 42
3.5. Results and discussion 42
3.6. Conclusions 4 5
3.7. References 45
Chapter 4 Oxygen transfer in a production scale bioreactor
4 . 1 . Introduction 46
4.2. Two-compartment model for oxygen transfer 46
4.3. A u x i l i a r y correlations 47 4.3.1. Oxygen transfer coefficient 47
4.3.2. Gas holdup 48 4.3.3. Power input 49 4.3.4. Pumping capacity 49 4.3.5. Total oxygen transfer capacity 50
4.4. Materials and methods 50
4.5. Results and discussion 51 4.5.1. Oxygen profile 51 4.5.2. Oxygen transfer rate 52 4.5.3. Computer simulation 53
4.6. Conclusions 53
4.7. References 54
Chapter 5 Dissolved oxygen concentration profiles in a production scale bioreactor
5.1. Introduction 55
5.2. Model equations 56
5.3. Materials and methods 57
5.4. Results and discussion 58 5.4.1. Profiles of the dissolved oxygen tension 58
5.4.2. Gas phase profiles 59 5.4.3. Oxygen transfer calculations 60
5.5. Conclusions 61
5.6. References 62
Chapter 6 Liquid circulation time distribution in a production scale bioreactor
6.1. Introduction 63
6.2. Techniques to determine the liquid circulation 64
6.2.1. Tracer injection method 64 6.2.2. Impeller pumping capacity 64 6.2.3. L i q u i d velocity measurements 64 6.2.4. F l o w follower methods 6 5
6.3. Materials and methods 65 6.3.1. Vessel and medium 6 5
6.3.2. Radio pill 66 6.3.3. Aerials 67 6.3.4. Radio receiver and data logger 69
6.3.5. Signal processing 70 6.3.6. Effect of gas holdup on the radio pill buoyancy 73
6.4. Interpretation model of the radio pill data 74
6.4.1. Mean circulation time 74 6.4.2. Circulation time distribution 76
6.5. Results and discussion 76 6.5.1. Mean circulation time 76 6.5.2. Circulation time distribution 79
6.6. Conclusions 81
6.7. References 82
A p p e n d i x 6.1. 83 Appendix 6.2. 85
Chapter 7 Determination of the liquid side oxygen transfer coefficient in a biological medium
7 1. Introduction 87
7.2. Materials and methods 87 7.2.1. Experimental set-up 87 7.2.2. Gas bubble formation 87
7.2.3. Medium 88
7.3. Results and discussion 88
7.3.1. Water 88 7.3.2. Medium 88
7.4. Conclusions 90
7.5. References 90
Chapter 8 A structured model for oxygen transfer in a stirred tank reactor
8.1. Introduction 91
8.2. Correlations from literature 91
8.3. Derivation of a structured model for oxygen transfer 95
8.3.1. General 95 8.3.2. Model for coalescence and dispersion of gas bubbles 9 5
8.4. Materials and methods 97
8.5. Results and discussion 97 8.5.1. Determination of the oxygen transfer rate and gas holdup 97
8.5.2. Mechanistic model 101 8.5.2.1. First order model 101
8.5.2.2. Second order model 101 8.5.2.3. Medium influences 102
8.6. Conclusions 103
8.7. References 103
Appendix 8.1. 105
Chapter 9 Influence of dissolved oxygen concentration of the oxygen kinetics of Glucono-bacter ox y dans
9.1. Introduction 107
9.2. Materials and methods 108 9.2.1. Organism and culture conditions 108
9.2.2. Experimental set-up 108 9.2.3. The oxygen electrode reaction vessel 108
9.2.4. Analytical methods 111 9.2.4.1. Biomass concentration 111
9.2.4.2 Glucose and gluconate 111 9.2.5. Linearity of the oxygen probes 111
9.3. Results and discussion 112 9.3.1. Normally aerated conditions 112
9.3.2. Oxygen limited conditions 115 9.3.3. High dissolved oxygen concentrations 116
9.4. Conclusions 117
9.5. References 117
Chapter 10 Scale-down aspects of the gluconic acid fermentation
10.1. Introduction 118
10.2. A i m of the study 118
10.3. Materials and methods 120
10.4. Results and discussion 120
Chapter 11 Scale-down and optimization studies of the gluconic acid fermentation
11.1. Introduction 124
11.2. Possible experimental set-ups for scale-down 124
11.2.1. General 124 11.2.2. Fluctuation of the D O T with a fixed frequency 125
11.2.3. Scale-down of a circulation time distribution 125
11.2.3.1. Formal correlation 125 11.2.3.2. Experimental correlation 126
11.3. Materials and methods 127 11.3.1. Organism and culture conditions 127
11.3.2. Experimental set-up 128 11.3.2.1. Fluctuation of D O T with a fixed frequency 128
11.3.2.2. Two-compartment system 128
11 3.3. Analytical methods 129 11.3.4. Detection of the circulation capacity 129
11.3.5. Calculation of the acid production rate 130 11.3.5 1. Fixed fluctuating frequency 130 11.3.5.2. Two-compartment system 131
11.4. Results and discussion 131 11.4.1. Fixed fluctuation frequency 131
11.4.2. Two-compartment system 132 11.4.3. Comparison of the different scale-down experiments 135
11.4.4 Optimization studies 136 11.5. Conclusions 138 11.6. References 140 List of symbols 141 Summary 145 Samenvatting 148 Curriculum vitae 152 12
Chapter 1
Introduction
1.1. General
In general, scale-up of a microbial process comprises the transfer of a new or an improved process from laboratory scale to production scale. Apart from bubble columns, processes at larger scale are often carried out in stirred tank reactors with one or more Rushton type turbines, see figure 1.1, although new fermenter concepts are developed (Schugerl, 1980). The trend to improve microbial processes asks for reliable rules for scale translation. The success of a new or improved process depends on the performance of the process at production scale and therefore good simulation of the production conditions at laboratory scale is necessary. However, in practice, when new strains are selected or when a new process is developed, the scale-up of the process is more or less considered as a necessary evil and is not always set-up properly. This results in production yields which are generally lower than expected from laboratory experiments, or the production reactor is overdesigned. In both cases this means higher production costs, than for a good optimized and scaled process. In this section first some scale-up procedures as reported in literature are shown. The classical methods from chemical engineering are discussed, followed by the methods used in bio-chemical engineering. A method based on scale-down experiments will be presented, followed by the introduction of the experimental system. Finally a regime analysis will be carried out for the full scale fermenter under investigation.
m o t o r drive f o a m breaker. aseptic seal gear box bearing assemblies gas exit baffle cooling j a c k e t turbine i m p e l l e r s
1.2. Scale-up problems
Basically a scale-up problem exists, when there is a transport of heat, mass or momentum in a system. This can be illustrated by a simple example: let's consider a plug-flow reactor with dispersion, and a first-order homogeneous reaction without temperature gradients. The balance for mass-transfer has the following shape:
Diffusion Convection ( ) + ( ) + (Production) = (Accumulation) (1.1) in - out in - out or 32C 9C 9C D — 5 - - v + kC = (1.2) 9 xz dx 3t
The dispersion term as well as the flow term are scale dependent. However with free cells, the kinetic term is scale independent (micro-kinetics). In case of agglomerates of cells, kinetics are scale dependent too (macro-kinetics) because macro-kinetics is a result of a combination of micro-kinetics and transport phenomena. Solving the micro balance equations for transfer of mass, heat or momentum is often very complicated and the flowterm is rather undefined. S o , the use of these balances is limited for design and scale-up. Therefore often rules of thumb are used as is illustrated in table 1.1., in which the scale-up criteria, as used by a number of fermentation industries are summarized.
