regime analysis and scale down

c=3

Regime analysis and scale-down: tools to investigate the performance of bioreactors

A. P. J. SWEERE*, K. Ch. A. M. LUYBEN* and N. W. F. KOSSENt

* Department of Biochemical Engineering, Delft University of Technology, Julianalaan 67, 2628 BC Delft, The Netherlands t Gist-Brocades, P.O. Box 1, 2600 MA Delft, The Netherlands

Summary. Scale-up and optimization of biotechnological processes on a large scale tend to be more methodically approached than the application of rules of thumb, experience, and trial and error. Methods frequently used in chemical engineering are adopted in biochemical engineering and are employed with great effect. A summary is given of methods and rules of thumb used in scaling up chemical processes. A procedure to scale up and optimize bioreactors is presented. It is based on the so-called scale- down approach. Some elements of this procedure, viz. theoretical regime analysis and small-scale investigations, are extensively demonstrated by examples. It is shown that a regime analysis based on characteristic times can give a quick estimation of the performance of bioreactors. Small-scale experiments based on the result of such analysis or on the results of a dimensional analysis can give valuable information for scale-up or optimization fermentation processes.

Keywords: Regime analysis; rules of thumb; scale-up; bioreactor design

Introduction

Many large-scale fermentation processes give a lower yield than is expected from laboratory-scale experiments. This is caused by differences in reactor performance at various scales. Laboratory-scale fermenters can be used with a high power input, resulting in a rapid mixing of the fermentation broth and a high mass-transfer rate. Only shear-sensitive systems, like plant cells and systems with a high viscosity, like mycel- ium broths, will give mass, heat and momentum transfer problems on a small scale. On a production-scale, the power input is restricted for economical and mechanical reasons, causing mixing and mass and heat transfer problems. So, it can be concluded that scale-up of fermentation processes introduces these problems. In fact, not enough is known about the hydrodynamics and the interaction of the hydrodynamics and other mechanisms in production-scale bioreactors. There are two ways to solve the problems arising during scaling up:

(a) By acquiring more knowledge about the hydrodynamics and the interaction with other mechanisms in order to get a complete description of what is happen- ing inside large-scale bioreactors;

(b) By developing scale-up procedures which give an adequate estimation of the performance of production- scale fermenters based on small-scale investigations.

Much research has been done with respect to the hydrodynamics of bioreactors. 1 However, the route to an adequate description of large-scale bioreactors is still very long, especially as most research is done on a small scale.

For years scale-up has been more or less an art in which a lot of experience, rules of thumb, and trial and error have been used to attain a proper result. At present, scale-up tends to a more methodical procedure. Oosterhuis 2 and Kossen and Oosterhuis 3 have reviewed the different scale-up methods and discussed their advantages and disadvantages. The methods include:

(1) fundamental method; (2) semi-fundamental method; (3) dimensional analysis/regime analysis ;3.9 11.13 (4) rules of thumb ;.-6 (5) scale-down approach/regime analysis; 2'7 (6) trial and error; (7) multiplication of elements. The literature gives many rules of thumb which can

be used to scale up processes. Table 1 gives some rules of thumb from Jordan 4 for the scale-up of chemical process equipment. From this table the conclusion can be drawn that, while a constant power per volume ratio can be used in almost every scale-up problem, an important exception is mixing. Regarding Table 1 it must be remarked that rules like k s = constant or k~a = constant can not be used as such, but have to be translated to rules based on operational parameters, for example N and v s .

Einsele 5'6 has surveyed the scale-up rules generally used in the European fermentation industries (Table 2). He concluded that these rules are not suitable as the sole scale-up procedure for microbial growth and production processes under large-scale conditions.

Often, none of the above-mentioned methods is, as such, adequate to scale up bioreactors, but com- binations of different methods can yield good results. The semi-fundamental method in combination with rules of thumb is the most widespread method. However, with a few exceptions the flow models are based on small-scale experiments. So, scale-up is based on extrapolation, which makes it very risky.

0141-0229/87/070386-13 $03.00 386 Enzyme Microb. Technol., 1987, vol. 9, July 1987 Butterworth Publishers

Regime analysis and sca le-down: A. P. J. Sweere et al.

Table 1. Some rules of thumb to scale up chemical reactors 4

Process Scale-up rule Remarks

1 Blending of liquids la Continuous, low viscosity

lb Continuous, high viscosity

Geometrical similarity P/V = constant /tr~ = constant or

= constant if z > trn Geometrical similarity P/V = constant t m = constant

l c Continuous, non-Newtonian liquid

Dispersion of non-mixable Geometrical similarity liquids P/V = constant

"L" or 7:/trn = constant 3 Suspension of solids Geometrical similarity

P/V = constant 4 Heat transfer of the liquid Geometrical similarity

phase P/V = constant or h = constant or vt~ p = constant

5 Overall heat transfer Geometrical similarity Vt i p = constant AT = constant

6 Gas absorption in Geometrical similarity mechanically stirred k~ a = constant or reactors vt~ o = constant or

a = constant or P/V = constant or v, = constant

7 Mass transfer to suspended k s = constant particles

8 Chemical reactors See blending of liquids

9 Fluidized-bed reactors

tr, depends on reactor scale; tr, = constant requires too much energy on a large scale; a change of T/tr, may cause a change of regime during scale-up

Only reasonable mixing times can be achieved with helix-shaped impellers laminar flow: N x tm= constant (not checked on a large scale) Only rapid mixing with relatively big impellers (high-energy input or special shaped impellers, e.g. helix)

Propeller is most effective; if the agitator has also another function, e.g. gas dispersion, then another agitator can be chosen If the resistance to heat transfer of the process is >80% of the total resistance, relationship between h and Re number must be known

U 1/L1/Z(L = characteristic length) the ratio of volume to heat transfer area is important

k~ a = constant is the best rule; however k. a = f(P/Vvs)

k s is constant if P/V and dp are constant and geometrical similarity One has to take into account other characteristic times than r and tin; a kinetic regime (small- and large-scale) has no scale-up problem Development at pilot-plant scale

Table 2 Rules of thumb used as scale-up criteria in the fermentation industry 5 (Reproduced from Margariter, A. and Zajie, J. E. Biotechnol. Bioeng. 1979, 20, 939-1001, by permission of Wiley Interscience, New York ~))

Scale-up criteria % of industries

Constant P/V 30 Constant k~ a 30 Constant vt~ p 20 Constant Po2 20

Dimensional analysis combined with regime analysis and small-scale experiments is much used to solve scale- up problems, especially mass, heat and momentum transfer problems.

Scale-down of rate-limiting mechanisms based on the results of regime analysis is a powerful tool to solve scale-up problems.

This review examines some elements of scale-down research, particularly its application to scale-up of fermentation processes, and especially regime analysis based on characteristic times and the scale-down of rate-limiting mechanisms.

