Topic: Aeration and Agitation

Magdalyne NongkynrihMobile No. : 8087464948Email id: magn.nong@gmail.com

Dr. P. A Pawar SirAssociate Prof. (Food Tech)Email id: papawar40@rediffmail.com

INTRODUCTIONThe majority of fermentation processes are

aerobic and therefore require the provision of oxygen. The oxidation of glucose may be represented as;C6H12O6 + 6O2 = 6H2O + 6CO2It is not possible to provide a microbial culture with all the oxygen it will need for the complete oxidation of glucose in one addition. Therefore, a microbial culture must be supplied with oxygen during growth at a rate sufficient to satisfy the organisms demand.

The oxygen demand of an industrial fermentation process is normally satisfied by aerating and agitating the fermentation broth.

However, the productivity of many fermentations is limited by oxygen availability and therefore, it is important to consider the factors which affect the fermenter’s efficiency in supplying microbial cells with oxygen.

This chapter considers the requirement for oxygen in fermentation processes, the quantification of oxygen transfer and the factors which will influence the rate of oxygen transfer into the solution.

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Typical Bioprocessing

Stock Culture Raw Materials

Shake Flasks

Seed Fermenter

Medium Formulation

Sterilization

Recovery

Purification Products

Air Agitator

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Aeration and Agitation

Important factor in a fermenters Provision for adequate mixing of its contents

Mixing in fermentation

to disperse the air bubbles

to suspend the cells

to enhance heat and mass transfer in the medium

All relate to Gas-liquid mass transfer

Aeration and Agitation

Aeration refers to the process of introducing air to increase oxygen concentration in liquids

Aeration may be performed by bubbling air through the liquid, spraying the liquid into the air or agitation of the liquid to increase surface absorption

Agitation – uniform suspension of microbial cells in homogeneous nutrient medium

Structural components involved in aeration and agitation

Agitator (impeller)

Baffles

Aeration system (sparger)

View looking down into a stainless steel fermentor

Agitator (impeller)

Achieve mixing objectives – bulk fluid and gas-phase mixing, air dispersion, oxygen transfer, heat transfer, suspension of solid particles and maintaining uniform environment throughout vessel contents.

Baffles

Four baffles incorporated into agitated vessels of all sizes to prevent vortex and to improve aeration efficiency

Metal strips roughly one-tenth of vessel diameter and attached radially to the wall

Minimizes microbial growth on baffles and fermenter walls.

Aeration system (sparger)

Introduces air into liquid of fermenter

Three basic types – porous sparger

1. Orifice sparger – a perforated pipe

2. Nozzle sparger – an open or partially closed pipe

3. Combined sparger-agitator

THE OXYGEN REQUIREMENTS OF INDUSTRIAL FERMENTATIONS

A culture's demand for oxygen is very much dependent on the source of carbon in the medium. Thus, the more reduced the carbon source the greater will be the oxygen demand.From Darling~ ton's and Johnson's equations (Table 9.1) it may be seen that the production of 100 grams of biomass from hydrocarbon requires approximately three times the amount of oxygen to produce the same amount of biomass from carbohydrate. However, it must be remembered that the high carbon content of hydrocarbon substrates means that high yield factors (g biomass g -1 substrate consumed) are obtained and the decision to use such substrates is based on the balance between the advantage of high biomass yield and the disadvantage of high oxygen demand and heat generation.

However, it is inadequate to base the provision of oxygen for a fermentation simply on an estimation of overall demand, because the metabolism of the culture is affected by the concentration of dissolved oxygen in the broth. The effect of dissolved oxygen concentration on the specific oxygen uptake rate (Qo2' mmoles of oxygen consumed per gram dry weight of cells per hour) has been shown to be of the Michaelis-Menten type, as shown in Fig. 9.1.

Fig. 9.1 it may be seen that the specific oxygen uptake rate increases with increase in the dissolved oxygen concentration upto a certain point(referred to as CCrit) above which no further increase in oxygen uptake rate occurs.

Thus, maximum biomass production may be achieved by satisfying the organism's maximum specific oxygen demand by maintaining the dissolved oxygen concentration greater than the critical level. If the dissolved oxygen concentration were to fall below the critical level then the cells may be metabolically disturbed. However, it must be remembered that it is frequently the objective of the fermentation technologist to produce a product of the micro-organism rather than the organism itself and that metabolic disturbance of the cell by oxygen starvation may be advantages to the formation of certain products.

