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below 0.55 has been recommended to prevent particle agglomeration (Andrews, 1988). Depending on bioparticle size and density, the liquid velocity will have to be adjusted to produce suitable bed porosity. Estimation of the solids holdup for expected operating conditions, along with required solids loading, is a requirement for sizing of the reactor.

The Richardson-Zaki correlation (Richardson and Zaki, 1954)

is well-accepted as a description of bed expansion in liquid-solid systems, and, with some modifications, is applicable to two-phase biofluidization (Myška and Švec, 1994). Bed expansion behavior in three-phase fluidization is more complex. This is illustrated by the observed initial contraction of some beds of small or relatively low density particles (especially pertinent to biofluidization) upon the addition of gas flow (Davison, 1989; Fan, 1989; Tang and Fan, 1989; Roustan et al., 1993). Fan (1989) provides an extensive listing of expansion correlations for three-phase fluidization and describes various approaches to predicting bed expansion in three-phase fluidization. The presence of biofilm, however, may cause these correlations to be in error, and additional work is needed in this area.

Gas Holdup. Determination and prediction of gas holdup is important in biofluidization because it provides an estimate of bed expansion and freeboard requirements and void space in the reactor, which is unavailable for bioreaction (Charles and Wilson, 1994; Bajpai et al., 1990). Estimates of gas holdup and expected bubble size can also assist in predicting oxygen transfer, a critical factor in aerobic bioprocesses, by providing an estimate of interfacial area for gas-liquid mass transport. Reported values for gas holdup range from 0.01 to as high as 0.45; values of 0.02 to 0.20 are typical (Davison, 1989; Tang and Fan, 1989; Bly and Worden, 1990; Tang and Fan, 1990; Potthoff and Bohnet, 1993; Sajc et al., 1995). Phase mixing is also affected by gas holdup, as described in Sec. 5.5.

Many factors affect gas holdup in three-phase fluidized systems, including bead size and density, liquid physical properties, temperature, sparger type, and fluid superficial velocities (Bly and Worden, 1990). System parameters such as reactor and gas distributor design can have

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such an impact on the bubble and liquid flow behavior that not only are phase holdups affected, but different bubble flow regimes can be established in two systems operated under the same conditions (Bly and Worden, 1990; Tang and Fan, 1990). Results from different bioreactors must be compared with caution; however, some generalities can be made.

Overall gas holdup increases with gas velocity in the dispersed bubble regime for both low and high density particle systems (Davison, 1989; Tang and Fan, 1989; Bly and Worden, 1990; Nore et al., 1992; Potthoff and Bohnet, 1993). As gas velocity increases and the system enters the coalesced and slugging regimes, the rate of increase in the overall gas holdup decreases (Bly and Worden, 1990).

The type and loading of solid particles can affect gas holdup, though the effect is somewhat unclear, undoubtedly because of system differences. Bly and Worden (1990) found that the addition of low density particles to two-phase systems generally increased gas holdups, while the addition of high density particles decreased gas holdups. This concurs with the observation of Davison (1989) that gas holdup decreased at the top of a three-phase low density particle system in the region where it became a two-phase system (above the top of the bed). Tang and Fan (1989, 1990), also working with low density particles, however, found that gas holdups decreased with the addition of the solid phase and that as the terminal velocity of the particles increased from 0.026 m/s to 0.055 m/s, the overall gas holdup decreased further. This was attributed to the higher tendency for bubble coalescence in beds of larger terminal velocity particles. Potthoff and Bohnet (1993) found no significant influence of low density solids loading on gas holdup. Karamanev et al. (1992), working with low density polyurethane particles, found that addition of solids decreased gas holdup and that the effect was greater in a draft tube fluidized bed bioreactor.

In a study of the effect of electrolyte concentration on gas holdup, Bly and Worden (1990) found a strong effect. A salt solution resulted in twice the gas holdup that distilled water did under otherwise identical operating conditions, because the salt solution suppressed bubble coalescence. Investigation of this phenomenon is important in biofluidization, because biological media commonly have high electrolyte concentrations.

Axial variation of gas holdup depends on operating conditions and the particular bioprocess occurring in the reactor. For a gas-producing fermentation, gas holdup increased from 0.0 to almost 0.5 with axial

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position as gas was produced until a point near the top of the bed, where the coalesced gas freely escaped as it rose into the solid-free region (Davison, 1989). In a study of three-phase fluidization of low density particles without gas-generating biomass, Tang and Fan (1989) found that the axial gas holdup variation could be regarded as negligible.

5.5Phase Mixing in a Three-Phase Reactor

The degree of mixing of the phases within a three-phase fluidized bed bioreactor is important to reactor performance. Depending on the degree of mixing, individual bioparticles may experience different substrate and product concentrations, thereby influencing the overall reactor kinetics. In mixed culture systems, such as are used in wastewater treatment, the degree of mixing may affect the population dynamics and species selection within the reactor (Gommers et al., 1986; Yang, 1987).