Scale-down procedure

Based on regime analysis Pace 7 proposed a method to scale up bioreactors

using experiments on a laboratory-scale or pilot-plant scale with the same behaviour as the full-scale plant. Oosterhuis 2 combined this method with regime analysis and applied the method to the optimization of the glu-

production scale

regime analysis application

t I simu[afi0n ~--

laboratory scale

Figure 1 Scale-down procedure

optimization m0del[ing

conic acid fermentation. Figure 1 shows the scale-down procedure as proposed by Oosterhuis 2. In this procedure, four parts can be distinguished: (1) regime analysis of the process at production scale; (2) simulation of the rate-limiting mechanisms at laboratory scale; (3) optimization and modelling of the process at laboratory scale; (4) optimization of the process at production scale by translation of the optimized laboratory conditions. These four parts can be elaborated as follows:

(1) Regime analysis must give answers to several questions. Which mechanisms are rate limiting, in other words which is the ruling regime? Is the regime ruled by one mechanism (pure regime) or more mechanisms (mixed regime)? Will there be a change in regime?

The analysis has to allow for changes of scale, changes in process parameters and the course of the process. An important factor in the performance of the

Enzyme Mic rob . Techno l . , 1987 , vo l . 9, Ju ly 387

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microorganisms is whether the existing regime will be characterized by substrate or nutrient limitation, fluctuations in the environment of the cells, e.g. in the concentration of a component, in the pH, in the temperature or shear rate, thus affecting the yield of biomass or products.

From the knowledge originating from regime analysis it can be concluded which mechanisms or features need further investigation on a small scale.

(2) The most important requirements for experiments on a laboratory scale is that they have to be representative of the conditions applying on a production scale. This determines the possibilities and the limits of small- scale experiments (see below).

(3) Optimization of the process on a laboratory scale and modelling of the investigated features form the third part of the scale-down procedure. In optimization one has to keep in mind that the optimized situation has to be translated to the production scale. Conse- quently, not all the results of optimization can be used.

With regard to the influence of fluctuations, the following remarks can be made. Fluctuations tend to increase during scale-up (decreased mixing), resulting in transient conditions for the microorganisms.

Much is known about modelling of balanced growth and product formation. However, little is known about growth and product formation under transient conditions. Barford 8 has reviewed some literature about modelling transients and lag phases. A distinction must be made between empirical and mechanistic models. Most of the models described in the literature are empirical, incapable of prediction and add little to the fundamental understanding of microbial dynamics. Few mechanistic models can be found in the literature. This is due to the fact that the biochemical and physiological information, which forms the basis of the mechanistic models, is unsufficient. Therefore, experimental procedures are still very important.

(4) In the fourth step, the optimized laboratory conditions are translated to a production scale. Models formed in the previous step can be used for this purpose. Rules used to scale down the process can now be used in scaling up the experimental conditions. The success of the scale-up depends on whether one has suc- ceeded in designing representative scale-down experiments.

Based on process analysis In fact, the scale-down step, i.e. the step from regime

analysis to experimental simulation, is based on constant characteristic times. As such, it is only a variation of the scale-down based on constant dimensionless numbers. There are two main reasons for the use of characteristic parameters instead of dimensionless numbers.

First, for biotechnological processes much is unknown about the behaviour of microbial cultures under large-scale (transient) conditions. This makes it impossible to express all mechanisms in dimensionless numbers, while it is often possible to make an estimation of, for example, the relaxation time of mechanisms (Figure 2).

Second, the reaction rate is often one of the rate- limiting mechanisms in fermentation processes. In scaling down, however, the reaction is mostly conceived

10-6 10 '~, 10-2 10 0 10 2 10 t~ 10 6 I I I I I I

Mass action Caw

IL

AItosteric controls Changes in enzymic "~ '=concentrations

m-RNA Selection control

character i s t i c time (s}

Mixing probtems

(fed-)bafch dynamics,CC-transients ,,m

Figure 2 Relaxation times of mechanisms inside microorganisms and of their environment in a bioreactor

dimensional mechanistic I analysis analysis

I I

~I regime analysis

l yes

experimental design

rules of literature experience thumb data and

correlations

Figure 3 Interaction of the methods used in process analysis

as an established fact. For instance, changes in pressure or temperature in order to influence the reaction rate, as used in chemical engineering, are hardly ever used in biochemical engineering. This means that the advantage of using dimensionless numbers, i.e. by changing the rate of mechanisms without changing the ratio of their rates, disappears if the reaction rate is present in the dimensionless numbers.

In conclusion, if the behaviour of the microbial culture is not the bottleneck of the process, an analysis of engineering problems may be based on dimensionless numbers. It must be remarked, however, that in engineering problems a complete description by means of dimensionless numbers may be impossible.

This results in an extension of the scheme presented in Figure 1. The first step in the scale-down procedure not only includes regime analysis, but also dimensional analysis, mechanistic analysis and the similarity principle. Therefore, it is better described as process analysis. Figure 3 shows the interactions of the mechanisms used in the analysis of the process. Complemen- tary knowledge may be supplied from rules of thumb, literature data and correlations and experience.

Process analysis (Figure 3) can be seen as a system- atic method, not restricted to regime analysis alone, to

388 Enzyme Microb. Technol., 1987, vol. 9, July

analyse the performance of a large-scale process, resulting in an experimental design for small-scale simulation of large-scale conditions.

Dimensional analysis is a widespread tool in chemical engineering and has been extensively treated in the literature.a,9,10 12 The potentials and limitations of this method have been discussed by Kossen and Oosterhuis 2 and Zlokarnik. la

While dimensional analysis starts from a list of relevant parameters, mechanistic analysis is based on a list of involved mechanisms. The rate of these mechanisms has to be expressed in characteristic parameters, like fluxes, pressures, heights or times. Further analysis may be based either on the characteristic parameters or on the ratio of these parameters, i.e. dimensionless numbers.

To obtain the same behaviour of systems on different scales the systems have to be similar. Four similarity states are important in chemical engineering: geometrical, mechanical, thermal and chemical, each state neces- sitating the previous ones. However, in engineering problems it is, on the whole, impossible to satisfy the similarity demand, resulting in the fact that neither all the characteristic parameters nor all the dimensionless numbers can be kept constant during scale-up or scale- down. So it has to be decided which mechanisms are the most important of the system under investigation: in other words, what is the ruling regime?

Dimensional analysis always results in geometrical similarity. In mechanistic analysis, geometrical similarity is not necessary, which offers a significant advantage. Regime analysis may however, reject the geometrical similarity which resulted from dimensional analysis.

Regime analysis based on characteristic times

Introduction The regime concept was introduced by Johnstone

and Thring 9 and is a necessary ingredient for the solution of engineering problems by means of dimensional analysis based on the similarity principle.

