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Superficial Velocity, cm/sec

Figure 18.4 F.ffect of superficial velocity, v, carrier particle diameter, d,„ and carrier particle density, p,„ on the hed height of a lluidi/.ed bed. H,,,„ relative to the reference height of the carrier particles, H«,,. The carrier particles are covered with a biolilm with a thickness of KM) ptm and a dry density of 65 g/I.. (From W. K. Shieh and J D. Keenan. Fluidi/ed hed biolilm reactor for wastewater treatment Advance* in Biochemical Engineering!Biotechnology 33:131-169. 1986. Copyright t) Springer-Verlag New York, Inc.: reprinted with permission.)

= e v, in which v is the applied superficial velocity and n is a coefficient. The value of n can be correlated with the Galileo number or with the Reynolds number calculated on the basis of the terminal settling velocity. It typically takes on values between 2 and 5 for clean particles, with larger values being associated with smaller Galileo or Reynolds numbers, i.e., smaller particles. Several correlations are available.

Selection of the carrier particle for an FBBR is an important consideration because it has several influences, as we will see shortly. One important consideration is the stability of the bed to fluctuations in flow rate; that is, to fluctuations in superficial velocity. If the expanded bed height is overly sensitive to such fluctuations, small variations in flow rate might carry particles out in the effluent, thereby destroying the bed. Figure 18.4 illustrates how carrier particle size and density affect bed height over the range of superficial velocities commonly encountered.The curves were obtained by simulation and the conditions employed are indicated in the figure. Those curves illustrate that the stability of a bed increases with increasing carrier particle size and density. Common silica sand has a density of around 2.65 g/cm\ which provides reasonable stability over a broad range of superficial velocities.

### 18.2.2 Effects of Biomass on Fluidization

The growth of biofilm on the carrier particles changes their fluidization characteristics. This is due to three things. First, growth of the biofilm will change the size of the particle. Second, unless the carrier particle has a density equivalent to the wet density of the biofilm, growth of the biofilm will change the overall effective density of the particle. Third, the surface properties of the biofilm will differ from those of the clean particle, thereby changing the relationship between the drag coefficient, C,„ and the Reynolds number. In addition, growth of the biofilm may change the sphericity of the particle, but that effect has been found to be small/4 and is not considered further here. Rather, we assume spherical particles.

Terminal Settling Velocity. Examination of Eq. 18.2 shows that the terminal settling velocity of a particle depends on its diameter, its density, and the drag coefficient. Since all of those characteristics are altered by growth of a biofilm, it becomes clear that biofilm growth changes the terminal settling velocity. The influence of biofilm thickness, L„ on bioparticle diameter, d,„ is very straightforward:

The influence of the biofilm growth on the overall effective density of the bioparticle, p,„ depends on the density of the carrier particle, pp, and the wet density of the biofilm, plw, as well as the relative volumes occupied by the carrier particle and the biofilm.12 " w Since the volume of a sphere is proportional to its diameter cubed, the relationship is:'1"

The biofilm wet density is related to its dry density, pul, and the weight fraction moisture content of the biofilm, P':"'

The value of moisture content has been found to be approximately 0.93 over a broad range of biofilm thicknesses."' We saw earlier that the biofilm dry density depends on its thickness, and the biofilm wet density also varies with biofilm thickness. Thus, it is not surprising that a number of investigators have reported different values for the wet biofilm density." Nevertheless, a value of 1.1 g/cnv has been assumed to be typical of biomass.::

The influence of biofilm growth on the drag coefficient has been studied by several investigators.'" All correlate the drag coefficient to the terminal Reynolds number, Re,, using an expression of the type:

Figure 18.5"J shows three relationships and compares them to the relationship of Schiller et al. (referenced in 24) for clean spherical particles. The equations are given in Table 18.1. Two things are evident from the figure. First, the growth of a biofilm increases the drag coefficient relative to that of a clean particle with equivalent terminal Reynolds number, i.e., equivalent diameter and density. Second, the rela-

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