Chapter 10
et al.
(1987) also applied the sulphite method to determine
in a stiired-tank reactor and found the
k}a =
where the influence of power input is much higher than indicated in table 10.4. Thus, application of the
sulphite method may result in a correlation that is not valid for normal fermentation media (even when these
are noncoalescing). The sulphite method is discussed further in Note 10.3.
In the experiments on which the present example is based, the power input was not measured directly, but
calculated from the measured stirring speed and the correlation in Eq. (6). This correlation is, however, not
generally valid, and it should be used only for preliminary calculations. Since determination of the power
input requires measurement of the torque on the impeller shaft inside the bioreactor (see Section 10.3.1), it
is convenient to use the stirring speed rather than the power input in empirical correlations for
10.1.4. Mass Transfer Correlations Based on Dimensionless Groups
There is a tradition in the chemical engineering literature to express correlations for various
transport coefficients in terms of dimensionless groups named after prominent members of the
engineering community. Unfortunately, these dimensionless groups have come to work as filters,
which tend to separate the treatment of these phenomena by chemical engineers from that done by
their colleagues active in the fields of biology or chemistry. (One could even argue that the
dimensionless groups to some extent separate the chemical engineers from their colleagues.)
Despite these drawbacks, there are several advantages to be gained from using dimensionless
groups. Most importantly, these groups show
in what way physical variables interact
in their effect
on the response variable. This is of great help in designing experiments for deriving empirical
correlations, and also for obtaining a qualitative understanding of how transport phenomena may be
influenced by operating conditions. A practical advantage is, furthermore, that dimensionless
equations can be used equally well with barrels, gallons, or liters, with a minimum risk of unit
conversion errors. Equations of the type given in Eq. (10.27), on the other hand, carry dimensions,
which are sometimes not easily realized or sufficiently clearly stated.
Dimensionless groups may be derived by two, principally different routes. If known, the governing
equation of the phenomenon of interest can relatively easily be transformed into a dimensionless
form. In the thus transformed equation dimensionless groups will appear as coefficients. Well-
known examples are e.g. the
Reynolds number
Froude number,
which appear in the
dimensionless form of the Navier-Stokes equation (see section 11.3.6).
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