Table 1.1. Scale-up criteria used by some fermentation industries (Margarites, 1978)
% of industries scale-up criterion used 30 power per volume ratio 30 oxygen transfer rate 20 impeller tip speed
20 oxygen tension
So, 20% of the industries uses a criterion based on flow phenomena, and 30% uses a criterion based on mass-transfer. However parameters like the oxygen transfer rate and the oxygen tension are closely related to power per volume ratio and impeller tip speed. Mostly the choice of such a criterion is empirical and not well founded by experimental data and model design. It can be shown that scale-up based on empirical criteria is rather complicated, see table 1.2.
In this table the values in every row give, for a particular scale-up criterion the ratio of the values for prototype and model of the variables mentioned at the top of the table. The calculations have been set-up for geometrically similar systems with = 10 I and V p = 1 0 m3, resulting in a linear scale-up of a factor 10. A s one can see different scale-up criteria
result in entirely different process conditions at production scale. Problems which appears when scale-up is based on such criteria will be illustrated from literature data.
Table 1.2. Different scale-up criteria and their consequences
value at 10 m scale-up criterion
equal P / V equal N(or tm)
equal tip speed equal Re-number 1 03 1 0s 1 02 0.1 P / V 1 1 02 0.1 1 0s N(or tr 0.22 1 0.1 0.01 N D 2.15 1 02 1 0.1 Re 21.5 1 02 10 1
A s a first example the protease production by a Streptomyces sp. is given. Takei et al. (1975) made a study of this production in a 0.03 mJ and a 0.2 m3 reactor. The activity of the
cells to produce protease is influenced by the oxygen transfer rate as can be seen in figure 1.2. A t higher oxygen transfer rates, the protease activity is influenced by scale dependent effects. S o , in this case a constant O T R value to maintain a constant oxygen transfer rate at the different scales is not the only valuable criterion for scale-up.
Another example is the production of gluco-amylase by an Endomyces sp. which affected by the oxygen transfer rate (Taguchi et al, 1968), see table 1.3 and figure 1.3. Increase of the impeller diameter at the production scale (30 m3) shows an increase of the k|a from 1.1
to 1.6 (min _ 1 ). This gave also a better production yield, see table 1.3.
F r o m figure 1.3 it can be seen that the relation between k | a and relative activity at produc-tion scale, differs from that at laboratory scale. S o , in this case an over-design of the pro-duction reactor results when this is based on the laboratory scale data.
P r o t e a s e activity f O D 660J 0.5 -O — o 301 x x 200L
i
activity reduction b y s c a l e - u p —- O T R ( m m o L / 1 s e c ) Relative activityC%) 1 1O0 -• laboratory scale (601) * production scale 3m3 + I. „ 30m3 30 <10~ 0 \l Figure 1^. Figure 1.3.Table 1.3 Gluco-amylase production by an Endomyces sp. (Taguchi et al, 1968) Scale of operation ( m3) 0.06 3 30 aeration (vvm) 1 0.5 0.33 agitation (rpm) 400 180 150 k J a (min _ 1 ) 2.28 1.73 1.14 1.58*) rel. activity (%) 95 100 61 91
*) Increase in k,a by reconstruction of the impeller from D = 0.79 to D = 0.94 m
1.3. Scale-up methods in use
1.3.1. Fundamental method
This method implies solving all the micro-balances for momentum-, mass-, and heat-transfer in the system. It will be clear that this is not possible for scale-up of a complete microbial process. However, for some scale-up problems, particularly when the flow is well defined (or absent), solving the micro-balances can be very useful.
1.3.2. Semi-fundamental method
Scale-up based o n simplified flow models (for example plug-flow with dispersion), to avoid the use of t o o complex momentum balance equations.
See f o r example Bryant (1977) and Mann et al. (1981).
1.3.3. Dimensional and regime analysis
These are very whidespread methods. comm6nly used in scale-up of chemical engineering problems. T h e use of these methods is also very helpful when scaling-down (or -up) a micro-bial process, and will be introduced in this study. In case of dimensional analysis, dimension-less numbers are obtained from the dimensiondimension-less balance equations or from similarity principles (Johnstone and Thring, 1957). However, as is already mentioned, it is often a problem to solve all the balance equations describing the whole system. Similarity is also very hard to achieve in case of a microbial reaction at different scales, especially for hydro-dynamic and chemical similarity. With the help of dimensional analysis a great number of dimensionless numbers can be obtained. This is extensively reviewed by Zlokarnik (1974). Because it is impossible to maintain all dimensionless correlations at the same value at the different scales, the use of regime analysis can be very helpful. F o r example, looking to a mixing problem in a stirred vessel, the Reynolds number and the Froude number have to be kept the same at the different scales. However this will be impossible for homologeous systems, because:
( N2D ) M = ( N2D ) p and ( N D2) M = ( N D2) p
Therefore we have to look for the rate limiting mechanisms in the reaction system. In this case, if the vessel is fully baffled, the Froude numbers play no role, and it will be sufficient to keep the Reynolds number in the turbulent regime.
When using regime analysis, the characteristic time constants of the individual parts of the process are compared with each other. The use of these time constants can also give insight into the complexity of the process. When different time constants are of the same order of magnitude, we are speaking of a mixed regime. In that case scale-down or -up of the process will cause problems. O n the other hand, when scale translation is performed with respect to one particular regime, that is rate limiting at the model scale it is possible that another regime is rate determining at prototype scale. Then we have a so-called change of regime. This can also cause problems.
1.3.4. Rules of thumb
In biochemical engineering, rules of thumb combined with extrapolation are c o m m o n l y used as a scale-up procedure, as was already mentioned. Some of these rules of thumb can be very useful, also for a scale-down procedure. Generally a constant value of a particular operating/equipment variable (for example k^a) is used. If this operating variable controls the rate determining regime at M and P this method is valuable. If not so, (change of regime or mixed regime) problems arise. In section 1.4 some attention will be paid to these methods.
1.4. Scale-up based on constant operating variables
Some examples of scale-up based on constant operating variables, as used very often in the fermentation technology, are already given. T h e properties which can be kept constant at the different scales are:
1. constant power/volume 2. constant k |a
3 . constant tip speed of the impeller 4. equal mixing times
5. a combination of P / V , vt|p and gas f l o w rate
These methods are based only on one of the important mechanisms in the reactor. T o keep the operating variables the same at different scales, empirical correlations are often used. Geometric similarity is generally implicitely assumed.
