where D is the drum diameter (m), L is the drum length (m), S is the fraction of the critical speed (see Sect. 8.4.1), F is the inlet air flow rate (kg-dry-air s-1), and Hin is the inlet air humidity (kg-vapor kg-dry-air-1).

For plug flow of the air, potentially Eq. (20.6) can be used to estimate hbg. On the other hand, the work of Hardin et al. (2002) gives an insight into what is necessary in order to determine bed-to-headspace transfer coefficients in a rotating drum bioreactor in which neither the well-mixed nor plug-flow regimes occur. They monitored the outlet humidity of a 200-L drum with a bed of moist wheat bran under various different operating conditions (Fig. 20.2). They then used a mathematical model of the flow patterns (which had been developed on the basis of residence time distribution studies to describe the flow pattern shown in Fig. 8.15) in order deduce the value of the transfer coefficient, "ka", which is a lumped overall transfer coefficient (i.e., the area term was not determined separately). Note that they defined "ka" in such a way as to have units of s-1, since it was used in combination with dimensionless concentrations of water vapor in the headspace air. The dimensionless concentration of water vapor was calculated from the humidity (H, kg-H2O kg-dry-air-1) as:

H sat H inlet

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