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Figure 18.7 Effect of relative biofilm thickness, d^/d,,, and carrier particle density, p,„ on the terminal settling velocity of a bioparticle, v,h, relative to the terminal settling velocity of its carrier particle, v,t,. (From J. Myska and J. Svec, The distributive properties of a fluidized bed with biomass. Water Research 28:1653-1658, 1994. Copyright © Elsevier Science Ltd.; reprinted with permission.)

Figure 18.7 Effect of relative biofilm thickness, d^/d,,, and carrier particle density, p,„ on the terminal settling velocity of a bioparticle, v,h, relative to the terminal settling velocity of its carrier particle, v,t,. (From J. Myska and J. Svec, The distributive properties of a fluidized bed with biomass. Water Research 28:1653-1658, 1994. Copyright © Elsevier Science Ltd.; reprinted with permission.)

for a broad range of particle sizes and densities is that of Shieh and Chen," which was developed from the data of Mulcahy and LaMotta:'s n = 47.36 Ga 1,000 < Ga < 15,000 (18.13)

where Ga is the Galileo number, given by:

The approach above has been used to demonstrate through modeling the effect of biofilm thickness on the degree of expansion of an FBBR containing sand with a diameter of 0.4 mm as the carrier particle."" The results are shown in Figure 18.8 in which the expanded bed height has been normalized relative to HRp as computed with Eq. 18.4. There it can be seen that even thin biofilms have a strong effect on the height of a fluidized bed. Consequently, during design, careful consideration must

Figure 18.8 Effect of biofilm thickness. L„ on the height of a fluidized bed. H,„. relative to the reference height of the carrier particles, H,(|.. The following conditions were assumed: dr = 0.4 mm, p,, = 2.65 g/cm\ v = I cm/sec, p,„ = 65 g/L. P' = 0.93. (From W. K. Shieh and J. D. Keenan, Fluidized bed biotilm reactor for wastewater treatment. Ativances m Biochemical Engineering!Biotechnology 33:131 - 169. 1986. Copyright V Springer-Verlag New York. Inc.; reprinted with permission.)

Figure 18.8 Effect of biofilm thickness. L„ on the height of a fluidized bed. H,„. relative to the reference height of the carrier particles, H,(|.. The following conditions were assumed: dr = 0.4 mm, p,, = 2.65 g/cm\ v = I cm/sec, p,„ = 65 g/L. P' = 0.93. (From W. K. Shieh and J. D. Keenan, Fluidized bed biotilm reactor for wastewater treatment. Ativances m Biochemical Engineering!Biotechnology 33:131 - 169. 1986. Copyright V Springer-Verlag New York. Inc.; reprinted with permission.)

be given to the configuration of an FBBR to ensure that it is capable of containing the desired amount of media once a biofilm of the desired thickness has developed.

Solids Mixing. The movement of particles in a fluidized bed is a very complex subject that is incompletely understood.'" In fact, the circumstances and assumptions associated with an analysis of mixing strongly influence the conclusions reached. Nevertheless, it is important to understand the basic forces at work in a fluidized bed as biofilm grows.

Andrews' has presented a very thorough analysis of the factors influencing solids mixing. First, it must be recognized that there are two counteracting tendencies affecting particle movement. One is the tendency of fluidized particles to move randomly, which is a disordering tendency. The other is caused by the development of particles of different size due to biofilm growth. If the terminal settling velocities of the various particles are not all the same, the bed tends to stratify, with rapidly settling particles near the bottom and slowly settling ones near the top. This is an ordering tendency, but whether such a tendency is stable depends on the density of the carrier particles.

Bioparticles containing carrier particles of low density, similar to the wet density of the biofilm, tend to stratify because the density doesn't change significantly as the biofilm grows. Only the diameter changes. The same is true for bioparticles without carrier particles, such as UASB granules. In that case, larger particles have a higher settling velocity, causing them to move to the bottom of the bed, where they are exposed to more substrate, causing them to grow even larger. Conversely, smaller particles move to the top, where they are exposed to less substrate, which causes the biofilm to grow more slowly, or even decrease in size because of decay and surface shear. This leads to stratification of the bed, with the possible development of bioparticle sizes well in excess of the optimal, thereby increasing the quantity of inactive biomass in the bed. Under such a situation, biomass wastage should be done from the bottom of the bed.

Bioparticles containing carrier particles of high density, on the other hand, tend to form well mixed beds, although a degree of stratification can be induced. With high-density carrier particles, the settling velocity of the bioparticles decreases as the thickness of the biofilm increases. As a consequence, larger bioparticles tend to move to the top of the bed. Once there, however, they receive less substrate, which causes them to decrease in size, thereby allowing them to move downward into a region of higher substrate concentration. Bioparticles with thin biofilms, on the other hand, move toward the bottom of the bed, where they are exposed to high substrate concentrations, causing more rapid growth and an increase in size. The resulting situation is unstable, inducing motion within the bed, leading ultimately to a relatively uniform bioparticle size throughout the bed.