1.4.1. Scale-up based on constant power/volume
This criterion is often used in the penicillin fermentation. A s a rule of thumb one uses a P / V ratio of 1.5 - 2.0 k W / m3 at different scales. When this criterion is used, a problem is
the decrease of power under aerated conditions for which very different relations exist in literature. In practice this decrease is of about 50% of the nongassed power consumption. For example Nagata (1975) gives an equation for the calculation of the gassed power con-sumption. A correlation obtained with help of dimensional analysis is also available (Reuss e t a l . , 1980).
However, these correlations are only based on a limited number of experimental data. In laboratory equipment, Warmoeskerken and Smith (1982) have performed a mechanistic study on the hydrodynamics around the stirrer. F r o m this study it was shown that the cavity formation behind the impeller blades is responsible for the power decrease by gassing. Gaden (1961) shows the use of a constant power/volume ratio in the penicillin fermentation. However, increasing of the used power/volume ratio at the production scales results in a higher yield at the production scale compared to that at laboratory scale, see figure 1.4.
1.4.2. Scale-up based on constant k(a
Because of the high oxygen consumption of a lot of microbial processes, a constant k|a at different scales is often used as a scale-up criterion. For example the following authors reported the use of this criterion:
* Bartholomew (1960), vitamin B12
* K a r o w a n d Bartholomew (1953), streptomycin * Taguchi at al. (1968), gluco-amylase
* Steel and Maxon (1966), novobiocin * Bartholomew (1960), penicillin
However, when designing a reactor, based on constant k | a , one needs a correlation to calculate k|a from the operating variables. V a n 't Riet (1979) gives some correlations to calculate k |a in low-viscous broths:
- 2 Pg 0.4 0.3
coalescing media: k (a = 2.6 »10 *(—) * ( vs) (1.4)
- 3 ,Pg<3.7 , 0.2
non-coalescing media: k,a = 2 * 1 0 *(—) *(v ) (1.5) V
in general: k , a = c * (—) * ( v ) (1.6) i \y s
These equations were obtained from a great amount of literature data. However, Bartholomew (1960) already indicated the scale-dependency of the parameters a, b, and c of the equation 1.6. This is clearly demonstrated by table 1.4. F o r constant values of the superficial gas velocity, v$,scale-up based on constant power input and based on constant kja should
coin-cide.
Table 1.4 Exponents of equation (1.6) at different scales, for coalescing media (Bartholomew, 1960)
Vessel size (I) a b
5 0.95 0.67
500 0.6-0.7 0.67 50000 0.4-0.5 0.50
In highly viscous fermentation broths, the viscosity is introduced in the k|a correlations ( R y u and Humphrey, 1972):
Pg a b - 0 . 8 6
k,a = c l - j ) * ( vs) *(v) (1.7)
Some authors note that k | a is also effected by the number of impellers (Fukuda et a l . , 1968) and the addition of anti-foam agents (Yagi and Yoshida, 1974). F o r bubble column reactors, there are also a great number of correlations to estimate the k |a from the operating variables (Heijnen and V a n 't Riet, 1982).
1.4.3. Scale-up based on constant tip speed
In viscous mycelial fermentations, a constant impeller tip speed is often used as a scale-up criterion, because of the shear sensitivity of the used micro-organisms for this kind of fermentations. Some authors (Wang and Fewkes, 1977) note that not only the impeller shear, but also the impeller pumping capacity is important. Others (Steel and M a x o n , 1962) however, are using only the impeller shear as a criterion.
1.4.4. Equal mixing times
Basically large scale reactors (with a volume larger than 5 m3) are poorly mixed compared
with small scale reactors. This is a c o m m o n cause for a changing of regime (kinetic regime at M-scale, transport regime at P). This can give problems for mass- and heat-transfer, especially in viscous broths. Pace (1978) shows the importance of mixing in xanthan fermen-tation, in which the rheology of the broth changes during fermentation.
T o estimate the mixing time, a lot of correlations can be used. F r o m an energy point of view (Heijnen et al., 1984) the following equation can be derived:
n „ I T / D )3 ( H / T )
N tm = °-6 3 / 9 '
V N p ( H p / D )
Jansen et al. (1978) have determined the mixing times for different sizes of vessels in the penicillin fermentation. In table 1.5 these figures are compared with those obtained from equation 1.8. T h e observed discrepancy between measured and calculated values can be explained b y :
* for H / T = 2.5, tm increases more than 2.5 as given by eq. 1.8,
* the measurements are made under production conditions, so the viscosity of the broth can influence the mixing time,
* aerated conditions increase the mixing time (Einsele and F i n n , 1980), * different criteria for being well mixed.
Table 1.5. Mixing times in different sizes of vessels (Jansen et al., 1978) for H/T = 2.5
V ^ m3) T(m) P(kW) P / V ( k W / m3)
measured calculated (from eq. 1.8)
1.4 1.1 3.8 2.7 29 12
45.0 3.5 120.0 2.7 67 26
190.0 4.4 240.0 1.3 119 31
1.4.5. Combination of different operating variables
Another possibility is to keep a combination of different operating variables at the same value at the different scales. Same tip speed, power/volume ratio and aeration rate at different scales is an often used combination. The following values are quite c o m m o n :
vt i p 'a r9e r tnan ^m/ s
P / V about 2 k W / m3
gas flow rate about 0.5 v v m ,
1.4.6. Comparison of the scale-up criteria
When the mentioned scale-up criteria are compared for geometrically similar vessels, the required stirrer speed at 10 m3 can be calculated (in a 10 I vessel the optimized conditions
were: N = 500 rpm, gasflow rate = 1 vvm), (Wang, 1979), see table 1.6:
Table 1.6 Comparison of scale-up methods (Wang et al., 1979)
method: N (rpm) for 10 m3
constant power/volume, nongassed 107
gassed 85
constant k ,a 79
constant shear (ND) 50
equal mixing times 1260
20
j i
(1.8)
The scale-up rules given above result in a constant value of one or two environmental con-ditions ( k | a or shear or mixing). Therefore other environmental concon-ditions can vary (see also table 1.2). The influence of the varying conditions on the behaviour of the micro-orga-nism is not considered by these methods.
1.5. Environmental approach
This approach pays more attention to the conditions the micro-organism will meet on its way through the reactor. It is based on small scale simulation of the environmental con-ditions in the production scale fermenter. Y o u n g (1979) summarized the 'micro-environ-ment', which can influence the process as follows:
chemical variables: carbon-, nitrogen-, phosphorous source, oxygen concentration, product formation, others (like p H , precursers, antifoam).
physical variables: temperature, viscosity, nonaqueous liquid or solid substrate/product distribution, power input, shear, microbial morphology.
The backbone of this approach is trying to keep all these variables and their fluctuations, which can influence the microbial system, the same at the different scales. Because of the possibility of changing of the regime when scale translation is conceived, and because of the fluctuations of the micro-environment on the production scale, it will be impossible to keep all aspects of the micro-environment the same at the different scales.
Basically the approach of Pace (1980) for scale-up is more realistic. In his study, first the rate limiting step is determined. F r o m this, the plant fermenter will be designed by optimizing the rate limiting step. For a given process an idealized approach to meet this.objective is: * establishment of the rate limiting biological step,
* establishment of the relations between the physiology of the micro-organism and the external environment,
* establishment of the relationship between the operating and equipment variables.
