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Group of studies that showed that the aeration rate has a relatively small effect

Group of studies that showed that the aeration rate has a relatively small effect

where uP is the average particle velocity in the moving layer (m s-1), d is the particle diameter (m), and 8 is the diffusivity of water vapor in air (m2 s-1). The particle diameter can be measured experimentally and the diffusivity of water vapor in air can be obtained from a reference book, such as McCabe et al. (1985). In order to calculate the average particle velocity in the moving layer, it is necessary to know (see Fig. 20.3):

• N, the rotational speed (revolutions per second), determined by the operator;

• y the dynamic angle of repose of the solids (degrees), determined experimentally. This was 37° in the system of Hardin et al. (2002);

• D, the drum diameter (m), determined by the drum design;

• h, the maximum height of the bed (m), which will be a function of the fractional filling of the drum. It can be calculated according to geometric principles or simply measured experimentally.

Firstly, two secondary variables, K and 5 need to be calculated. K can be estimated from the following equation (Savage 1979):

Fig. 20.3. Detail of the drum in the tumbling flow regime, showing the nomenclature used in the calculations of the mobile layer thickness, "s". From Hardin et al. (2002) with kind permission of Elsevier mobile layer

Fig. 20.3. Detail of the drum in the tumbling flow regime, showing the nomenclature used in the calculations of the mobile layer thickness, "s". From Hardin et al. (2002) with kind permission of Elsevier where f is a dimensionless factor of porosity, equal to 0.8 for most materials. CV is a dimensionless constant associated with the bed viscosity, equal to 0.6 for most materials and g is gravitational acceleration (9.81 m s-2). Once K has been calculated, the thickness of the mobile layer of solids (s, m) can be calculated by solving the following equation, which is quadratic in s (Blumberg and Schlünder, 1996):

xN[D(h - s) - (h - s)2)- Ks2 5 + 2xNs(0.5D - h + s) = 0 . (20.15)

With both K and s it is possible to calculate the average particle velocity in the mobile layer. This is done using an equation of Blumberg and Schlünder (1996)

The effective Peclet number can now be calculated. Hardin et al. (2002) did this and plotted the experimentally-determined value of "ka" against the calculated value of Peef (Fig. 20.4). For their drum they obtained the relationship:

It would be necessary to undertake a broader study to investigate whether this correlation is generally valid for all rotating drum bioreactors. Such a study would need to involve a number of different rotating drum bioreactors of different length to diameter ratios and with different air inlet and outlet positions and designs. Further, as part of this study, it would be necessary to determine the particular air flow patterns within the headspace of each bioreactor. This is not a small task.

effective Peclet number (Peff)

Fig. 20.4. Experimental "ka" values plotted against the calculated value of the Peclet number (Hardin et al. 2002). The line of best fit is forced through the origin, giving Eq. (20.17). Adapted from Hardin et al. (2002) with kind permission of Elsevier effective Peclet number (Peff)

Fig. 20.4. Experimental "ka" values plotted against the calculated value of the Peclet number (Hardin et al. 2002). The line of best fit is forced through the origin, giving Eq. (20.17). Adapted from Hardin et al. (2002) with kind permission of Elsevier

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