Bubble columns and air-lift reactors are not mechanically agitated and, therefore, rely on the passage of air to both mix and aerate.
(i) Bubble columns
The flow pattern of bubbles through a bubble column reactor is dependent on the gas superficial velocity (cm second ~1). At gas velocities of below 1-4 cm second the bubbles will rise uniformly through the medium (Van't Riet and Tramper, 1991) and the only mixing will be that created in the bubble wake. This type of flow is referrred 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 air flow is such that it blows the medium out of the vessel. This requires superficial gas velocities approaching 1 m second^1 which are not attainable on commercial scales (Van't Riet and Tramper, 1991).
The volumetric mass transfer coefficient (KLa) in a bubble column is essentially dependent on the superficial gas velocity. Heijnen and Van't Riet (1984) reviewed the subject and demonstrated that the precise mathematical relationship between KLa and superficial gas velocity is dependent on the coalescent properties of the medium, the type of flow and the bubble size. Unfortunately these characteristics are rarely known for a commercial process which makes the ap-
plication of these equations problematical. However Van't Riet and Tramper (1991) claimed that 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 Vf is the superficial air velocity corrected foj local pressure.
However, viscosity has an overwhelming influence on KLa in a bubble column which Deckwer el al. (1982) expressed as:
where tt 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. Van't Riet and Tramper (1991) suggested that the upper viscosity limit for a bubble column was 100 X 10 3 N s m 2 at which point the K, a would have decreased 50 fold compared with a reactor batched with water.
(ii) Air-lift reactors
The structure of air-lift reactors is discussed in Chapter 7. The 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. The reactor consists of a vertical loop of two connected compartments, the riser and down-comer. Air is introduced into the base of the riser and escapes at the top. The degassed liquid is more dense than the gassed liquid in the riser and flows down the downcomer. Thus, a circulatory pattern is established in the vessel — gassed liquid going up in the riser and degassed liquid coming down the downcomer.
For 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 (Chen, 1990). However, it should be remembered that the circulation in an air-lift results in the bubbles being in contact with the liquid for a shorter time than in a corresponding bubble column. 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 (F^)0 7. The advantage of the air-lift lies in the circulation achieved, but this is at the cost of a lower K, a value.
As for a bubble column flooding will not occur within the normal operating superficial air velocities and should not be a problem on a large scale.
The degree of agitation has been demonstrated to have a profound effect on the oxygen-transfer efficiency of an agitated fermenter. Banks (1977) claimed that agitation assisted oxygen transfer in the following ways:
(i) Agitation increases the area available for oxygen 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 (see Chapter 8). The assessment of electrical consumption is suitable only for use with large-scale vessels.
THE RELATIONSHIP BETWEEN KLa AND POWER CONSUMPTION
A large number of empirical relationships have been developed between KLa, power consumption and superficial air velocity which take the form of:
where P is the power absorption in an aerated system
V is the liquid volume in the vessel Vs is the superficial air velocity k, x and y are empirical factors specific to the system under investigation. Cooper et al. (1944) measured 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 Kta value was claimed to be almost directly proportional to the gassed power consumption per unit volume. However, Bartholomew (1960) demonstrated that the relationship depended on the size of the vessel and the exponent on the term Pg/V varied with scale as follows:
Value of exponent on Pg/V
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