1.6. Scale down approach
1.6.1. Introduction
The conclusion from what is presented in the preceeding parts is that there is a strong need to a sophisticated approach to scale-up problems. Therefore a method is introduced which is based on scale-down experiments. The ~im of this method is to try to simulate at labo-ratory scale the conditions for the micro-organism which it meets at the production scale. Therefore, first a good analysis of a production scale reactor is necessary. S o , one need good rules to scale-down phenomena like mass transfer, mixing, gass bubble residence, fluid shear, etc.
Oldshue (1966) suggested to break d o w n the fermentation process in individual steps and to establish the effects of these seperate steps on the microbial process. For the penicilin fermentation, he gave the following essential elements (Oldshue, 1978):
* effectiveness of the existing mixer,
* influence of the oxygen transfer rate on microbial growth and product formation, * the role of the cell concentration upon the mass transfer rate (change of viscosity during
FERMENTOR CONFIGURATION
BUBBLE AGE DISTRIBUTION
i t e r a t i o n a r t - u p d a t r e v i s e d d a t a MASS TRANSFER MODEL _ (KINETIC
-MODEL I QXYSEH UPTAKE RATEl
MASS BALANCE
FINAL RESULT 1^
Figure 1.5
Block diagram for fermentation design by a simulation method (Ovaskainen et a/., 1976)
Ovaskainen et al. (1976) proposed a method based on the simulation of the production scale by a mathematical model (figure 1.5). In this model the kinetic behaviour of the micro-organism is an essential step, so one has to know the influence of the production scale conditions upon the growth and product formation of the micro-organism. This asks for good scale-down experiments to establish these influences.
However, kinetic models describing the behaviour of micro-organisms under different and transient conditions are scarce. Development of these models and determination of their parameters is very time consuming. Therefore this method is not of practical use for in-dustry yet.
T o carry out scale-down experiments, it will not be necessary to scale-down the complete process. A s already mentioned, with help of regime analysis (determination of the time constants) it is possible to predict the rate limiting steps of the process at the industrial scale.
This means that information will be needed about the process at production scale. This can be obtained from measurements at that scale, when process optimization has to be carried out, or when a new process has to be performed in an already existing reactor.
However, also the use of more or less empirical correlations can be very useful to estimate the rate limiting process steps. This will be especially necessary for a newly developed reac-tor, which is in most cases only a preliminary design. For this purpose the same correlations can be used with their limitations as were presented for scale-up based on constant opera-ting variables.
The cardinal point of the scale-down approach is, that after establishment of the rate limit-ing mechanisms of the production scale or, of the 'design scale' of the production reactor, these conditions will be scaled-down to laboratory scale.
The aim of these experiments will be the study of the influence of the production con-ditions upon the microbial system in a laboratory reactor or reactor system.
The main aim of this thesis is to find out whether such an approach is a sound one.
Regime analysis
Application
scale-- d o w n production scale
laboratory scale scale - u p
Simulation Optimization
Figure 1.6 Scale-up/down procedure for microbial production processes
The development of rules to predict the environmental conditions at full scale is a pre-requisite for this approach.
Then, with help of these experiments, also reliable optimization studies can be carried out at laboratory scale. A reactor model of the production scale reactor will be a more or less essential tool for good scale-down. The knowledge of the fundamental microbial kinetics can be useful but is optional. Figure 1.6 shows schematically the proposed method.
T o prove the applicability of this method, a particular microbial product formation, as well as a production scale reactor configuration have been chosen as a model system.
1.6.2. The microbial model system
As a model system the gluconic acid fermentation by Gluconobacter oxydans (ATCC621 Hj is used throughout the whole study, because the fundamental microbial kinetics with respect to the glucose metabolism are well understood, from batch and continuous culture studies (Olijve and K o k , 1979 a, b), figure 1.7.
For glucose concentrations exceeding 15 m M , glucose is oxidized directly to gluconate. A t low pH values, the oxidation of glucose and gluconate via the pentose phosphate pathway is repressed, so only gluconate is formed as an oxidation product. During our studies the pH was kept at pH = 3.5, to be sure of gluconate formation.
Basically, as was mentioned before, the knowledge of the fundamental kinetics is not neces-sary for the scale-down approach described here. The knowledge of the pathways and kinetics is essential however to explain why environmental conditions do have an effect,
5-KETOGLUCONATE ATP ADP c y t j o x ) GLUCOSE «-A N«-ADP c y t ( r e d ) ^GLUCONO-6-LACTONE 3NADPH2 NADPHo GLUCOSE 6-PHOSPHATE • ATP, ADP NADPhL c y t ( r e d ) 2-KET0GLUC0NATE 6-PH0SPH0GLUC0NATE ^NAD(P)H2 _ N A D ( p ) c o2^ r <^ ~ - > NAD(P)H? RIBULOSE 5-PHOSPHATE
i
f u r t h e r m e t a b o l i s m i n t h e pentose phosphate pathwayFigure 1.7 Pathways of glucose oxidation by Gluconobacter oxydans (Oli/ve and Kok, 1979a)
1.6.3. Production scale reactor
A n ordinary type production scale reactor is used", which is very common in the ferment-ation industry (Aiba et al., 1973). Figure 1.1 shows schematically this type of reactor. T h e baffled vessel is stirred by two, six-bladed ' R u s h t o n ' type of turbines. Gas is sparged through a star shaped gas sparger just below the lower impeller. Table 1.7 gives the principal reactor dimensions.
Table 1.7. Production scale reactor dimensions
impeller/vessel diameter D/T 0.32 —
number of impellers n 2
-impeller blade width/-impeller diameter W / D 0.2
-impeller speed N 1.3 or 2.6 s"1
baffle diameter/vessel diameter Db/ T 0.09
-liquid height/vessel diameter H/T up to 1.8
-gas flow/reactor volume * time Q up to 0.5 m3/ m3. m i n
liquid volume V up to 2 5 m3
The description of the used laboratory scale reactors will be given in the subsequent chap-ters.
1.7. Regime analysis
By comparison of the time constants of the proposed reactor and process, it is possible to establish the rate limiting mechanisms. The different time constants which are important for the gluconic acid fermentation (an aerobic product formation) at production scale will be reviewed below:
1.7.1. Time constants for transport phenomena
1.7.1.1. Oxygen transfer
The time constants for oxygen transfer from gas to liquid is defined by the reciprocal k | a :
tQT= 1/k,a (1.9)
For design purposes kja can be calculated according to V a n ' t Riet (1979), relation (1.4) and (1.5).
1.7.1.2. Circulation time
The time constant for mixing of the gas-liquid dispersion is expressed by the circulation time, which can be calculated f r o m :
V
t = — (1.10)
c 2 0p
in which the circulation capacity of a turbine type of stirrer can be calculated according to Revill (1982):
0 p = 0.75 N D3 (1.11)
In a reactor with more than one stirrer, the circulation time has to be calculated for one stirrer compartment. In that case the compartment volume V as used to calculate the circu-lation time can be estimated f r o m :
V = — T2 * T (1.12)
1.7.1.3. Gas residence time
The residence time of the gas bubbles is derived from the gas holdup in the reactor:
T Q - < 1 - 0 - £ (113 >
1.7.1.4. Oxygen transfer from an individual gas bubble
(1.14)
or:
ƒ (
CJH-C (1.14a)
so, the time constant of this differential equation is:
t
OT,b
=i^
(1.15)1.7.1.5. Heat transfer
The time constant for heat transfer follows directly from an overall heat balance over the reactor:
in which:
A = surface of the cooling/heating device, <x = overall heat transfer coefficient.
