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This correlation reveals that a typical value of k, is 0.01 cm/s for FBBR conditions, which some believe is sufficiently high to allow external mass transfer resistance to be ignored.21 Consequently, this is frequently done to simplify computations.1 M|L' The most exact approach, however, would be to consider both internal and external mass transfer resistance as was done in Chapter 15.

The effectiveness factor approach is the most common method of handling simultaneous reaction and transport in the biofilm, although all of the approaches in Chapter 15 have been used. While models12 are available that use effectiveness factors for intrinsic Monod kinetics through the use of relationships like that in Figure 15.9, more assume the limiting case of either zero order (Ssh » Ks) or first order (Ssi, < Ks) intrinsic kinetics. For zero order kinetics in the absence of external mass transfer resistance, the effectiveness factor is defined as the biofilm volume containing substrate divided by the total biofilm volume."1 Consequently, when the biopar-ticle is fully penetrated with substrate, the effectiveness factor has a value of 1.0. For first order kinetics in the absence of external mass transfer resistance, the effectiveness factor has been defined as the substrate flux into the spherical bioparticle divided by the intrinsic rate when all of the biofilm is surrounded by substrate at the bulk substrate concentration."'

For both first and zero order kinetics in the absence of external mass transfer resistance, the effectiveness factor can be correlated with an appropriate Thiele mod ulus. Furthermore, the correlations can be reduced to single curves for each type of kinetics by using an appropriate characteristic biofilm thickness, Lu, which is defined biofilm volume biorilm exterior surface area d,: - $ 6dh

For zero order kinetics, the zero order effectiveness factor, can be correlated with a modified zero order Thiele modulus, <}>/,„, defined as:2K

The correlation is shown in Figure 18.11, and is described well by the following empirical equation:2*

Figure 18.11 Relationship between the bioparticle zero-order effectiveness factor, t),.z, and the modified zero-order Theile modulus, <t>Zm. (From W. K. Shieh and J. D. Keenan, Fluidized bed biofilm reactor for wastewater treatment. Advances in Biochemical Engineering!Biotechnology 33:131-169, 1986. Copyright © Springer-Verlag New York, Inc.; reprinted with permission.)

Figure 18.11 Relationship between the bioparticle zero-order effectiveness factor, t),.z, and the modified zero-order Theile modulus, <t>Zm. (From W. K. Shieh and J. D. Keenan, Fluidized bed biofilm reactor for wastewater treatment. Advances in Biochemical Engineering!Biotechnology 33:131-169, 1986. Copyright © Springer-Verlag New York, Inc.; reprinted with permission.)

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