In fact, the regime concept is very similar to analyses based on the rate-controlling step used in chemical engineering. Although not demonstrated for scale-up purposes, the use of microbalances in combination with the rate-controlling step is extensively treated in literature. 14 This approach is mainly used for mass transfer with chemical reaction in gas-solid and liquid-solid systems, liquid-liquid and gas-liquid systems, liquid- liquid-solid and gas-liquid-solid systems, and systems with solid-phase catalysis. In some cases it can also be used as the method in scaling up (fundamental method).

As mentioned above, regime analysis must provide information about the performance of the process. This is based on a comparison of the rate of the mechanisms which may play a role in the process, and the comparison can be made experimentally or theoretically, quali- tatively or quantitatively.

Examples of experimental regime analyses have been given by LevenspieP 4 and Kossen and Oosterhuis. a Also, the method presented by Moes 15 to analyse the liquid flow in (large-scale) fermenters can be conceived as experimental regime analysis.

Regime analysis and scale-down: A. P. J. Sweere et al.

Experimental regime analysis cannot answer all the questions which have to be solved, e.g. whether change of regime will occur during scale-up. This question can be solved by theoretical regime analysis.

Theoretical regime analysis can be subdivided into regime analysis based on characteristic parameters (e.g. characteristic times) and parameter sensitivity analysis. Here, only regime analysis based on characteristic times will be treated. It is based on a comparison of the rates of different mechanisms, expressed in characteristic parameters which can often be obtained accurately enough by the use of rules of thumb. A comparison of these characteristic parameters will yield the rate- limiting mechanisms, or regime of the process. In this review, regime analysis based on characteristic times will be demonstrated by means of some examples.

Characteristic times In comparing rate processes, time is the most conve-

nient characteristic parameter. For other processes, stresses, heights (e.g. HETP, the height equivalent to a theoretical plate), or other parameters may give a better insight into the problem. ~'4" 16.1 v

Characteristic time is a measure of the rate of a mechanism and can be considered as the time needed by that mechanism to smooth out a change to a certain fraction. A low value of a characteristic time means a fast mechanism; a high value means a slow mechanism.

In literature terms like time constant, process time (constant) and relaxation time are also used. The term time constant is commonly used for first-order processes only, and is equal to the time needed for a mechanism to proceed to 63% conversion. The time constant of a process can be composed from the time constants of several mechanisms. To prevent confusion, the term characteristic time is introduced to character- ize the rate of mechanisms. Using the definition for the characteristic time given above it is possible to charac- terize non-linear processes and processes of a higher order with only one characteristic time. An example is the characterization of liquid mixing in fermenters by means of a mixing time. Characteristic times can be determined experimentally or theoretically. Examples of experimental determination of characteristic times are liquid mixing and liquid circulation times in mechanically stirred fermenters. 2Ja

Theoretical values of characteristic times may be determined in several ways (Table 3). The characteristic time based on the ratio of a capacity and a flow seems a very useful definition to make a rapid estimation of the rate of various mechanisms. Parameters like dispersion coefficients and mass transfer coefficients have to be

Table 3 Theoretical methods to determine characteristic times

Method Example

1 Rules of thumb and t m = 4tc~ r literature correlations tc~ r = V/(2Hr N~2D 2)

2 Differential equations:

(a) Mass, heat and momentum E) d2C ' v de ' r 0 balance L 2 dx '2 L dx' C

(b) Accumulation by one dC d2C mechanism only dt - [~ dx 2

3 Ratio of capacity and f low (Co.g/m - Coj ) tmt J --

k, a(Co.g/m - Co.,)

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Review

estimated by correlations from the literature or from small-scale experiments. If the parameters are not known from the literature, the reaction kinetics also have to be measured. The characteristic times from differential equations seem to be more accurate, but require solution of the equations and have the draw- back that they are based on an estimation of the parameters and a simplified model.

It is clear from the above that the characteristic times of physical mechanisms in bioreactors can be estimated fairly easily by correlations found in the literature. However, the performance of a bioreactor may also be ruled by physiological mechanisms. Characteristic times of substrate consumption or product formation can be calculated by means of the integrated Michaelis- Menten kinetics for batch growth:

dCs #max CsCx - - - - - (1 ) dt Y~x K~+Cs

or by the ratio of capacity and flow:

Cs Y~, tsc - - - - (K s + C,) (2)

rs ~max Cx

Michaelis-Menten kinetics only give a description of balanced growth. If they are used to give an estimation of the characteristic times under dynamic conditions one has to be aware of the deviation Michaelis-Menten kinetics may give, especially at low substrate concentrations. Under dynamic conditions, mechanisms inside the cells (Figure 2) may change the performance of microbial cultures, resulting in a behaviour distinct from balanced growth. From a comparison of characteristic times of mechanisms inside microorganisms and of mechanisms in their environment it can be concluded that there are mechanisms inside microorganisms with characteristic times of the same order of magnitude as those of changes in the environment to which they will be exposed. So, the behaviour of the microorganisms may change during the process, thus influencing growth and product formation.

There are several examples of the use of characteristic times.

Table 4 Dimensions of production-scale fermenter for gluconic acid production 2

Impeller/vessel diameter Number of impellers Impeller blade width/impeller diameter Impeller speed Baffle diameter/vessel diameter Liquid height/vessel diameter Gas flow (reactor volume time) Liquid volume

0.32 2 0.2 1.3 or 2.6 litre s -1 0.09 up to 1.8 up to 0.5 vvm up to 25 m 3

Table 5 Characteristic times (s) of the mechanisms which are important in gluconic acid production 2

Transport phenomena Oxygen transfer 5.5 (non-coal)-11.2 (coal) Circulation of the liquid 12.3 Gas residence 20.6 Transfer of oxygen from a

gas bubble 290 (non-coal)-593 (coal) Heat transfer 330-650

Conversion Oxygen consumption, zero order 16 first order 0.7 Substrate consumption 5.5 x 104 Growth 1.2 x 104 Heat production 350

is of the same order of magnitude, so the conclusion can be drawn that oxygen gradients are likely to occur. From a comparison of the gas residence time and the time for oxygen transfer from the gas phase it is clear that no exhaustion of the gas phase will occur. Heat transfer will balance heat production. From a comparison with the liquid circulation time it can be concluded that no temperature gradient will be present in the fermenter.

It has to be remembered that the correlations used only give a rough estimation of the characteristic times, so only the order of magnitude can be considered and compared.

This regime analysis has formed the basis of small- scale investigations of the influence of fluctuating oxygen concentrations on gluconic acid production and in mass transfer studies.