A problem for the calculation of the heat transfer time will be, however, the accurate estimation of the overall heat transfer coefficient of the reactor. Much literature is known about heat transfer in ungassed stirred tank reactors. For gas-liquid systems, however, the literature is scarce. Steiff (1980) shows a correlation to calculate the overall heat transfer coefficient. T h e influence of stirring and gassing upon this parameter is not quite clear, but values are given ranging from 4000 - 8000 ( W / m2 K ) .
1.7.2. Time constants for conversion
1.7.2.1. Oxygen consumption
The time constant for oxygen consumption is derived from the integrated 'Michaelis-Menten' equation, if this form of kinetics is assumed for oxygen consumption:
O2, 0 "C02, c r
max (1.17)
in w h i c h :
oxygen concentration at t = 0
C Q ^cr = critical oxygen concentration.
Only the two extrema of this equation will be used:
Zero-order type of kinetics, if C Q > ^ 02
(0) max
t o e = co2 / ro2 (117a)
and a first-order type of kinetics, if C Q < K Q :
(1) „ max
b e = K02/r02 «1-17b)
Because in most cases C Q > K Q , the time constant for oxygen consumption can be cal-culated as given by relation (1.17a). However, it is not a priori clear what the concentration will be in the production reactor. If the time constants for oxygen transfer and oxygen con-sumption t '0' are compared (in which for C n , the saturation concentration CX is taken),
O C ° 2 u2
it can be shown whether there will be an oxygen limitation or not.
If t '0' > t Q j , there is no oxygen limitation and C Q = C Q . Then the use of C Q in
equa-O C 2 2 2
tion (1.17a) is justified.
If t^0' < tn T, there will be an oxygen limitation in the reactor, so the actual concentration
O C
in the reactor will be very low (approximately equal to K Q ). For comparison of the oxy-2 /1 \ gen consumption time with other time constants, for example the circulation time, IQQ has to be used then.
1.7.2.2. T i m e constant f o r substrate utilization
Basically, for this time constant the same assumptions can be made as for the oxygen con-sumption time. In batch processes, C g can be taken equal to the substrate concentration at inoculation time. For continuous or fed-batch processes, for the calculation of the sub-strate utilization time, the actual concentration in the reactor has to be taken into account. In that case often a 'Michaelis-Menten' form of kinetics will be used. Because in the system under investigation C g > K g , the time constant for substrate utilization reads:
tSC = - m # - ( 1"1 8 )
s
1.7.2.3. T i m e constant for growth
In batch processes, the time constant for growth can be obtained from the reciprocal speci-fic growth rate:
tG= " w > "1 <1-19>
For continuous processes, this time constant becomes equal to the reciprocal dilution rate.
1.7.2.4. T i m e constant for heat production
inside and the cooling/heating liquid is used for this purpose, this will have the result that if t|_|y = t|_|p all the heat produced is removed from the system. T h e n , the heat production time can be calculated f r o m :
PCp A Tk
H M + rH S
in w h i c h :
AT|y- = temperature difference between reactor interior and cooling/heating liquid, 3 max
rH M = r i e a t Pr° d u c t i o n by the m i c r o - o r g a n i s m s ,r| _ |= ^ 6 0 * 1 0 * TQ * V | ( J ) , Cooney et
al., 1969). 2
rH S = neat Pr° d u c t i o n by stirring, approximately equal to the gassed power input in the
liquid PQ.
1.7.3. Conclusions
The different time constants were calculated, using the correlations given above. Table 1.8 shows these time constants.
Table 1.8 Time constants for the gluconic acid fermentation, if carried out in a production scale reactor
Transport phenomena
oxygen transfer circulation of the liquid gas residence
transfer of oxygen from a gas bubble heat transfer 5.5 (non-coal.) - 11.2 (coal.) (s) 12.3 (s) 20.6 (s) 290 (non-coal.) - 593 (coal.) (s) 330-650 (s) Conversion
oxygen consumption, zero-order first-order substrate consumption growth heat production 16 (s) 0.7 (s) 5.5 * 1 04 (s) 1.2 * 1 04 (s) 350 (s)
T h e comparison of the different time constants leads to the following conclusions:
For batch processes the time constants for substrate consumption and growth are much larger than the time constants for transport processes. So they have no influence on the environmental conditions. Of course, the duration of the fermentation process is determined by these time constants.
The time constants for oxygen transfer and oxygen consumption are of the same order of magnitude. Therefore there exists a possibility of oxygen limitation in the reactor. If the
oxygen consumption time (first-order kinetics, K Q IXQ ), is compared with the circulation
time, the conclusion is that there will be a large oxygen concentration gradient in the reactor.
* F r o m the comparison of the time constant for oxygen transfer from a gas bubble with the gas residence time, can be concluded that the gas bubbles will not be exhausted when leaving the reactor.
* If the time constants for heat production and heat transfer are compared with each other, than it can be seen that these constants are of the same order of magnitude, which means that the heat produced can be removed from the system. If these time constants for heat production and heat transfer are compared with the liquid circulation time, it can be con-cluded that no temperature gradients will appear.
S o , in this study the emphasis will lie upon the down-scaling of the oxygen transfer pheno-mena in the production scale reactor. With the help of these down-scale experiments, opti-mization studies will be possible at laboratory scale, which can lead to an optimized process. In particular the influence of (alternating) oxygen concentrations on the microbial kinetics has to be studied. The literature data about flow and oxygen transfer in large scale fermen-ters are very scarce. The use of the existing equations for scale-up is questionable because of their black box nature and the lack of large scale verification. Therefore additional infor-mation is needed about:
* oxygen transfer in a production scale bioreactor,
* modelling of the liquid flow in a production scale reactor. These subjects are the core of this study.
1.8. Organization of this thesis
This study is a part of the research program of the Bio-enginering Laboratory of the Delft University of Technology. A part of this study, the development of the radio-pill flow follower method to estimate the large scale flow behaviour of the liquid, as described in chapter 6, is carried out in collaboration with A K Z O Corporate Research, A r n h e m , The Netherlands.
In this study the development of a scale-up procedure based on down-scaling principles and the application of this procedure on a microbial production fermentation, was essential. Therefore, the microbial system (glucose oxidation by Gluconobacter oxydans) as well as the production scale reactor, served as model systems.
T h e chapters of this thesis can be read independently, but contribute all to the total pro-cedure. Some of them are used to obtain more fundamental information. The subjects of these chapters are briefly outlined below.
