H sat H inlet

model containing a description of flow patterns within the drum headspace (determined on the basis of residence time distribution studies)

estimate of "ka"

Fig. 20.2. Experimental set-up used by Hardin et al. (2002) for investigating mass transfer between the bead and the headspace in a 200-L rotating drum bioreactor

The term for overall water transfer from the bed to the dead volume in the head-space (Rw, s-1) would then be written as:

where cbed is the dimensionless saturation water vapor concentration at the temperature of the bran.

The results of Hardin et al. (2002) are summarized in Table 20.1. Note that the experimentally determined values of "ka" vary over 4-fold, with the rotational rate of the drum having a strong influence. For example, for experiments done at the same aeration rate of 155 L min-1 and the same percentage filling of 30%, the value of "ka" varied from 0.0472 s-1 at 0.9 rpm to 0.2024 s-1 at 9 rpm.

In order to use these results in a model of a drum, that is, to calculate an appropriate value for "ka" for any particular combination of operating conditions, it is necessary to combine the various operating conditions, namely the % filling, the aeration rate, and the rotational rate, into a single variable. This is done by defining an effective Peclet number (Peef), given by Hardin et al. (2002) as:

Table 20.1 Experimentally determined values of the bed-to-headspace water mass transfer coefficient, as determined by Hardin et al. (2002) for a variety of operating conditions. Adapted from Hardin et al. (2002) with kind permission of Elsevier

Rotational speed

Air Rate





(L min-1)

Filling (%)



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