Equally, provision of a dissolved oxygen concentration far greater than the critical level may have no influence on biomass production, but may stimulate product formation. Thus, the aeration conditions necessary for the optimum production of a product may be different from those favouring biomass production.

Hirose and Shibai's (1980) investigations of amino acid biosynthesis by Brevibactelium flavum provide an excellent example of the effects of the dissolved oxygen concentration on the production of a range of closely related metabolites. These workers demonstrated the critical dissolved oxygen concentration for B. flavum to 0.01 mg dm3 and considered the extent of oxygen supply to the culture in terms of the degree of 'oxygen satisfaction’, that is the respiratory rate of the culture expressed as a fraction of the maximum respiratory rate. Thus, a value of oxygen satisfaction below unity implied that the dissolved oxygen concentration was below critical level. The effect of the degree of oxygen satisfaction on the production of a range of amino acids is shown in Fig. 9.2.

From Fig. 9.2 it may be seen that the production of members of the glutamate and aspartate families of amino acids was affected detrimentally by levels of oxygen satisfaction below 1.0, whereas optimum production of phenylalanine, valine and leucine occurred at oxygen satisfaction levels of 0.55, 0.60 and 0.85, respectively.

The biosynthetic routes of the amino acids are shown in Fig. 9.3, from which it may be seen that the glutamate and aspartate families are all produced from tricarboxylic acid (TCA) cycle intermediates, whereas phenylalanine, valine and leucine are produced from the glycolysis intermediates, pyruvate and phosphoenol pyruvate.

An example of the effect of dissolved oxygen on secondary metabolism is provided by Zhou et al. 's (1992) work on cephalosporinC synthesis by Cephalosporium acremonium. These workers demonstrated that the critical oxygen concentration for cephalosporin C synthesis during the production phase was 20% saturation. At dissolved oxygen concentrations below 20% cephalosporinC concentration declined and penicillin N increased. The biosynthetic pathway to cephalosporin C is shown in Fig. 9.4, from which it may be seen that there are three oxygen-consuming steps in the pathway:

FIG. 9.4. The biosynthesis of cephalosporin C, indicating the oxy-gen consuming steps:(i) isopenicillin-N-synthase,(ii) deacetoxycephalosporin C synthase (commonly called expandase),(iii) deacetyl cephalosporin C synthase (commonly called hydroxylase)

(i) Cyclization of the tripeptide, a-amino-adipyl-cysteinyl-valine into isopenicillin N.(ii) The ring expansion of penicillin N into deace-toxycephalosporin C (DAOC).(iii) The hydroxylation of DAOC to give deacetyl-cephalosporinC.The oxygen demand of a fermentation largely depends on the concentration of the biomass and its respiratory activity, which is related to the growth rate.

OXYGEN SUPPLYOxygen is normally supplied to microbial cultures in the form of air, this being the cheapest available source of the gas. The method for provision of a culture with a supply of air varies with the scale of the process:i. Laboratory-scale cultures may be aerated by means

of the shake-flask technique where the culture (50 to 100 cm3) is grown in a conical flask (250 to 500 cm3) shaken on a platform contained in a controlled environment chamber.

ii. Pilot and industrial-scale fermentations are normally carried out in stirred, aerated vessels, termed fermenters.

Bartholomew et at. (1950) represented the transfer of oxygen from air to the cell, during a fermentation, as occurring in a number of steps:i. The transfer of oxygen from an air bubble into

solution.ii. The transfer of the dissolved oxygen through

the fermentation medium to the microbial cell.

iii. The uptake of the dissolved oxygen by the cell.

The rate of oxygen transfer from air bubble to the liquid phase may be described by the equation: Where

CL : is the concentration of dissolved oxygen in the fermentation broth(mmoles dm3 ),t : is time (hours)dCL/dt : the change in oxygen concentration over a time period, i.e. the oxygen-transfer rate (mmoles O2 dm-3 h-1),

KL : the mass transfer coefficient (cm h-1)a : the gas/liquid interface area per liquid volume (cm2 cm-3),C* is the saturated dissolved oxygen concentration (mmoles dm-3 )

KL may be considered as the sum of the reciprocals of the resistances to the transfer of oxygen from gas to liquid and (C* - CL) may be considered as the 'driving force' across the resistances. It is extremely difficult to measure both KL and 'a' in a fermentation and, therefore, the two terms are generally combined in the term KLa, the volumetric mass-transfer coefficient, the units of which are reciprocal time (h-1).