Chapter 1 deals with the general introduction; in this chapter the microbial model system is introduced and also the reactor dimensions of the production scale reactor are given. This chapter gives also an introduction in scale-up methods for microbial production processes. F r o m the derivation of the process time constants it is concluded that mixing and oxygen
In chapter 2 power input measurements at production scale are given, chapter 3 deals with gas holdup measurements at different scales. The intention of both of these chapters is the characterization of the reactor systems as used.
Chapter 4 and 5 give a description of the oxygen transfer phenomena at large scale. Also the results of local oxygen transfer measurements are reported, from which can be concluded that in fact the micro-organisms will be exposed to oxygen concentration fluctuations at large scale.
In both chapters it is tried to interpret the oxygen transfer data with a less unstructured model for oxygen transfer. For that purpose the ' V a n ' t Riet' equations (1.4 and 1.5) are modified for application at production scale. However the model as used is still largely unstructured. S o , also attempts are made to give a more structured model for oxygen fer in a stirred tank reactor. T h e presented model is based o n : the liquid side oxygen trans-fer coefficient, k| (chapter 7), the gas holdup (chapter 3) and coalescing phenomena (chap-ter 8). Some preliminary results of the application of such a model at a laboratory scale stirred tank reactor, is given in chapter 8. These studies are not strictly necessary for the whole scale-up procedure but are optional and were only made to obtain more fundamental knowledge of these very important mechanisms.
The same concerns chapter 9 in which the fundamental kinetics of oxygen for
Gluconobac-ter oxydans are presented.
In chapter 6 a procedure for the determination of the liquid f l o w phenomena at large scale is presented. This procedure was developed in collaboration with A K Z O Corporate Research. The chapter gives the results of radio-pill flow follower measurements at production scale, from which the liquid flow behaviour can be estimated.
This information and the results of local oxygen concentration measurements at large scale (chapter 4 and 5) are the base of the down-scale experiments as are presented in chapter 10 and 11. In chapter 10 a two-compartment reactor system at small scale is presented. In chapter 11 this system for scale-down experiments is compared with other experimental systems. These down-scale experiments are also used for optimization purposes.
1.9. References
A i b a , S., Humphrey, A . E . , Millis, N . F . , Biochemical Engineering', A c . Press, New Y o r k , 1973.
Bartholomew, W . H . , A d v . A p p l . M i c r o b i o l . , 2 (1960), 289-300. Bryant, J . , A d v . Biochem. Eng., 5 (1977), 101-124.
Cooney, C . L . , Wang. D.I.C., Mateles, R.I., Biotechnol. Bioeng., 11 (1969), 269-281. Einsele, A . , F i n n , R.K., Ind. Eng. Chem. Process Des. Dev., 19 (1980), 600-603. Fukuda. H., Sumino, Y . , Kanzaki, I., J . Ferment. Technol., 46 (1968), 829-839. Gaden, E . J . , Sci. Repts. 1st. Super Sanita, 1 (1961), 161 176.
Heijnen, J . J . , Riet, K., V a n ' t , 4th Eur. Conf. on M i x i n g , Noordwijkerhout, The Netherlands, 1982, paper F 1 .
Heijnen, J . J . , Kossen, N.W.F., Riet, K. v a n ' t , Roels, J . A . , to be published (1984).
Jansen, P . H . , Slott, S., GLirtler. H., Proc. 1st Eur. Conf. of Biotechnol., Interlaken, Swit-zerland, 1978.
Johnstone, R . E . , Thring M.W., 'Pilot plants, models and scale-up methods in chemical engineering', Mc Graw H i l l , New Y o r k , 1957.
Karow, E.O., Bartholomew, W . H . , Agricul. and Food Chem., 1 (1953), 302-306. Mann, Ft., Mavors, P.P., Middleton, J . C . , Trans. Instn. C h e m . Eng., 59 (1981), 271-278. Margarites, A . , Zajic, J . E . , Biotechnol. Bioeng., 20 (1978), 939-1001.
Nagata, S., ' M i x i n g , principles and applications', J . Wiley & Sons, New Y o r k , 1975. Oldshue, J . Y . , Biotechnol. Bioeng., 8 (1966), 3-24.
Oldshue, J . Y . , Process Biochem., 13 (1978), nov., 16-18 + 24. Olijve, W., K o k , J . J . , A r c h . Microbiol., 121 (1979a), 283 290. Olijve, W., K o k , J . J . , A r c h . Microbiol., 121 (1979b), 291-297.
Ovaskainen, P., Lundell, Ft., Laiho, P., Process Biochem., 11 (1976), may, 37-39 + 55. Pace, G.W., A d v . School on Microbiol, and Biotechnol., Queen Elizabeth College, L o n d o n , England, 1980.
Pace, G.W., The C h e m . Eng., (1978), nov., 833-837.
Reuss, M., Bajpai, R.K., Lenz, R., Niebelschütz, H., Papalexiou, A . , 6th Int. Ferment. S y m p . , L o n d o n , Ontario. Canada, 1980, paper F-7.2.1.
Revill, B.K., 4th Eur. Conf. on M i x i n g , Noordwijkerhout, The Netherlands, 1982, paper B 1 . Riet, K. v a n ' t , Ind. Eng. C h e m . Process Des. Dev., 18 (1979), 367-375.
R y u , D.Y., Humphrey, A . E . , J . Ferment. Technol., 50 (1972), 424-431. Schügerl, K., Chem.-lng.-Techn., 52 (1980), 951-965.
Steel, R., M a x o n , W.D., Biotechnol. Bioeng., 4 (1962), 231 240. Steel, R., M a x o n , W . D . , Biotechnol. Bioeng., 7 (1966), 97-108.
Steiff, A . , Poggemann, R., Weinspach, P . M . , Chem.-lng.-Techn., 52 (1980), 492-503. Taguchi, H., et al., J . Ferment. Technol., 46 (1968), 823-828.
Takei", H., Mizusawa, K., Yoshida, F., J . Ferment. Technol., 53 (1975), 151-158. Wang, D.I.C., Fewkes, C . J . , Devel. Ind. Microbiol., 18 (1977), 39-56.
Wang, D.I.C., 'Fermentation and Enzyme Technology', J . Wiley & Sons, New Y o r k , 1979. Warmoeskerken, M . M . C . G . , S m i t h , J . M . , 4th Eur. Conf. on Mixing, Noordwijkerhout, The Netherlands, 1982. paper G 1 .
Y a g i , H. , Yoshida, F., J . Ferment. Technol., 52 (1974), 905-916. Y o u n g , T . B . , A n n . of the New Y o r k A c a d , of Sei., 326 (1979), 165-180. Zlokarnik, M., Aehnlichkeitstheorie in der Verfahrenstechnik, Bayer, 1974.
Chapter 2
Power input measurements in a production scale
bioreactor
2.1. Introduction
As already mentioned ,in the introduction of chapter 1, most of the aerobic production fermentations are carried out in baffled vessels, with one or more ' R u s h t o n ' type turbine impellers.
In this standard type reactors, the power input is one of the most frequently used para-meters to describe the mass transfer, heat transfer, mixing, etc. A t laboratory scale a tremendous amount of fundamental research has been done to understand the mechanism of the impeller power consumption under gassed conditions. G o o d reviews are given by Zlokarnik (1973), Nagata (1975) and V a n ' t Riet (1975).
