Bartholomew's vessels contained more than one impeller, whereas those of Cooper et al. contained only one. It is probable that the upper impellers would consume more power relative to their contribution to oxygen transfer than would the lowest impeller, thus affecting the value of the exponent term. Thus, it is important to appreciate that such relationships are scale-dependent when using them in scale-up calculations.
Many workers have produced similar correlations and these have been reviewed by Van't Riet (1983) and Winkler (1990). Van't Riet (1983) summarized the various correlations for coalescing air-water dispersion systems as falling within 20-40% of:
The common feature of these relationships is that the values of x and y are less than unity. Winkler (1990) pointed out that this means that increasing power input or air flow becomes progressively less efficient as the inputs rise. Thus, high oxygen-transfer rates are achieved at considerable expense.
From this discussion it is evident that the KLa of an aerated, agitated vessel is affected significantly by the consumption of power during stirring and, hence, the degree of agitation. Although it is not possible to derive a relationship between KLa and power consumption which is applicable to all situations it is possible to derive a relationship between the two which is operable within certain limits and should be a useful guide in practical design problems. If it is accepted that such relationships between power consumption and KLa are of some practical significance, it is of considerable importance to relate power consumption to operating variables which may affect it. Quantitative relationships between power consumption and operating variables may be useful in:
(i) Estimating the amount of power that an agita tion 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.
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