Gluconic acid production Oosterhuis 2 used gluconic acid production by Glu-

conobacter oxydans as a model system to study the influence of large-scale conditions upon a microbial system. The study was aimed at the optimization of gluconic acid production using the scale-down method (Figure 1). Gluconic acid is produced in an aerobic batch process at a scale of ~25 m 3. The fermenter is equipped with two Rushton-type impellers, a star- shaped sparger just below the lowest impeller and four baffles. Table 4 gives the relative dimensions of the production-scale fermenter. To get an impression of the rate-limiting steps, regime analysis was carried out. Table 5 gives the characteristic times of the different mechanisms which play a role in the process. The following conclusions can be drawn from the table. Sub- strate consumption and growth have no influence on the performance of the process. The times for oxygen consumption and oxygen transfer to the liquid phase are of the same order of magnitude. Therefore, oxygen limitations may occur. Also, the liquid circulation time

Design of an installation for the microbial desulphurization of coal

Huber 19 and Bos z used regime analysis based on characteristic times to design an installation for the microbial desulphurization of coal. For optimal design of the reactor two major conditions must be met. Biomass is the catalyst for the oxidation of pyrite to sulphate, so that biomass limitation must be prevented. The environment of the microorganisms must be optimal for pyrite oxidation.

In relation to the first point, Huber 19 has stated that a reactor configuration consisting of a mixed-flow reactor followed by a plug-flow reactor would be most adequate, because of the first-order pyrite oxidation process. ~4 For this plug-flow reactor, a series of Pachuka tanks was suggested. A plug-flow reactor as such would result in washout of biomass. Therefore, an intensively mixed fermenter has to be used in front of it to generate an effective inoculum. Limitation of biomass can then be avoided if the residence time in this well- stirred fermenter is greater than the characteristic time

390 Enzyme Mic rob . Techno l . , 1987 , vo l . 9, Ju ly

Table 6 Characteristic times (s) relevant to the microbial desulphurization of coaP 9,20

Liquid mixing 60-118 Oxygen transfer 80-641 Oxygen consumption 3.4 x 105 Settling of the particles 2.5 x 104 Growth 8.6 x 104

Table 7 Specification of the installation for the microbial desulphurization of coal ~ 9,2o

Configuration Cascade of 10 pachuka tank reactors

Capacity 100 000 ton y- Gas velocity 0.02-0.003 m s -1 Diameter pachuka tank reactor 10 m Height pachuka tank reactor 20 m Pyrite content 0.5% Pyrite removal 90%

of biomass growth:

z > tx(= 1//~) (3)

Optimal conditions for pyrite oxidation demand that depletion of oxygen and settling of the coal particles has to be prevented throughout the fermenter. To achieve this, three conditions have to be met: no overall oxygen depletion:

tmt,1 < toc (4)

no gradients in oxygen concentration:

tm, 1 < trot,1 (5)

no sedimentation of the coal:

tm, I < t se t t (6)

If the kinetics of the desulphurization reaction are known the oxygen demand can be calculatedJ 9 Based on the required capacity of the installation and the conditions in equations (3)-(6) the reactor can be designed. Table 6 gives the values of the characteristic times. From these values it can be concluded that mass transfer determines the performance of the reactor. The time for oxygen consumption is much greater than the time for oxygen transfer, so no oxygen limitation will occur. Also, oxygen gradients and sedimentation of the coal particles will not be a problem. The analysis has resulted in the design of an installation for the desulphurization of coal with the specifications given in Table 7.


!

s s

I s

s . s

106 - . ~.~. "" - - J s s s s

s s p i S

s s

s s

"~ . - / . tp ,.~ ~ . ~ . . _ _ .,,..~

102- ~

L -~ I I i i i 0.01 0.1 1 10 1 00

reacf0r volume (m 3)

Figure 4 Estimated values of the characteristic times in the fluidized-bed reactor: 21 ta,=axial dispersion time; to,re = liquid circulation time; tp = product formation time

Design of an IBE production process Schoutens 21 has studied the design of a large-scale

process for the production of butanol from whey per- meatc with immobilized Clostridium cells. For the design of scale models of a gas-lift loop reactor (GLR) and a fluidized-bed reactor (FBR) with liquid circulation, regime analysis of a large-scale reactor was carried out. The characteristic times of liquid mixing, liquid circulation and product formation are given in Table 8. From experiments in a continuous stirred-flow reactor (CSTR) it was concluded that diffusion and reaction inside the beads were of no importance to regime analysis.

The criterion for designing a 10 litre FBR was a comparable degree of mixing at a 50 m a and 10 litr scale. Because production time is independent of scale, this would result in the same concentration gradients. For the 50 m 3 fermenter a height-to-diameter ratio (H/D) of 3 was chosen. Figure 4 shows the characteristic times as a function of reactor volume. To get the same ratio of tci Jtm, l an HID ratio of 25 has to be chosen for

Table 8 Specifications and characteristic times of a fluidized-bed reactor (FBR) with recycle and two gas-lift loop reactors (GLR) for continuous IBE fermentation 21

Parameter FBR GLR1 GLR2

Volume (m 3) 50 65 0.010 Bead fraction (-) 0.45 0.35 0.35 Dilution rate (h -1) 0.3-0.5 0.2-0.4 0.2-0.4 superficial Liquid velocity (m s - I ) 5 x 10 -3 0.5-1.0 0.2-0.3 superficial Gas velocity (m s -1) - - (1.0-3.0) x 10 -2 Production time (s) (7.2-12.0) 103 (9.0-18.0) x 103 Liquid circulation 600-1200 20-40 time (s) Axial dispersion (6.~69.0) x 105 700-1000 60-500 time (s)

(1.0-3.0) x 10 -2 (9.0-18.0) x 103 5-20

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Rev iew

the model system. The analysis resulted in the design of an FBR with HID = 25, and H = 2 m. To simulate large-scale gas production, a gas inlet was constructed.

From the characteristic times of the 65 m 3 GLR (Table 8) it can be concluded that a change of the hydrodynamic regime is unlikely when scaling down to laboratory scale. The one criterion that determines the design of the model GLR is to avoid wall effects of the bubbles and beads. Finally, a GLR with external loop was chosen with V = 15 litre, H = 1 m and D r = D d = 0.08 m.

Bakers' yeast production In designing or optimizing a fermentation process,

information can be gained from regime analysis if the characteristic times are calculated as a function of process parameters such as stirrer speed or gas flow rate. These calculations can give information about changing regimes during optimization or scale-up, or as the process proceeds.

In a study of the influence of a continuously changing environment on growth and metabolite production by microorganisms, fed-batch bakers' yeast production has been chosen as a model system. 22

Bakers' yeast is sensitive to changes in glucose concentration (Crabtree effect) and changes in oxygen concentration (Pasteur effect). A high glucose concentration or a low oxygen concentration will result in excretion of ethanol by the yeast. Under anaerobic conditions, glycerol is produced and transient conditions may lead to the production of glycerol, acetic acid, succinic acid, pyruvic acid and other products. The production of these metabolites, even if this is followed by their consumption in a later part of the process, 23 causes a reduction of biomass yield. It is therefore important to know whether limitations or gradients of oxygen, substrate or nutrients will occur.

Regime analysis is carried out for a bubble column fermenter of 150 m 3 with an operational volume of 120 m 3. Air is supplied by means of perforated horizon- tal pipes near the bottom of the column.