Control of bed height in an FBBR requires continual wastage of biomass. Otherwise, nonoptimal sized bioparticles develop and the bed height becomes very large.' Common practice is to waste biomass from the top of a bed containing high-density carrier particles. This induces stratification in the bed because the size of any individual bioparticle is continually changing, preventing the development of a steady-state biofilm. By continually wasting large bioparticles from the top and returning clean carrier particles, which then migrate to the bottom where they exposed to high substrate concentrations, the bed is maintained in a dynamic state. Consequently, stratification of such beds is a common occurrence.221 The above analysis is based on the assumption of a uniform carrier particle size. If there are significant differences in carrier particle size, the bed tends to stratify based on carrier particle size rather than bioparticle size.2 As a consequence, larger support particles tend to stay at the bottom where they accumulate biofilm beyond the optimum thickness, while smaller carrier particles migrate to the top from where they can be ineffectually cycled through the biomass wastage device. Consequently, it is important for FBBRs to have a uniform particle size.

18.2.3 Relationship Between Fluidization and Biomass Quantity

It is clear from the preceding that there is a complex relationship between the fluidization regime imposed on an FBBR and the quantity of biomass that may be present. Consequently, it is difficult to intuitively reason out the relationship. Luckily, however, it is a straightforward task to calculate the biofilm thickness that would be associated with a given fluidization regime, provided that sufficient substrate is sup-

plied to maintain that biofilm. If that thickness can be assumed to be representative of the average thickness that could be maintained in an FBBR with a given fluidi-zation regime, then the biomass concentration can be calculated.212!< ,n

An iterative approach must be used to calculate the biofilm thickness that can be maintained in an FBBR. Figure 18.9 summarizes an approach based on that of

Figure 18.9 Algorithm for computation of the biofilm thickness associated with a fluidized bed.

Shieh and Keenan.2S First, the characteristics of the FBBR must be established, including the desired superficial velocity, v, the FBBR cross-sectional area, A^., the desired fluidized bed height, Hlsb, the mass of carrier particles, Mp, their diameter, dp, and their density, pp. In addition, the properties of the fluid such as its density and viscosity must be established, as should the biofilm moisture content, P'. The computation begins by assuming a biofilm thickness. The assumed value is given the symbol LfJ to denote it as an assumed value. The biofilm dry density associated with the assumed biofilm thickness can be determined from information such as that in Figure 18.2 or an appropriate empirical equation, allowing the biofilm wet density to be calculated with Eq. 18.9. The bioparticle diameter can be calculated with Eq. 18.7, and that, in turn, can be used to calculate the bioparticle density with Eq. 18.8. The terminal settling velocity of the bioparticle can then be calculated with Eq. 18.2 (substituting db for dp and pb for pp) using a relationship for Cn such as one of the ones in Figure 18.5 as expressed with Eq. 18.10. The coefficient n in the Richardson-Zaki equation can then be estimated with Eq. 18.13, allowing the porosity of the fluidized bed to be calculated with Eq. 18.6. It can then be used to calculate the bed height. The calculated value is denoted as H„bc. The value of H,ilv is then compared to the desired bed height used to begin the computations. If they are equal, then the assumed biofilm thickness is correct and can be taken as the true thickness, L,. If Hubc > Hub, then the assumed biofilm thickness is too large and a new smaller value should be assumed for repeating the computations. Conversely, if HBbt < HHb, a larger biofilm thickness should be assumed. Finally, once the correct biofilm thickness has been found, the concentration of biomass per unit volume of fluidized bed, X1J( can be calculated with:

The procedure illustrated in Figure 18.9 can be used to investigate the effect of biofilm thickness on the biomass concentration in an FBBR. The result of such an exercise is shown in Figure 18.102S for sand as the carrier particle with a diameter of 0.4 mm. The biomass dry density was assumed to be constant with a value of 65 g/L, which is consistent with Figure 18.2 over the range of biofilm thicknesses considered. Examination of the figure reveals that a biofilm thickness of 100 pLm maximizes the concentration of biomass. Beyond that thickness, the increase in biomass associated with a thicker biofilm is offset by the reduction in the number of particles per unit volume due to increased bed expansion. If the objective was to maximize biomass concentration, then a biofilm thickness of 100 p.m should be chosen. It should be recognized, however, that such a strategy may not optimize overall FBBR performance. To do that, consideration must also be given to the effectiveness of the biofilm.2" We examine that question below.

It should also be recognized that Eq. 18.15 simply determines the biomass concentration and biofilm thickness that could be maintained by the hydrodynamic conditions in the bed. It does not tell whether they can be supported by the substrate loading on the bioreactor or whether a desired effluent substrate concentration can be achieved. One way to estimate whether a desired film thickness can be supported is to compare it to a steady-state biofilm. Because we wish to maintain the biofilm in a dynamic state, the biofilm thickness in the FBBR must be equal to or less than the steady-state biofilm thickness. To calculate the steady-state biofilm thickness,

100 L um

Figure 18.10 Effect of biofilm thickness, L,, on the biomass concentration, X,„ in an FBBR. The following conditions were assumed: dp = 0.4 mm, pp, = 2.65 g/cm\ v = 1 cm/sec. p„, = 65 g/L, P' = 0.93. (From W. K. Shieh and J. D. Keenan, Fluidized bed biofilm reactor for wastewater treatment. Advances m Biochemical Engineering/Biotechnology 33:131-169, 1986. Copyright © Springer-Verlag New York, Inc.; reprinted with permission.)

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