## Sizing A Fluidized Bed Biological Reactor

The sizing of an FBBR proceeds in a logical and straight forward manner, utilizing the information presented earlier in this chapter. As with all other biological processes, the parameters in the model must be specified, as must the influent flow rate and concentration, and the desired substrate removal across the system. Shieh and Keenan"1 have presented procedures for estimating the needed parameters. The sizing of the FBBR entails choosing a porosity, the carrier particle, the optimal biofilm thickness, the superficial velocity and the associated recirculation and bioreactor cross-section, and the bed height."

Andrews2 advocates using the smallest porosity that prevents the particles from agglomerating or having a collision frequency that would cause excessive shear. He states that a porosity of 0.60 is a reasonable compromise for the minimum porosity in the fluidized bed, which would be at the base. If the porosity is fixed, the next decision is to select the nature of the carrier particles. This is an important decision because everything else follows from it. We saw in Figure 18.4 that carrier particle size and density have an important impact on the stability of the bed. Light, small particles form a bed that is susceptible to large fluctuations in expanded bed height by small variations in superficial velocity. Sand (p,, = 2.65) with a particle diameter of around 0.5-0.6 mm is commonly used because it is readily available and offers good stability.

Having chosen the porosity and the carrier particle, it is now possible to choose the biofilm thickness that maximizes the average volumetric reaction rate in the system, which is equivalent to the product of the effectiveness factor times the biomass concentration. Using the average substrate concentration across the tower, the effectiveness factor can be calculated as a function of biofilm thickness using the characteristic biofilm thickness, L,,, given by Eq. 18.18 and the appropriate modified Thiele modulus. If it is necessary to consider external mass transfer resistance in determining the effectiveness factor, then the superficial velocity associated with each biofilm thickness has to be computed for use in the appropriate mass transfer coefficient correlation. The biomass concentration can be calculated with Eq. 18.23, which was derived by substituting Eq. 18.12 into Eq. 18.15:

It should be recalled that the dry density of the biofilm is a function of its thickness, as shown in Figure 18.2. Consequently, an appropriate correlation should be used with Eq. 18.23. The optimal biofilm thickness is obtained by plotting the product of the effectiveness factor times X„ as a function of the biofilm thickness and selecting the value that maximizes the product.

Once the optimum biofilm thickness has been chosen, the superficial velocity required to achieve the desired porosity can be calculated with Eq. 18.6. The terminal settling velocity of the bioparticle can be calculated with Eq. 18.2 after replacement of pp with pb and dp with d,„ The value of the coefficient n can be calculated with Eqs. 18.13 and 18.14. At this point, a check should be made to ensure that the required superficial velocity does not exceed the terminal settling velocity of the clean carrier particle or any bioparticle desired in the bioreactor. If it does, and there is no error in the computations, then the chosen carrier particle is not feasible for the desired biofilm thickness and another must be selected.

Having selected the superficial velocity, it is now possible to determine the required cross-sectional area and associated height for the FBBR. The superficial velocity in an FBBR is equivalent to the total hydraulic loading in a packcd tower, which was given by Eq. 16.8. Thus:

Since the superficial velocity is known, can be calculated after the recirculation ratio, a, has been chosen. Several factors go into the selection of a.:K When an aerobic two-phase FBBR is being used, oxygen is provided by dissolving it in the recirculation stream. When high-purity oxygen is used for the supply, approximately 60 mg/L of oxygen can be dissolved in wastewater and used in the FBBR with less than 1% loss.'" Thus, the amount of recirculation required can be calculated from a mass balance on chemical oxygen demand (COD) across the FBBR. Recirculation can also be provided to maintain a constant superficial velocity across the FBBR when the influent flow is variable. Often, however, it is best to set the influent equal to the highest expected flow rate across the system and to add to it the amount of recirculation required to transfer the needed oxygen, and to use those values in Eq. 18.24 to calculate the cross-sectional area.

Finally, after selection of a and A^, the tower height, H,«,, can be calculated. This requires use of the appropriate reactor flow submodel as described in Section 18.3.3. If the recirculation flow is small, then a model for plug-flow or plug-flow with dispersion would be appropriate. Alternatively, a tanks-in-serics model could be used as well. On the other hand, if the recirculation rate is high, it might be possible to treat the entire bioreactor as a CSTR. In addition, if the bed is likely to be stratified with a variety of bioparticle sizes, that expectation can be incorporated into the reactor flow submodel. The computational procedure involved depends on the type of model employed. The goal, however, is to determine the residence time or expanded bed height required to achieve the required effluent substrate concentration. Once H„i, is known, then the mass of carrier particles, Mn, can be calculated with Eq. 18.12.

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