Tables 9a and 9b give the characteristic times of the mechanisms which may play a role in the performance of the fed-batch fermentation. A distinction has been made between mechanisms which have a clear effect on the process and mechanisms which have a characteristic time which is much smaller or much larger. The equations used to calculate the characteristic times are given in Appendix A and the parameters used in these calculations are given in Table AI.

Figure 5 shows the characteristic times of liquid mixing and circulation, mass transfer and oxygen consumption as a function of the superfical gas flow rate in a bubble column. These graphs have been calculated for the final situation in fed-batch production at a volume of 120 m 3 and a height-to-diameter ratio of 4. Such a plot allows easy comparison of the rates of the various mechanisms. The time needed for oxygen transfer to the liquid phase is much longer than that for oxygen consumption, so oxygen depletion will occur in the fermenter. If this is combined with a high mixing time for the liquid phase and a zone with a high oxygen transfer rate, for example near the sparger, then oxygen gradients are likely to occur.

The influence of the height-to-diameter ratio, H/D,

Table 9 (a) Characteristic times of the relevant mechanisms in bakers' yeast production in a bubble column fermenter

Mechanism Definition Magnitude (s)

Mix ing

L iqu id phase tmj = L 2 /D E,, 101 - 10 3

Gas phase tm,g = L 2/D E.o 1 O- 1 _ 103 Liquid circulation to, r = 2L/vc~ r 101 - 102 Gas flow tQ = (1 - c)L/v, 1 - 102 Oxygen transfer

Liquid phase trn j = 1/k~ a 1 -- 10 2 Gas phase tmt.g = cm/(k~ a(1 - ~)) 103 - 106

Substrate consumption tsc = C,/r~ 101 - 102 Oxygen consumption toc = Co,Jr o 1 Substrate addition t,a = V. Cd() v . C,o ) 101 - 102

(b) Characteristic times of yeast production which are not relevant to the final performance of the reactor

Mechanism Definition Magnitude

Fed-batch process tp 10 5 Growth of biomass t X = 1/l l 10 4 Heat transfer tht = V Pl ' c . / (U A . AT) 10 3 Heat production thp = V ' P l ' C./(rh + P/V) 10 3 Micro-mix ing

Diffusion t o (see Appendix A) 10-2-1 Turbulent erosion tte (see Appendix A) 1 -10 2 Laminar stretching t~s (see Appendix A) 10 -3

103

u E

4-

t..

102_ ~ liquid mixing

101- ~ " ~d

circulation

~. . . . . .~s s transfer

100 i oxygen consumption

10 -1 I 1 I I I I 50 100 1 SO 200 250 300 350

superficia[ gas vet0cify (mm/s)

Figure 5 Estimated values of the characteristic times of fed- batch bakers" yeast production as a function of the superficial gas velocity in a 120 m 3 bubble column reactor with a height-to- diameter ratio of 4

on characteristic times is shown in Figure 6. If H/D is < 0.3 or > 3 the reactor performance is governed by the liquid mixing: a pure regime. If H/D is >0.3 and

10 ~


10 3 -

I 10 2-

101

"-~ 10 0 L -

L -

qO

liquid mixing

mass transfer

oxygen consumption

I I I

0 I 2 3 4

- -~m.~ height diameter ratio

Figure 6 Estimated values of the characteristic times of fed- batch bakers' yeast production as a function of the height- to-diameter ratio of a bubble column reactor (V= 120 m3; ~g= 1 vvm)

that macro-mixing of the liquid phase in the reactor is determined by the smallest dimension of the column. The characteristic times for mass transfer and oxygen consumption are independent of the height of the column. From the ratio of these times the conclusion can be drawn that oxygen limitation will always occur.

A similar analysis can be made for substrate concentration in the fermenter (Figure 7). This figure shows some characteristic times as a function of batch time. In these calculations the gas flow rate was 5 cm s-1 and the volume increased from 80 to 120 m 3 in 10 h. Liquid circulation time and liquid mixing time increase, due to the volume increase. The times for substrate addition and substrate consumption decrease, due to an increase in the biomass concentration. From the ratio of liquid mixing time and the liquid circulation time to substrate addition time and substrate consumption time it can be concluded that substrate gradients will occur and that the intensity of these substrate gradients increases during the fermentation. A characteristic of a fed-batch process is the limitation of the added component. From the ratio of substrate consumption and addition time it can be concluded that substrate limitation will probably occur.

In conclusion it can be said that the following aspects need further investigation: liquid mixing; mass transfer; and the influence of periodic changes on microorganisms.

Much research has been done with respect to liquid mixing and mass transfer in bubble column reactors. This has resulted in models describing oxygen transfer and liquid mixing in laboratory-scale fermenters. More research is needed on the performance of large-scale fermenters, e.g. on liquid mixing patterns and concentra-

10 2.

liquid mixin(.

QJ E

.u

t _

~.J to

liquid circulation

substrafe consumption subsfrafe addition

101 [ , , , , , 0 2 # 6 8 10 12

time (h}

Figure 7 Estimated values of the characteristic times of fed- batch bakers" yeast production as a function of batch time in a bubble column reactor (V = 80-120 m3; at V = 120 m 3, H/D = 4, v, = 0.05 m s- 1 )

tion profiles. However, large-scale experiments are needed for some of these investigations. The third aspect which needs further investigation is well suited to laboratory experimentation, provided that the experimental set-up creates the same conditions as those met on a production scale.

Conclusions and discussion From the examples presented above, it can be con-

cluded that regime analysis is a suitable tool in the optimization, design and scale-up of bioreactors. The analysis can also play an important role in the experimental set-up. Regime analysis can be based on various characteristic quantities, but in the analysis of bioreactors the characteristic time seems to be an optimal choice. This is due to the fact that the mechanisms compared are very diverse and because the theoretically determined characteristic times can be easily compared with experimentally determined times.

A quantitative regime analysis is only possible if the relationships between the operational parameters and the dependent parameters are available to calculate the characteristic times of the mechanisms involved. Other- wise, knowledge about the system has to be completed by experimental research, often on a small scale, or necessitates working with qualitative analysis. Knowl- edge of the reaction kinetics is especially important and has to be measured, in general.

Optimization provides the advantages of an existing process, which opens the possibility of large-scale experiments. However, production-scale experiments are very time-consuming and expensive and do not always lead to the desired results. This may be caused

Enzyme Microb. Technol . , 1987, vol. 9, Ju ly 393

Review

by the fact that the methods of measurement designed or tested on a small scale are not suitable on a large scale and have to be adjusted. Consequently, theoretical analysis of the process is also very important.

Despite the fact that regime analysis seems very promising and the fact that the results seem very realis- tic, the method has to be proven further by experimental verification at a production scale. Oosterhuis z predicted oxygen limitation and oxygen gradients from the results of regime analysis of gluconic acid production. The oxygen gradients and local oxygen depletion were confirmed by measuring dissolved oxygen profiles during fermentation in a 25 m 3 bioreactor. Pre- diction of circulation time was checked by means of flow-follower (radio-pill) experiments.