The larger the KLa, the higher the aeration capacity of the system. The KLa value will depend upon the design and operating conditions of the fermenter and will be affected by such variables as aeration rate, agitation rate and impeller design. These variables affect 'KL' by reducing the resistances to transfer and affect 'a' by changing the number, size and residence time of air bubbles.

It is convenient to use KLa as a yardstick of fermenter performance because, unlike the oxygen-transfer rate, it is unaffected by dissolved oxygen concentration.

The dissolved oxygen concentration reflects the balance between the supply of dissolved oxygen by the fermenter and the oxygen demand of the organism. If the KLa of the fermenter is such that the oxygen demand of the organism cannot be met, the dissolved oxygen concentration will decrease below the critical level (Ccrit).

If the KLa is such that the oxygen demand of the organism can be easily met the dissolved oxygen concentration will be greater than Ccrit and may be as high as 70 to 80% of the saturation level. Thus, the KLa of the fermenter must be such that the optimum oxygen concentration for product formation can be maintained in solution throughout the fermentation.

Determination of KLaDetermination of KLa in a fermenter is important in to

establish its aeration efficiency and quantify effects of operating variables on oxygen supply.

It is important to remember at this stage that dissolved oxygen is usually monitored using a dissolved oxygen electrode which records dissolved oxygen activity or dissolved oxygen tension (DOT) whilst the equations describing oxygen transfer are based on dissolved oxygen concentration.

Thus, to translate DOT into concentration the solubility of oxygen in the fermentation medium must be known and this can present difficulties.

A number of different methods are available

1. The Sulphite oxidation techniqueMeasures the rate of conversion of a 0.5m solution of sodium sulphite to sodium sulphate in the presence of a copper or cobalt catalyst

Na2SO3 + 1/2 O2 Na2SO4

Oxidation of sulphite is equivalent to the oxygen-transfer rate.

The dissolved oxygen concentration, for all practical purposes, will be zero and the KLa may then be calculated from the equation: (where OTR is the oxygen transfer rate)

Disadvantages i) slow, ii) effected by surface active agentsiii) Rheology of solution not like media

Cu++ or Co++

2. Gassing out techniques

Estimation of KLa by gassing out involves measuring the increase in dissolved O2 of a solution during aeration and agitation

The oxygen transfer rate will decrease during the period of aeration as C L approaches C* due to the decline in the driving force (C* - CL).

The oxygen transfer rate, at one time, will be equal to the slope of the tangent to the curve of values of dissolved oxygen concentration against time of aeration, as shown in Fig. 9.5.

2. Gassing out techniques: This involve initially lowering the oxygen value to a low level. Two methods have been employed to achieve this lowering of the dissolved oxygen concentration - the static method and the dynamic method.(i) Static Method O2 concentration of the solution is lowered by gassing out with

liquid N2

The deoxygenated liquid is then aerated, agitated and increase in dissolved O2 is monitored with oxygen probe.

The integration of equation (9.1) yields:

Thus, a plot of In (C* - CL) against time will yield a straight line of slope -KLa, as shown in Fig 9.6.

Advantage: It is very rapid than sulphite method (15 mins). May utilise fermentation medium and dead cells. Use of a membrane-type electrode, the response time of

which may be inadequate to reflect the true change in the rate of oxygenation over a short period of time.

Disadvantage: Use for small scale vessels, there are severe limitations to its

use on large scale fermenters which have high gas residence times.

The air supply to such a vessel is resumed after deoxygenation with nitrogen, the oxygen concentration in the gas phase may change with time as the nitrogen is replaced with air.

(ii) Dynamic Method: Taguchi and Humphrey (1966) utilized the respiratory activity of

a growing culture in the fermenter to lower the oxygen level prior to aeration.

Complex nature of fermentation broths the probe used to monitor the change in dissolved oxygen concentration must be of the membrane-covered type which may necessitate the use of the response-correction factors referred to previously.

The procedure involves stopping the supply of air to the fermentation which results in a linear decline in the dissolved oxygen concentration due to the respiration of the culture, as shown in Fig. 9.7.

In Fig. 9.7 the slope of the line AB is a measure of the respiration rate of the culture. At point B the aeration is resumed and the dissolved oxygen concentration increases until it reaches concentration X. BC, the observed increase in dissolved oxygen concentration is the difference between the transfer of oxygen into solution and the uptake of oxygen by the respiring culture as expressed by the equation:

where x is the concentration of biomassQo2 is the specific respiration rate (mmoles of oxygen g -1

biomass h-1 ).The term xQo2 is given by the slope of the line AB in Fig. 9.7.