Therefore many relations are available to predict the gassed power consumption. However, most of these correlations are empirical and cannot be used for production scale reactors without restriction (Brown, 1981).
On the other hand, more mechanistic research has been done by V a n 't Riet (1975) and Warmoeskerken (1982). These authors have shown that the decrease of the impeller power input at an increased gasflow rate can be explained by the effect of cavity formation behind the impeller blades. However, their theories still have not been tested at production scale bioreactors with one or more impellers.
In this study measurements of the power input in a production scale bioreactor were per-formed. T h e aim of these measurements is to apply the cavity formation principle to describe the power consumption in an aerated production scale reactor.
The understanding of the hydrodynamic phenomena around the stirrer, especially in pro-duction scale reactors, is one of the first steps in the development of scale-up rules for mixing and mass-transfer, in this type of reactors.
2.2. Experimental procedure
2 2.1. Equipment
The dimensions of the reactor used, are given in table 1.7 (chapter 1). The dish bottomed vessel is equiped with four baffles (each 9% of the tank diameter) and two six-bladed turbine impellers. A i r is supplied through a star-shaped sparger, just below the lower impeller. Control of the airflow is possible by means of an industrial rotameter, which is calibrated by a 'Pitot-tube' in the off-gas line. The impellers are driven by an electrical motor via a belt drive and a gearbox for speed reduction. The upper and lower part of the impeller axis are equiped with bearing devices. T w o stirrer speeds are possible:
N = 1.3 (s"1) and N = 2.6 ( s ' M .
2.2.2. Procedure for the measurement o f the power c o n s u m p t i o n
The most direct method to determine the impeller power consumption is the measurement of the torque in the impeller axis by strain gauges and a torque transducer. However, this equipment is very expensive for large scale power input measurements. Therefore we have determined the electrical power with a Siemens industrial wattmeter. The electrical power, however, is diminished in an unpredictable way in the beltdrive and the bearing, figure 2.1. Furthermore, the efficiency of an electrical motor is a function of the total power consumed.
By measuring the temperature increase of the fluid under non-gassed conditions, it is possible to determine the total efficiency of the drive equipment. F r o m a heat balance it can be shown that the heat loss through the vessel wall during the measurements is less than 1% of the total power input. This is because of the fact that the vessel is equiped with a cooling jacket, which for this experiment was filled with air. Furthermore, the total vessel is enclosed by an isolation jacket. T o minimize the heat loss to the air in the head space, the fluid temperature and the air temperature are brought at the same value, before starting the measurements. The fluid temperature, as well as the air temperature are determined by a Pt100 thermocouple, connected with a recorder. For all measurements, the recorded temperatures show a linear increase with time during the experiments. Therefore the power can be calculated f r o m : P = V p C p d T / d t (2.1) G r o t s E l e c t r i c a l P o w e r f u n c t i o n o f p o w e r f u n c t i o n o f p o w e r g e a r b o x Figure 2.1.
Distribution of the electrical power in the
A l l experiments are carried out with deionized water (process water) at temperature of 303 K.
2.3. Results and discussion
2.3.1. Ungassed power input
The losses of power in the motor, belt, gearbox and bearing devices were proved experi-mentally. The total losses amount about 20% of the power for the lower stirrer speed and about 11% for the higher stirrer speed, which is shown by figure 2.1.
Measurements of the ungassed power input were made with one and two impellers. The power number can be calculated f r o m :
N = ^ - E - (2.2)
For one impeller we found N p = 3.5 and for two impellers: N p = 11.2. It is also possible to calculate the power number from an empirical correlation as given by M o o - Y o u n g (1961):
160 * D, , * W * (D - D, ,)
ND = b l - ^ (2.3)
D
F r o m this correlation Np is calculated for one stirrer to be Np = 6.0. The fact that a lower
value is found for Np can be explained by the entrainment of air through the liquid surface. The drop in the power number caused by gas suction is more pronounced with one impeller than with two impellers. This can be explained by the fact that with two impellers the gas is entrained only in the upper stirrer region and not in the lower one. However, as Nienow (1979) reported, gas entrainment plays only an important role when no gas is sparged through the vessel. S o , the gassed power input measurements will not be influenced by gas entrainment.
It can also be concluded that for the ungassed power number Np = 5.5 per stirrer can be assumed as a reliable value, which is close to the value obtained by the empirical correlation of M o o - Y o u n g (1961), equation 2.3.
2.3.2. Gassed power input
As already mentioned there are a lot of empirical correlations available to predict the gassed power input from parameters like the stirrer speed and the gasflow. T o show the non-uniformity of these correlations, some of them are compared with experimental data, figure 2.2.
Reuss (1980) used dimensional analysis to obtain the following correlation:
Pg/ P0 = 0.0312 * F r 0 1 6 . R e0064 * NQ 0 3 8 * ( T / D )0 8 (2.4)
This relation was fitted in systems with a liquid volume up to 30 m3 and a T / D ratio
1 . 8 < T / D < 3.7, with confidence limits of 15%.
Hughmark (1980) used a correlation obtained from 248 literature data:
B r o w n (19811 H u g h m a r k ( 1 9 S 0 ) R e u s s , e t a l ( 1 9 8 0 ) x t h i s i n v e s t i g a t i o n 1 5 0 * 10 ' N Q I - I
Figure 2.2 Power aeration curve for H/T - 0.47, N = 2.6 s'1, compared with literature data
Pn/ Pn = 0 . 1 . ( — ) ° -25. ( g o N V N2D gWV 0 . 6 7 ' 0 . 2 ( 2 . 5 )
This relation is claimed to be valid for systems with a liquid volume up to 5 1 m and a superficial gas velocity up to 0 . 0 5 3 (m/s).
Brown ( 1 9 8 1 ) correlated his experimental data from a production scale reactor with the following empirical interdependency:
Pg/ P0 = a exp (- bQ) ( 2 . 6 )
in which the factors a and b are influenced by the gasflow rate and the stirrer diameter. F r o m figure 2 . 2 it can be seen that none of the correlations fits our results well. In all our experiments, figure 2 . 3 , we observed a decrease of the gassed power input to 3 0 - 4 0 % of the ungassed power, at aeration numbers up to N Q > 0 . 1 .