The results of regime analyses used to design install- ations for the desulphurization of coal and to design a reactor for the IBE fermentation can only be verified after an installation of the predicted scale has been built.

In the case of the bakers' yeast production, experimental verification of the conclusions on a large scale from regime analysis and of the calculated characteristic times has not yet been possible.

Experimental simulation of large-scale conditions

Introduction Process analysis leads to design of small-scale experi-

ments for the simulation of large-scale conditions. This may result in scale models of the large-scale fermenter or segment models. It is clear that scale models are aimed at an overall study of the reactor performance whereas segment models are aimed at a more thorough investigation of parts of the process. Examples of both kinds of models are treated below.

Hydrodynamics and cell physiology are both characterized by a lack of sufficient knowledge, leading to problems in scaling up bioreactors.

If it is assumed that the biomass cannot be changed or replaced, then most problems are connected with the hydrodynamics of the system and the interaction between the hydrodynamics and the physiology of the biomass. To obtain relevant information for the solution of these problems the different subjects and their interaction need further investigation.

Scale-down based on dimensionless numbers

As mentioned above, dimensional analysis is often used to solve scale-up problems. If all dimensionless numbers can be kept constant, small-scale experiments are easy to design and translation of their results is uncomplicated. However, this is an ideal situation. Usually, not all dimensionless numbers can be kept constant unless unusual experimental set-ups are used or the number of dimensionless numbers is reduced by application of regime analysis. Let us look at some examples, though not all are based on bioreactor design.

In the scale-down of gas-liquid flow through pipes, six dimensionless numbers (Re, Fr, We, Eu, p', r/') have to be kept constant, and the systems have to be geo- metrically similar. 24 The dimensionless numbers can be derived from dimensional analysis or from the dimensionless Navier-Stokes equation, the equation of con-

tinuity and the state equation. If the gravitational acceleration is constant, a scale factor of only three can be achieved. However, if a rotating experimental set-up is used, a scale factor of 10 can be reached. 24

A nice example of the scale-down procedure and the power of small-scale experiments is the investigation of Bolle et al. 25 into the performance of a large-scale (1340m 3) upflow anaerobic sludge blanket (UASB) reactor.

The content of a UASB reactor can be mixed by the gas produced, provided that the influent is well distrib- uted over the sludge bed. Results obtained from experiments with a 800 m 3 UASB reactor have shown that an influent distribution system with one inlet point per 10 m 2, placed near the bottom of the reactor, in combination with a constant injection velocity is insuffi- cient. This set-up resulted in large dead-spaces and large short-circuiting fows. To study these phenomena, a scale model was designed and built. The model design was based on a dimensional analysis resulting in 14 dimensionless numbers. As expected, not all numbers can be kept constant during scale-down. Since most problems with full-scale reactors originate from problems with the distribution of the influent in the sludge- bed, most attention was paid to the behaviour of the liquid flow in the sludge bed. In particular, the modified Froude number had to be kept constant during scale- down.

Based on the assumption Amode~/A . . . . to r = 1/400, this analysis resulted in the design of a scale model with the dimensions: H = 0.26 m; L = 0.8 m; W = 0.6 m; dv = 0.1 mm. Besides this scale model, a model segment was used to study the sludge bed around an influent inlet point. Small-scale experiments were carried out with a continuous influent flow, on/off switching of the influent flow and minimum/maximum switching of the influent flow.

Based on the results of these experiments and on a substrate consumption time of 4.5 min on a full scale, a scheme was proposed of 2 min maximum flow and 2 min minimum flow. Stable short-circuiting flows were avoided using these switching times. These results were verified by means of large-scale experiments from which it was concluded that min/max switching of the inlet flow gave negligibly small short-circuiting flows and no dead spaces. In contrast, on/off switching resulted in less efficient use of the sludge bed. Continuous influent supply led to overloading and washout of the sludge particles.

Scale-down based on characteristic times

Regime analysis based on characteristic times gives information about the rate-limiting mechanisms of the process and the presence of nutrient limitations and concentration profiles. From this, it can be concluded what complementary knowledge about the system and what experiments are needed to optimize the process.

From regime analysis of gluconic acid production (see above) Oosterhuis concluded 2 that the cells were exposed to a continually changing oxygen concentration. Scale-down was based on constant characteristic times for liquid circulation and oxygen consumption. Two 'segment' models were used for experimental simulation. One model consisted of a batch fermenter with a periodically changing gas inlet concentration. The inlet

394 Enzyme Microb. Technol., 1987, vol. 9, July

Table 10 Comparison of a 50 m 3 fluidized-bed reactor (FBR) and a 65 m 3 gas-lift loop reactor (GLR) 21

Property FB R G LR

Reactor productivity + +/ - Biocatalyst attrition rate + + Reactor construction + +/ - Construction bottom plate - + Ease of operation + + Foaming + - Gas release + + Combination with simultaneous + - recovery processes

+, Favourable; -, unfavourable or attention needed

gas flow changed from air (20 s) to nitrogen gas (60- 180 s). Not only did a reduction in productivity occur due to the anaerobic periods but negative effect on the potential capacity to produce gluconic acid was also observed.

The other model was a configuration with two fermenters and an exchange flow between them. One fermenter was sparged with air and one with nitrogen gas. While circulating through the aerobic and anaerobic fermenter, no reduction of the potential capacity of the cells to produce gluconic acid was observed. The reduction of overall productivity could be related to the fraction of the volume which was anaerobic.

Regime analysis of the IBE process 21 resulted in the design of two scale-models: a 10 litre fluidized-bed reactor (FBR) with recycle and a 15 litre gas-lift loop reactor (GLR). The design of these models was based on constant characteristic times of production, and a constant ratio of the times of liquid circulation and axial dispersion of the liquid (see section above).

Hydrodynamic studies resulted in liquid-mixing models consisting of a 10 tanks in series model (FBR) and a 100 tanks in series model (GLR). Combination of the FBR mixing model, a plug-flow model with recycle and a CSTR model with a kinetic model, shown that this overall model only had low sensitivity for the hydrodynamic parameters. However, experimental comparison of the FBR and GLR showed a better performance of the FBR, leading to 22% higher production rate per unit reactor volume and a slightly higher outlet product concentration. These differences were caused by the higher solids hold-up in the FBR and the plug-flow with recycle character of the liquid mixing. For these and other reasons (Table 10) the FBR was preferred for large-scale application in the IBE process with immobilized Clostridia.

Interaction between cell physiology and liquid hydrodynamics

Much has been published about the hydrodynamics of mechanically stirred 26'27 and gas stirred fermenters. 28-33 Little, however, has been published about the performance of large-scale bioreactors. Therefore, complementary research has to be carried out on a large scale unless the conditions can be scaled down to the laboratory scale. However, the hydrodynamics are difficult for adequate scale-down. It is possible that interesting scale-down experiments have been reported in the literature, but because they cannot be found under this subject heading they are difficult to find.