Equation (9.4) may be rearranged as:

Thus, from equation (9.5), a plot of CL versus dCL/dt + xQo2 will yield a straight line, the slope of which will equal -1/KLa, as shown in Fig. 9.8. This technique is convenient in that the equations may be applied using DOT rather than concentration because it is the rates of transfer and uptake that are being monitored so that the percentage saturation readings generated by the electrode may be used directly.

The occurrence of oxygen-limited conditions during deoxygenation may be detected by the deviation of decline in oxygen concentration from a linear relationship with time, as shown in Fig. 9.9.

When the oxygen demand of a culture is very high it may be difficult to maintain the dissolved oxygen concentration significantly above Ccrit during the fermentation so that the range of measurements which could be used in the KLa determination would be very small. Thus, it may be difficult to apply the technique during a fermentation which has an oxygen demand close to the supply capacity of the fermenter.

Both the dynamic and static methods are also unsuitable for measuring KLa values in viscous systems. This is due to the very small bubbles (< 1 mm diameter) formed in a viscous system which have an extended residence time compared with 'normal’ sized bubbles.

Thus, the gassing out techniques are only useful on a small scale with non-viscous systems.

Advantages:• Can determine KLa during an actual fermentation• Rapid technique• Can use a dissolved oxygen probe of the membrane type

Disadvantages:• Limited range of dissolved oxygen levels can be studied• Must not allow oxygen levels to fall below Ccrit

• Difficult to apply technique during a fermentation with a high oxygen demand

• Relies on measurements taken at one point

3. The oxygen-balance technique

The KLa of a fermenter may be measured during a fermentation by the oxygen balance technique which determines, directly, the amount of oxygen transferred into solution in a set time interval. The procedure involves measuring the following parameters: i. The volume of the broth contained in the vessel, VL (dm3).ii. The volumetric air flow rates measured at the air inlet and

outlet, Qi and Qo' respectively (dm3 min-1).iii. The total pressure measured at the fermenter air inlet and

outlet, Pi and Po, respectively (atm. absolute).iv. The temperature of the gases at the inlet and outlet, Ti and

To, respectively (K).v. The mole fraction of oxygen measured at the inlet and outlet,

Yi and Yo' respectively.

The oxygen transfer rate may then be determined from the following equation (Wang et al., 1979):

where 7.32 X 105 is the conversion factor equalling (60 min h-1) [mole/22.4 dm3 (STP)] (273 K/1 atm).The ideal gaseous oxygen analyser is a mass spectrometer analyser which is sufficiently accurate to detect changes of 1 to 2%. The KLa may be determined, provided that CL and C* are known, from equation (9.1):

Advantage: The oxygen-balance technique appears to be the

simplest method for the assessment of KLa. It can measure aeration efficiency during a

fermentation. Disadvantage: The balance method is the most desirable

technique to use and the extra cost of the monitoring equipment involved should be a worthwhile investment.

FLUID RHEOLOGY

Fluids may be described as Newtonian or non- Newtonian depending on whether their rheology (flow) characteristics obey Newton's law of viscous flow.

Consider a fluid contained between two parallel plates area A and distance x apart. If the lower plate is moved in one direction at a constant velocity, the fluid adjacent to the moving plate will move in the same direction and impart some of its momentum to the 'layer' of liquid directly above it causing it, to move in the same direction at a slightly lower velocity.

Newton's law of viscous flow states that the viscous force, F, opposing motion at the interface between the two liquid layers, flowing with a velocity gradient of du/dx, is given by the equation:

where is the fluid viscosity, which may be considered as the resistance of the fluid to flow.Equation (9.7) may be written as:

F/ A is termed the shear stress (T) and is the applied force per unit area, du/dx is termed the shear rate (y) and is the velocity gradient. Thus:

Equation (9.8) conforms to the general relationship:

where K is the consistency coefficient. n is the flow behaviour index or power law index.For a Newtonian fluid n is 1 and the consistency coefficient is the viscosity which is the ratio of shear stress to shear rate.Thus, a plot of shear stress against shear rate, for a Newtonian fluid, would produce a straight line, the slope of which would equal the viscosity. Such a plot is termed a rheogram (as shown in Fig. 9.10).

A plot of shear stress against shear rate for a non-Newtonian liquid will deviate from the relationship depicted in Fig. 9.10, depending on the nature of the liquid. Several types of non-Newtonian liquids are recognized and typical rheograms of types important in the study of culture fluids are given in Fig. 9.11, and their characteristics are discussed below.