Results of the gassed power measurements are given in figure 2 . 3 . It is shown that all curves have an inflection point:
d2 (Pg/P0>
d ( Nn)2
( 2 . 7 )
(-) LO 0 . 5 • h/T= 0.31, N = 1.3 . h/T= 0.31, N = 2.6 1 lmpeMer o h/T= 0.25, N = 1.3 • h/T = 0.25, N = 2.6 * Inflection points 5 0 1 0 0 1 5 0 * 1 0 2 Impellers
Figure 2.3. Power/aeration curves in the production scale reactor
N o I-)
the stirrer blades. In small scale equipment (T = 0.44 and T = 0.64 m) Warmoeskerken (1982) showed that the 3-cavity formation point can be correlated to the tip speed of the impeller and the superficial gas velocity by:
vt ¡ p= - 0 . 2 6 + 1 1 5 v ; * ( .Dv0.5 T (2.8)
F r o m this criterium a critical aeration number, N Q can be calculated for the achievement of three stable cavities:
« ( T T N D + 0.26) TTD¿
Q ~ 4 6 0 x 7 5 7 7 N D3
( 2 . 9 )
This results in the following critical aeration numbers:
N = 1 . 3 (s_ 1) : N * = 0 . 0 4 1 ( - )
N = 2 . 6 (s_ 1) : N Q = 0 . 0 3 9 ( - )
F r o m the power/aeration curves, figure 2 . 3 , the inflection points are calculated, according to Warmoeskerken ( 1 9 8 2 ) . For this purpose the curves are approximated by higher order polynomial equations. This resulted in the critical aeration numbers as presented in table
Table 2.1. Inflection points in the power/aeration curves h/T N * ( N = 1.3s"1) N Q ( N = 2.6s"M 1 impeller 0.25 0.065 0.040 0.46 0.055 0.047 2 impellers 0.14 0.090 0.058 0.31 0.080 0.051 0.35 0.058 0.048
These observations show that there possibly is an influence of the dimensionless impeller clearance (the net liquid height above the upper impeller), h/T but not of the number of stirrers. S o , for each stirrer speed a mean value for the cavity formation point can be cal-culated from the experimental data:
N = 1.3 (s'1) : N * = 0 . 0 7 ( ± 0 . 0 1 5 )
N = 2 . 6 (s"1) : N Q = 0 . 0 5 ( ± 0 . 0 0 7 )
The great absolute variance is caused by the fact that at very low gasflow rates no accurate measurements were possible of the gasflow (because of the minimum gas valve opening required). The calculated critical aeration numbers, however, are of the same order of magnitude as the observed inflection points. T o observe these inflection points more accurately, more sophisticated measurements will be necessary.
2.4. Conclusions
The empirical correlations to predict the gassed power consumption are less useful for a large scale reactor as used in this study. The correlation as suggested by Reuss ( 1 9 8 0 ) fits our re-sults within an accuracy of about 2 0 % . Here, as a good rule of thumb, it can be said that the gassed power consumption will decrease to 3 0 - 4 0 % of the ungassed power input, if the aera-tion number is about 0 . 1 , which is a c o m m o n operating value.
The appearance of an inflection point in the power/aeration curve is a more or less scale independent phenomenon and suggests that also at large scale three great cavities behind the stirrer blades do exist.
There is some evidence that the hydrodynamics of the stirrer region is influenced by the number of stirrers and by the impeller clearance.
This study shows that the theories of cavity formation as proposed by V a n ' t Riet ( 1 9 7 5 ) and Warmoeskerken ( 1 9 8 2 ) are probably applicable to large scale equipment. This mecha-nistic approach is therefore an important step in the direction to understand phenomena like mass transfer and mixing in production scale stirred tank reactors.
2.5. References
B r o w n , D.E., Instn. Chem. Eng. S y m p . Series, 6 4 (1981), N 1 .
Hughmark, G . A . , Ind. Eng Chem. Process Des. Dev., 19 (1980), 638-641. M o o - Y o u n g , M . , Calderbank, P . H . , Trans. Instn. C h e m . Eng., 39 (1961), 337. Nagata, S . , ' M i x i n g , principles and applications', J . Wiley & Sons, New Y o r k , 1975. Nienow, A . W . , Chapman, C M . , Middleton, J . C . , The Chem. E n g . J . , 17 (1979), 111-118. Riet, K. van 't, T u r b i n e agitator hydrodynamics and dispersion performance', P h . D . Thesis, Delft University of Technology, The Netherlands, 1975.
Reuss, M., Bajpai, R . K . , Lenz, R., Niebelschütz, H., Papalexiou, A . , 6th Int. Ferment. S y m p . , London. Ontario, Canada, 1980, paper F-7.2.1.
Warmoeskerken, M . M . C . G . , S m i t h , J . M . , 4th Eur. Conf. on M i x i n g , Noordwijkerhout, The Netherlands, 1982, Paper G 1 .
Zlokarnik, M., Chem.-lng.-Techn., 4 5 (1973), 689-692.
Chapter 3
Estimation of the gas holdup in different scale
stirred tank bioreactors
3.1. Introduction
For aerobic microbial production processes, gas-liquid mass transfer of oxygen gives rise to problems in reactor design. For design purposes generally the oxygen transfer coefficient k | a, obtained from empirical correlations is used. This results, however, often in a poorly designed production reactor in view of mass transfer considerations. Therefore the use of more structured models to estimate the overall oxygen transfer capacity of the reactor will be necessary, as is also outlined in the chapters 4, 5 and 8 of this thesis.
If such models are used, the knowledge of the gas holdup in the reactor will be essential. In literature there are a lot of correlations available to estimate the gas holdup in stirred tank reactors. However, most of such correlations are empirical and not well suited for scale-up purposes, which is comparable to the situation for power input correlations (chapter 2).
Most of these correlations correlate the gas holdup to the operating variables like the gasflow (or the superficial gas velocity) and the gassed power input of the stirrer. The coefficients of these equations differ widely as will be shown in this chapter.
In this study holdup data, obtained from literature correlations, will be compared with measured data. Therefore, measurements are performed in different sizes of vessels. Also a more structured holdup correlation will be given, which can be used very simply for scale-up purposes. The coefficients of this equation are determined in a laboratory scale reactor which is geometrically similar to a pilot- and production scale reactor. With the coefficients obtained this way, the correlation will be used to predict the gas holdup in reactors at different scales.
3.2. Correlations from literature
A s already mentioned, in most equations for the estimation of the gas holdup, the holdup is given as a function of the superficial gas velocity and the gassed power input by:
( 1 - 6 ) = a ( ^ )b <vsf (3.1)
V *
Some values of the coefficients of this equation, obtained from literature data are given in table 3.1.
Table 3.1. Literature values of the coefficients of equation (3.1)
a b c reference reactor scale (m3)
0.68 0.14 0.75 Dickey (1980) 2.78 0.49 0.28 0.60 Rushton (1968) 0.0095 - 0.592 0.13 0.33 0.67 V a n ' t R i e t ( 1 9 7 5 ) 0.005; 0.067 0.023 0.47 0.65 Rautzen (1976) ? *) 0.33 0.50 Hughmark (1980) 0.01 - 51.0 *) see eqn. (3.3)
Hughmark gave the following relation:
Q v N2D4 y p d , N2D4
(1 - £ ) = 0.74 ( — ( — )/ 2 (F )A
N V g W V ^/ J a V ^/ J
which can be rewritten for water with the assumption for = 2.5 mm into:
Pg 0.33 , 0.5 ,D4 / 3 , T (1 - e ) = 0.034(—) (v ) (-) W% H2 / (3.2) (3.3) V T
Table 3.1 shows that the coefficients of the holdup correlation differ remarkably, although the same variables are used in these equations. Especially when large scale reactors are used
1.0 ~i 1 1 i i — n- H 1 1 I I T 1 1 1 I I I
d - e i ( - ) I'
Figure 3.1. Literature correlations for calculation of the gas holdup as a function of the superficial gas velocity for P/V = 2.0 kl/V/m3