It is clear that it will be no problem in the study of cell physiology, especially growth and metabolite pro-


Table 11 Characteristic times of fluctuations to which microorganisms are exposed on a large-scale and small-scale

Investigation Time (s) Remarks (ref)

Domestic sewage treatment 105

Repeated fed-batch 104-105 Mixing problems 10-102 Dropwise feeding in 1-102 continuous culture Pulse feeding 10 Two-fermenter system 10-102 Stimulus response analysis 102-10 s Step signal 10z-105

Day and night rhythms in feed supply and temperature (48) (49) (2, 5, 41, 42, 46, 47) (38, 39)

(43) (2) (50-52) (39, 53-55)

duction, at a small scale. However, it is commonly found that the environment to which the cells are exposed on a large scale is not similar to that on a small scale, the more so because periodic fluctuations in the environment may occur on a large scale.

The conclusion can be drawn that the behaviour of cells studied on a laboratory scale may be quite different from that on a large scale.

This usually results in a reduction of the yield of biomass and the required metabolite. It is also possible, though, that a periodically changing process parameter results in increased formation of certain metabolites. 34 In these cases, fluctuations have to be optimized for optimal product yield. The characteristic times of these fluctuations are usually of another order of magnitude than those of liquid mixing. So it is not expected that imperfect mixing will give a significant increase in product yield.

Much research has been done concerning the response of microorganisms to fluctuations in their environment. Reviews have been published by Barford, s Harrison and Topiwala, 3s Cooney et al. 36 and Pickett. 37 In investigating the influence of a changing environment on microorganisms, a distinction has to be made between a single change (for example impulse or step signal, batch) and continuous changes. The latter can be divided into periodical (e.g. sinusoidal, block signal, repeated fed-batch) and not-periodical (e.g. noise, fed-batch). Table 11 gives a survey of changes and their characteristic times to which microorganisms are exposed in order to study their metabolism. Just a few studies are concerned with the influence of imperfect mixing on microbial metabolism. With respect to mixing problems, transients of a (fed-)batch and a continuous culture are not very relevant, unless there is an interaction between these transients and the transients due to imperfect mixing. Therefore, only periodic transients will be treated.

Small-scale fermenters used for physiological investigations are commonly well mixed, so that fluctuations to simulate mixing effect have to be created artificially. Brooks and Meers 3s'39 have shown the influence of a dropwise feeding of a continuous culture: a drop frequency of 2.4 min-1 can reduce the biomass yield by 10%. More features described for microorganisms measured in physiological studies can probably be explained by imperfect mixing and its effect on the metabolism of the microorganisms. 4

Different experimental set-ups can be used to simulate the effect of imperfect mixing on a microbial culture (Table 12).

Enzyme Mic rob . Techno l . , 1987 , vo l . 9, Ju ly 395

Review

Table 12 Experimental set-ups which can be used to simulate the behaviour of large-scale bioreactors

Type Ref.

Well-mixed fermenter Coupling of well-mixed fermenters Plug-flow- reactor with recirculation Coupling of plug-flow and well-mixed fermenters Bubble column reactors Loop reactors

2, 41, 43-45 2

48, 49

A well-mixed fermenter can be used, but to simulate bad mixing it has to be used with increased viscosity or a continually changing parameter.

Vardar and Lilly 41 used a cycling top-pressure to simulate cycling dissolved oxygen tension (DOT) and hydrostatic pressure gradients in large-scale vessels used for penicillin production. The top pressure was changed sinusoidally between 1 and 2 bar with a period of 2 min. This resulted in a cycling DOT between 23% and 37% air saturation. It was found that the fluctuating DOT led the organisms to a metabolism which cor- responded to a lower DOT than the mean value imposed. Fluctuating conditions did not result in an irreversible change in metabolic activity.

Sokolov 42 studied the influence of changes in pH and dissolved oxygen tension on the specific growth rate of Candida utilis, Saccharomyces cerevisiae and Candida scottii. During a phase of exponential growth, cultures of these organisms were exposed to fluctuations with periods of 2-60 min. No negative influences, but rather accelerated growth, were observed.

Periodic fluctuations of glucose concentrations in a continuous culture of bakers' yeast, Saccharomyces cerevisiae, caused a reduction in biomass yield. 43 Also, hysteresis was observed in the biomass concentration, going from low to high dilution rates and back. Hyster- esis was also observed by Furukawa, 44 who investigated the influence of oxygen concentration on yeast metabolism in a continuous culture without any imposed fluctuations. So, it might be concluded that continuous culture rather than imposed fluctuations are responsible for the hysteresis.

By coupling well-mixed fermenters, the residence time distribution (RTD) or circulation time distribution (CTD), which will occur in large-scale fermenters, can be simulated. In each fermenter different conditions can be established, corresponding to the conditions in different zones of large-scale fermenters. 2

It is clear that in plug-flow reactors gradients will occur. But, as mentioned above, pure plug-flow will cause washout of the cells, so some degree of back- mixing or recirculation is needed.

Another possibility is the combination of a well mixed fermenter and a plug-flow reactor with or without recirculation. The so-called maximum- mixedness fermenters, consisting of a zone with intense mixing and a zone with little mixing, can be regarded as a combination of a well-mixed and a plug-flow reactor. Tsai 45 has concluded from theoretical considerations that in such systems the substrate utilization will be optimal. However, this is based on the Monod equation to describe microbial growth, and does not take into account the influence of the periodically changing environment in this system on the microorganisms.

Katinger 46 has worked with a maximum-mixedness

fermenter (a tubular closed-loop fermenter) to simulate the mixing phenomena of a large-scale recycle fermenter used for single cell protein production from n-paraffin. The recycle time in the small-scale system was in the order of 1 min up to several minutes. Candida tropicalis utilizing pure n-alkanes was used as a model system. With a more intensified transient limitation, Katinger observed an increase of the yield of biomass on substrate Y~x, a reduced oxygen demand Yox, and a declin- ing respiration coefficient RQ. More efficient energy generation or utilization of substrate energy must have been responsible for the increased Y~x and decreased Yox.

In her study of the influence of liquid-phase bulk mixing and mass transfer on penicillin production, Tuffnel147 used a reactor configuration consisting of a well-mixed reactor and bubble column fermenter. Thus, in simulation of a large-scale fermenter two zones can be distinguished: a well-mixed zone in which agitation is very good, and a bubble zone in which agitation is very poor. This system can also be regarded as a maximum-mixedness fermenter, although the plug-flow reactor will be characterized by a considerable amount of back-mixing.

Loop reactors and bubble column reactors can be conceived as a combination of well-mixed and/or plug- flow reactors. A disadvantage of these systems is the more complicated hydrodynamics.

Conclusions and discussion

It is important to base small-scale experiments on large- scale data, or estimations about the conditions at a production scale.