Some of the following fluid rheology:

1. Binghamplastic rheology2. Pseudoplastic rheology3. Dilatant rheology4. Casson body rheology

1. Bingham plastic rheologyBingham plastics are similar to Newtonian liquids apart from the fact that shear rate will not increase until a threshold shear stress or yield stress or yield value, is exceeded. A linear relationship of shear stress to shear rate is the yield stress is exceeded and the slope of this line is termed the coefficient of rigidity or the plastic viscosity. Thus, the flow of a Bingham plastic is described by the equation:

where n is the coefficient of rigidity. is the yield stress.Examples of these fluids include toothpaste and clay.

2. Pseudoplastic rheology

The apparent viscosity of a pseudoplastic liquid decreases with increasing shear rate. Most polymer solutions behave as pseudoplastics.The flow of a pseudoplastic liquid may be described by the power law model, equation (9.9), i.e.:

The flow-behaviour index is less than unity for a pseudoplastic liquid, the smaller the value of n, the greater the flow characteristics of the liquid deviate from those of a Newtonian fluid. Equation (9.9) may be converted to the logarithmic form as:

3. Dilatant rheology

The apparent viscosity of a dilatant liquid increases with increasing shear rate. The value of the flow-behaviour index is greater than 1, the greater the value the greater the flow characteristics deviate from those of a Newtonian fluid. Example is liquid cement slurry.

4. Casson body rheologyA type of non-Newtonian fluid, termed a Casson body, which behaved as a pseudoplastic in that the apparent viscosity decreased with increasing shear rate but displayed a yield stress and, therefore, also resembled a Bingham plastic.The flow characteristics of a Casson body may be described by the following equation:

where Kc is the Casson viscosity.

FACTORS AFFECTING KLa VALUES INFERMENTATION VESSELS

A. The effect of air-flow rate on KLa

1. MECHANICALLY AGITATED REACTORS

2. NON-MECHANICALLY AGITATED REACTORS

i. Bubble columns

ii. Air-lift reactors

3. THE RELATIONSHIP BETWEEN KLa AND POWER CONSUMPTION

4. THE RELATIONSHIP BETWEEN POWER CONSUMPTION AND OPERATING VARIABLES

B. The effect of medium and culture rheology on Kla

1. MEDIUM RHEOLOGY

2. THE EFFECT OF MICROBIAL BIOMASS ON KLa

i. Agitator design for non-Newtonian fermentations

ii. The manipulation of mycelial morphology

3. THE EFFECT OF MICROBIAL PRODUCTS ON AERATION

C. The effect of foam and antifoams on oxygen transfer

A. The effect of air-flow rate on KLa1. MECHANICALLY AGITATED REACTORSThe effect of airflow rate on KLa values in conventional agitated systems is illustrated in Fig. 9.12.

The quantitative relationships between aeration and KLa for agitated vessels are considered in the subsequent section on power consumption. If the impeller is unable to disperse the incoming air then extremely low oxygen transfer rates may be achieved due to the impeller becoming 'flooded'.

Flooding is the phenomenon where the air-flow dominates the flow pattern and is due to an inappropriate combination of airflow rate and speed of agitation.

The flooding could be avoided if:

where FS is the volumetric airflow rate at the pressure conditions of the lower stirrer (m 3 sec-1)N is the stirrer speed (sec-1),D is the stirrer diameter (m),g is the gravitational acceleration(m sec-2).

The different flow patterns produced by a disc turbine that occur under a range of aeration and agitation conditions (Fig. 9.13).

Figure 9.13 A shows the flow profile of a non-aerated vessel and Figs 9.13 B to F the profiles with increasing airflow rate. As air-flow rate increases the flow profile changes from one dominated by agitation (Fig. 9.13 B)to one dominated by air flow (Figs9.13 D to F) until finally the air flow rate is such that the air escapes without being distributed by the agitator (Fig. 9.13 F).

2. NON-MECHANICALLY AGITATED REACTORSBubble columns and air-lift reactors are not mechanically agitated and, therefore, rely on the passage of air to both mix and aerate.i. Bubble columnsThe flow pattern of bubbles through a bubble column reactor is dependent on the gas superficial velocity(cm sec-1). At gas velocities of below 1-4 cm sec-1 the bubbles will rise uniformly through the medium and the only mixing will be that created in the bubble wake. This type of flow is referred to as homogeneous. At higher gas velocities bubbles are produced unevenly at the base of the vessel and bubbles coalesce resulting in local differences in fluid density. The differences in fluid density create circulatory currents and flow under these conditions is described as heterogeneous as shown in Fig. 9.14.

Flooding in a bubble column is the situation when the airflow is such that it blows the medium out of the vessel. This requires superficial gas velocities approaching 1 m sec-1 which are not attainable on commercial scales.The relationship derived for non-coalescing, non-viscous, large bubbles (6 mm diameter)will give a reasonably; accurate estimation for most non-viscous situations:

where Vsc is the superficial air velocity corrected for

local pressure.

However, viscosity has an overwhelming influence on KLa in a bubble column which expressed as:

where π is the liquid dynamic viscosity (N s m-2 ).The practical implication of this equation is that bubble columns cannot be used with highly viscous fluids.

ii. Air-lift reactorsThe difference between a bubble column and an air-lift reactor is that liquid circulation is achieved in the air-lift in addition to that caused by the bubble flow.A given air-lift reactor and medium KLa varies linearly with superficial air velocity on a log-log scale over the normal range of velocities.Thus, the KLa obtained in an air-lift will be less than that obtained in a bubble column at the same superficial air velocity, i.e. less than 0.32(Vs

c)0.7

The degree of agitation has been demonstrated to have a profound effect on the oxygen-transfer efficiency of an agitated fermenter.The agitation assisted oxygen transfer in the following ways:i. Agitation increases the area available for oxy-gen

transfer by dispersing the air in the culture fluid in the form of small bubbles.

ii. Agitation delays the escape of air bubbles from the liquid.

iii. Agitation prevents coalescence of air bubbles.iv. Agitation decreases the thickness of the liquid film at

the gas-liquid interface by creating turbulence in the culture fluid.

The degree of agitation may be measured by the amount of power consumed in stirring the vessel contents. The power consumption may be assessed by using a dynamometer, by using strain gauges attached to the agitator shaft and by measuring the electrical power consumption of the agitator motor.

3. THE RELATIONSHIP BETWEEN KLa AND POWERCONSUMPTION

A large number of empirical relationships have been developed between KLa, power consumption and superficial air velocity which take the form of:

Where Pg is the power absorption in an aerated systemV is the liquid volume in the vesselVs is the superficial air velocityK, x and y are empirical factors specific to the sys-tem under investigation.

The KLas of a number of agitated and aerated vessels (up to a volume of 66 dm3 ) containing one impeller, using the sulphite oxidation technique, and derived the following expression:

Thus, it may be seen from equation (9.15) that the Kla value was claimed to be almost directly proportional to the gassed power consumption per unit volume. The KLa of an aerated, agitated vessel is affected significantly by the consumption of power during stirring and, hence, the degree of agitation.

Quantitative relationships between power consumption and operating variables may be useful in:i. Estimating the amount of power that an

agitation system will consume under certain circumstances, which could assist in fermenter design.

ii. In providing similar degrees of power consumption (and, hence, agitation and, therefore, KLas in vessels of different size.

4. THE RELATIONSHIP BETWEEN POWER CONSUMPTIONAND OPERATING VARIABLES

The relationship between power consumption and operating variables in baffled, agitated vessels using the technique of dimensional analysis. The power absorption during agitation of non-gassed Newtonian liquids could be represented by a dimensionless group termed the power number, defined by the expression:

where Np is the power number,P is the external power from the agitator,ρ is the liquid density,N is the impeller rotational speed,D is the impeller diameter.

Thus, the power number is the ratio of external force exerted(P) to the inertial force imparted (ρ N 3D5) to the liquid. The motion of liquids in an agitated vessel may be described by another dimensionless number known as the Reynolds number which is a ratio of inertial to viscous forces:

where NRc is the Reynolds number and is the liquid viscosity.Another dimensionless number, termed the Froudenumber, relates inertial force to gravitational force and is given the term:

where NFr is the Froude number andg is the gravitational force.

The power number was related to the Reynolds and Froude numbers by the general expression:

where c is a constant dependent on vessel geometry but independent of vessel sizex and y are exponents.In a fully baffled agitated vessel the effect of gravity is minimal so that the relationship between the power number and the other dimensionless numbers becomes:

Therefore substituting from equations (9.16 and 9.17)

Values for P at various values of N,D, ρ and may be determined experimentally and the Reynolds and power numbers for each experimental situation my then be calculated. A plot of the logarithm of the power number against the logarithm of the Reynolds number yields a graph termed the power curve is shown in Fig.9.15.