Many experimental set-ups can be used to simulate large-scale fermentation processes on a small scale. The choice of set-up depends on: the system which has to be simulated; the equipment present and financial resources; and the expertise with specific fermenters with regard to both experimental work and knowledge (including modelling) of the hydrodynamics of the system.

Mixing effects can increase as well as decrease the yield of biomass and the required metabolite. This will depend on: the character of the fluctuations (parameter, amplitude, frequency); the process (batch, fed-batch, continuous); and the organism. The expression of fluctuations depends on the reduction of product yield or production rate, and formation of by-products, or even loss of viability.

Little attention has been paid to the formation of by- products, although this can give considerable information on the metabolism of the organisms studied under transient conditions. A better understanding of growth and (by-)product formation is needed to develop adequate models to describe the behaviour of the microorganisms under large-scale conditions.

The advantage of the scale-down procedure is that, if it works well, pilot-plant investigation can be circum- vented. A distinction must be made between optimizing an existing process and designing and scaling up a new process. In the second case, in particular, the pilot plant has some important tasks apart from process development, namely the training of operators and other per- sonnel who have to deal with the new process; production of a small amount of the product for market

396 Enzyme Mic rob . Technol . , 1987, vol . 9, Ju ly

research; safety studies; study of accumulation and pol- lution characteristics; study of resources and construc- ting materials.

There are, also, however, limits to small-scale investigations which make it necessary to use a scale larger than laboratory scale. The scale may be limited by sample volume, installation of probes, viscosity of the liquid and inhomogeneities.

It can be concluded that, although pilot-plant investigation is very time-consuming and costly it offers some possibilities not offered by laboratory-scale studies. The final decision as to whether a pilot plant will be built or not has to be an economic one.

Nomenc la ture

A a

C Cp D D DE dp Eu e Fr 9 H Hr h k I a

K ks

L Ls ls

M m N P P R Re F h F T t ti U V /)b /)s /)tip We ro, .Y~x x

area (m 2) specific area based on liquid volume (m- 1) concentration (kg m-3) heat capacity (J kg- 1 K - 1) diameter (m) diffusion coefficient (m 2 s 1) effective dispersion coefficient (m 2 s- 1) particle diameter (m) Euler number (--) energy input per unit mass (J kg- 1) Froude number (-) gravitational acceleration (m s-2) height (m) height of impeller blade (m) heat transfer coefficient (W m 2 K - 1) volumetric mass transfer coefficient based on liquid volume (s- 1) Michaelis-Menten constant (kg m-3) mass transfer coefficient for mass transfer to the solid phase (m s- 1) length (m) scale of the reactor (m) scale of a volume element caused by turbulent erosion and laminar stretching of the volume element (m) molecular weight (kg mol- 1) gas-liquid distribution coefficient (kg kg- 1) stirrer speed (s- 1) power input (W) pressure (N m 5 2) gas law constant (J mol- 1 K - 1) Reynolds number (-) heat production rate (J m -3 s-1) reaction rate (kg m- 3 s- 1) temperature (K) time (s) characteristic time (s) overall heat transfer coefficient (W m -2 K-1) volume (m 3) bubble rise velocity (m s- 1) superficial gas velocity (m s- 1) impeller tip speed (m s- 1) Weber number (-) yield of biomass on oxygen (kg dry wt kg- 1) yield of biomass on substrate (kg dry wt kg- 1) length (m)

Greek q #max

symbols dynamic viscosity (Pa s) (maximum) specific growth rate (s h)


v kinematic viscosity (m 2 s - 1) p density (kg m-3) z mean residence time (s) qbg gas flow rate (m 3 s-1) q~v feed flow rate (m 3 s- 1) to heat production per kg oxygen consumed

(J kg 1)

Subscripts cir liquid circulation D diffusion d downcomer section of loop reactor g gas phase hp heat production ht heat transfer 1 liquid phase ls laminar stretching m mixing mt mass transfer o oxygen oc oxygen consumption p process r riser section of loop reactor s substrate sa substrate addition sc substrate consumption sett settling of particles sO feed substrate te turbulent erosion x biomass

Superscripts ' dimensionless parameter

References

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2 Oosterhuis, N. M. G., PhD Thesis, Delft University of Tech- nology, 1984

3 Kossen, N. W. F. and Oosterhuis, N. M. G. in Biotechnology (Rehm, H. J. and Reed, G., eds) VCH Verlagsgesellschaft, Wein- heim, 1985, vol. 2, 572-605

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12 Becker, H. A. Dimensionless Parameter: Theory and Methodology Applied Science Publishers, London, 1976

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Review 17 Bemer, G. G. PhD Thesis, Delft University of Technology, 1979 18 Einsele, A. Chem. Rundschau 1976, 29 (25), 53 19 Huber, T. F., Kossen, N. W. F., Bos, P. and Kuenen, J. G. Proc.

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Appendix A: Parameters and equations used in regime analysis of the bakers' yeast production

The parameters of the reg ime analys is are g iven in Tab le A1. The fo l lowing equat ions have been used: mix ing and mass t ransfer : 2a

DEj = 0.36(gD4vs) 1/3

DE,g = 78(0 s D) 3/2

vci r = 0.9(oDvs) 1/3

1 -- e = vd(vb + /3cir)

k I a = 0.32v '7

Energy input :

P = pg (og RT / (VM) In (p l /p2 )

rh = (/)#max Cx/Yox

Kinet ics :

r, = ,/~max/Ysx C s Cx/(k, + Cs)

ro = ~am,x~ Yox Co Cx/(ko + Co)

Micro -mix ing : the equat ions for s t i r red tank reactors 56 has been used as an es t imat ion of the macro -mix ing in a bubb le co lumn reactor :

tls >~ (2v/e) 1/2

tte = 3.85ls vs/12D - 2/3 e - 1/4

t D = 3/5(12/6D) 12/D = 24(L2/e) + 6(v/e)ln(v/D)

Tab le A1 Values of parameters used in regime analysis of the bakers' yeast product ion

cp= 4 .2k J kg -1 K -1 m= 30 .0kgkg -1 C s = 0.150 kg m 3 R = 8 .314 J mo1-1 K -1

Cso = 250.0 kg m 3 U = 1.3 kW m -2 K -1 C X= 45.0 kg m -3 V = 120.0 m 3

C. ( t=0)= 10 .0kgm -3 V( t=0) = 80 .0m 3 g = 9.8 m s -2 v b = 0.25 m s -1

ko = 5 .10 -5 kg m -3 Yox = 1.0 kg kg -1 k s = 0.5 kg m -3

Y,, = 0.53 kg kg -1 Pm=x = 0.4 h -1

pg = 1.2 kg m -3 Pl = 1000.0 kg m -3 ~v = 4.0 m 3 h -1 to = 14.2 x 103 kJ (kg 02) -1 D = 0 .673 x 10 -~ m 2 s -1

398 Enzyme Mic rob . Techno l . , 1987, vo l . 9, Ju ly

regime analysis and scale down

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