From Fig. 9.15 the power is divisible into three clearly defined zones; i. The laminar or viscous flow zone where the

logarithm of the power number decreases linearly with an increase in the logarithm of the Reynolds number.

ii. The transient or transition zone, where there is no consistent relationship between the power and Reynolds numbers.

iii. The turbulent flow zone, where the power number is a constant, independent of the Reynolds number so that the value of x is zero and the value of the Reynolds number is in excess 104

If the values of the exponent, x are substituted into equation (9.21) for the zones of viscous and turbulent flow then the following terms are given:

Power consumption on the small scale may be represented as:

And on a large scale as:

Where the subscripts sm and L refer to the small and large scale respectively. Maintaining the same power input per unit volume:

Where V is the volume. Assuming the vessels to be geometrically similar then c will be the same regardless of scale and as the same broth would be employed p would remain the same for both systems.

For geometrically similar vessels

Therefore substituting for Dsm/DL in eq. (9.26)

A number of workers have produced correlations of gassed power consumption, ungassed power consumption and operating variables, that of being widely used:

where Q is the volumetric airflow rate.The following correlation from 248 sets of published data:

where Q is the volumetric airflow rate,g is the acceleration due to gravity,W is the impeller blade width.Using dimensional analysis:

where Na is the aeration number and equals Q/NDT is the vessel diameter.

B. The effect of medium and culture rheology on KLa

The rheology of a fermentation broth has a marked influence on the relationship between KLa and the degree of agitation. The objective of this section is to discuss the effects of medium and culture rheology on oxygen transfer during a fermentation. The rheology of the broth is affected by the composition of the original medium and its modification by the growing culture, the concentration and morphology of the biomass and the concentration and rheological properties of the microbial products. Therefore, fermentation broths vary widely in their rheological properties and significant changes in broth rheology may occur during a fermentation.

1. MEDIUM RHEOLOGYFermentation media contain starch as a carbon source which may render the medium non-Newtonian and relatively viscous. As the organism grows it will degrade the starch and thus modify the rheology of the medium and reduce its viscosity. The study of the growth of Streptomyces aureofaciens on a starch-containing medium. Before inoculation, the medium displayed Bingham plastic characteristics with a well-defined yield stress and an apparent viscosity of approximately 18 pseudopoise; after 22 hours the organism's activity had decreased the medium viscosity to a few pseudopoise and modified its behaviour to that of a Newtonian liquid; from 22 hours onwards the apparent viscosity of the broth gradually increased, due to the development of the mycelium, upto a maximum of approximately 90 pseudopoise and the rheology of the broth became increasingly pseudoplastic in nature.

2. THE EFFECT OF MICROBIAL BIOMASS ON KLa

i. Agitator design for non-Newtonian fermentations

The biomass concentration and its morphological form in a fermentation has been shown to have a profound effect on oxygen transfer. However, the highly viscous non-Newtonian broths of fungal and streptomycete fermentations present major difficulties in oxygen provision, the productivities of many such fermentations being limited by oxygen availability.

The difference in the pattern of oxygen uptake between unicellular and mycelial fermentations as illustrated in Fig. 9.16. In both unicellular and mycelial fermentations the pattern of total oxygen uptake is very similar during the exponential growth phase, up to the point of oxygen limitation.However, during oxygen limitation, when arithmetic growth occurs, the oxygen uptake rate remains constant in a unicellular system whereas it decreases in a mycelial one. The only possible explanation for such a decrease is the increasing viscosity of the culture caused by the increasing mycelial concentration.

Figure 9.17 illustrate the effect of Penicillium chrysogenum mycelium on KLa. The KLa decreased approximately in proportion with the square root of the broth viscosity, i.e.:

ii. The manipulation of mycelial morphologyThe biomass of mycelial organisms grown in submerged culture may vary from the filamentous type, in which the hyphae form a homogeneous suspension dispersed through the medium, to the 'pellet' type consisting of compact, discrete masses of hyphae. The filamentous form tends to give rise to a highly viscous, non-Newtonian broth where as the pellet form tends to produce an essentially Newtonian system with a much lower viscosity making oxygen transfer much easier.

The KLa attained in the lovastatin Aspergillus terreus fermentation was 20h-1 with a filamentous culture and 80 h-1 with a pelleted one at the same power input. Thus, the morphological form of a mycelial organism in submerged culture has a major effect on the broth rheology and may, therefore, be expected to influence aeration efficiency.

3. THE EFFECT OF MICROBIAL PRODUCTS ON AERATION

The product of a fermentation contributes relatively little to the viscosity of the culture broth. However, the exception is the production of bacterial polysaccharides, where the broths tend to be highly viscous non-Newtonian.Normally, microbial polysaccharides tend to behave as pseudoplastic fluids, although some have also been shown to exhibit a yield stress.

The yield stress of a polysaccharide can make the fermentation particularly difficult because, beyond a certain distance from the impeller, the broth will be stagnant and productivity in these regions will be practically zero.Thus, bacterial polysaccharide fermentations present problems of oxygen transfer and bulk mixing similar to those presented by mycelial fermentations. An air-lift loop reactor is designed incorporating a pump to circulate the highly viscous broth.

C. The effect of foam and antifoams on oxygen transfer

The high degree of aeration and agitation required in a fermentation frequently gives rise to the undesirable phenomenon of foam formation. In extreme circumstances the foam may overflow from the fermenter via the air outlet or sample line resulting in the loss of medium and product, as well as increasing the risk of contamination. The presence of foam may also have an adverse effect on the oxygen-transfer rate.

Thus, it is desirable to break down a foam before it causes any process difficulties and this may be achieved by the use of mechanical foam breakers or chemical anti-foams.

All antifoams are surfactants and may, themselves, be expected to have some effect on oxygen transfer. Antifoams tend to decrease the oxygen-transfer rate, it also cause the collapse of bubbles in foam but they may favour the coalescence of bubbles within the liquid phase, resulting in larger bubbles with reduced surface area to volume ratios and hence a reduced rate of oxygen transfer.

THE BALANCE BETWEEN OXYGEN SUPPLY AND DEMAND

This section attempts to bring these two aspects together and considers how processes may be designed such that the oxygen uptake rate of the culture does not exceed the oxygen transfer rate of the fermenter.The volumetric oxygen uptake rate of a culture is described by the term, Qo2x, where Qo2 is the specific oxygen uptake rate (mmoles O2 g-1 biomass h-1 ) and x is biomass concentration (g dm-3 ). Thus, the units of Qo2x are mmoles oxygen dm-3 h-1 .

It is necessary that the oxygen-transfer rate of the fermenter matches the oxygen uptake rate of the culture whilst maintaining the dissolved oxygen above a particular concentration. A fermenter will have a maximum KLa by balancing the supply and demand. This may be achievedby:i. Controlling biomass concentration.ii. Controlling the specific oxygen uptake rate.iii. A combination of (i) and (ii).

i. Controlling biomass concentration

The highest biomass concentration (termed the critical biomass or xcrit ) which can be maintained under fully aerobic conditions in a fermenter of known KLa. Thus, xcrit is the biomass concentration which gives a volumetric uptake rate (Qo2Xcrit) equal to the maximum transfer rate of the fermenter, i.e. KLa (C* - Ccrit). If Ccrit is defined as the dissolved oxygen concentration when: Qo2 = 0.99Qo2maxthen the volumetric oxygen uptake rate when the dissolved oxygen concentration is Ccrit will be: 0.99Qo2max 'xcrit .

If the oxygen transfer rate were equal to the uptake rate when the dissolved oxygen concentration equals Ccrit then:

Equation (9.29) may be used to calculate xcrit for a fermenter with a particular KLa value:

Equation (9.30) may also be modified to calculatebiomass concentration which may be maintainedfixed dissolved oxygen concentration above Ccrit:

This is shown graphically in Fig. 9.20.

The upper graph represents the relationship between the dissolved oxygen concentration and the volumetric oxygen transfer rate achievable in three fermenters (plots 1, 2 and 3 represent fermenters of increasing KLa values) while the lower graph represents the relationship between biomass and the volumetric oxygen uptake rate of the culture.

ii. Controlling the specific oxygen uptake rate

Very few commercial fermentations are operated in continuous culture, fed-batch culture is widely used in industrial fermentations and provides an excellent tool for the control of oxygen demand.The most common way in which the technique is applied to control oxygen demand is to link the nutrient addition system to a feed-back control loop using a dissolved oxygen electrode as the sensing element. If the dissolved oxygen concentration declines below the set point then the feed rate is reduced and when the dissolved oxygen concentration rises above the set point the feed rate may be increased.

These techniques are particularly important in the growth-stage of a secondary metabolite mycelial fermentation prior to product production when the highest growth rate commensurate with the oxygen transfer rate of the fermenter is required.