Liquid Mixing. It has generally been found that liquid mixing in a three-phase fluidized bed of low density particles is similar to that of beds of high density particles (Gommers et al., 1986) and is strongly dependent on the regime in which the fluidized bed is operating (Fan, 1989). Axial dispersion models are generally used to describe the degree of liquid mixing, and the presence of a gas phase has been found to have a strong effect. A near absence of axial liquid mixing (dispersed bubble regime), near complete mixing, or a mixing state somewhere between these two may occur, depending on reactor conditions (Fan, 1989). Reactor diameter has an influence on mixing, with increased influence of the gas phase on liquid mixing as the diameter increased (Gommers et al., 1986).

Of interest to biofluidization is the effect of low gas flow rates, such as those found in gas-producing bioprocesses, on liquid mixing. Davison (1989) estimated the axial dispersion in both inert and fermenting threephase fluidized bed bioreactors and found that gas flow rates comparable to that produced by the fermenting organisms increased axial dispersion. Gommers et al. (1986) obtained similar results previously, though it was noted in this study that very small (1–2 mm) bubbles produced in some bioprocesses may not have as great an effect on hydrodynamics as do larger, sparged bubbles, though flow rates may be comparable. Schoutens et al. (1986a, 1986b, 1986c) found similarly small bubbles with little effect on liquid mixing in their study of a fermenting three-phase fluidized bed bioreactor. In the design of a three-phase fluidized bed bioreactor, the extent of biogas production and whether the small biogas bubbles coalesce into larger bubbles should be considered for their effect on phase mixing.

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Solids Mixing and Stratification. Bioparticle size and density has been demonstrated to strongly influence solids mixing in three-phase fluidized bed bioreactors (Bly and Worden, 1990). Small, light particles were more readily drawn into bubble wakes than were large, heavy particles and are, therefore, subject to greater mixing (Tsuchiya et al., 1992). Increased gas velocity has been shown to increase axial solids dispersion; increased liquid circulation velocity, as when the static liquid to static solid bed height ratio is reduced, decreased axial solids dispersion (Tang and Fan, 1989). Fluidization regime is also important, with the larger bubbles of the coalesced and slugging regimes producing increased solids dispersion.

The above is true for nonbiological fluidization as well as for biofluidization. An important difference is the changing nature of solids mixing and stratification in biofluidization as a result of biofilm formation, as was discussed in Sec. 5.3.

5.6Mass Transfer

Mass transfer considerations are critical in any bioprocess. In typical, aerobic, suspended cell fermentations, the major concern is the oxygen transfer rate, determined by the overall mass transfer coefficient, kla, and the driving force. In three-phase biofluidization, in which the cells are immobilized as a biofilm or within carrier particles, the situation is further complicated by possible intraparticle diffusion limitations. Numerous recent studies have addressed these issues.

Gas-Liquid Mass Transfer. Gas-liquid mass transfer within the three-phase fluidized bed bioreactor is dependent on the interfacial area available for mass transfer, a; the gas-liquid mass transfer coefficient, kl; and the driving force that results from the concentration difference between the bulk liquid and the bulk gas. The latter can be easily controlled by varying the inlet gas concentration. Because estimations of the interfacial area available for mass transfer depends on somewhat challenging measurements of bubble size and bubble size distribution, much of the research on increasing mass transfer rates has concentrated on increasing the overall mass transfer coefficient, kla, though several studies look at the influence of various process conditions on the individual parameters. Typical values of kla reported in the literature are listed in Table 19.

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Table 19. Typical Values of kla as Reported in the Literature

Fluid velocities can have a significant effect on k la. Increased gas velocity within the dispersed bubble regime has been found by many investigators to substantially increase k la (Tang and Fan, 1990; Karamanev et al., 1992; Nore et al., 1992; Roustan et al., 1993). Increased liquid velocity also appears to increase k la (Kang et al., 1991); Tang and Fan (1990) determined that the increase in k la was due to an increase in kl.

Particle properties and solids loading have also been shown to have a significant effect on kla. Decreased particle density has been found to increase kla (Nore et al., 1992; Tang and Fan, 1990), and increased particle size also increased k la (Kang et al., 1991); the latter appears to be caused by an effect on k l , because bubble size and, therefore, interfacial area, was not affected (Sun and Furusaki, 1988).

The addition of high density particles, such as those used in traditional three-phase fluidization applications, decreased k la (Kang et al., 1991; Roustan et al., 1993); increased bubble coalescence was suggested as the cause. Adding large, low density particles, of the type often used in three-phase biofluidization, was found in one study to increase k la at low solids loadings (Karamanev et al., 1992), but to decrease k la as solids holdup increased. Other investigators report a continuous decrease in k la with increased solids concentration (Sun and Furusaki, 1988; Tang and Fan, 1990); however, Roustan et al. (1993) reported little effect of low density solids holdup on k la. Contrary to studies of three-phase fluidized

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bed reactors containing rigid solids, the loading of the soft solids (polyurethane) in a draft tube three-phase fluidized bed bioreactor or in a conventional three-phase fluidized bed bioreactor did not strongly affect the volumetric mass transfer coefficient (Karamanev et al., 1992). Another study suggested that the presence of low density particles (polyurethane) promoted bubble coalescence, thereby decreased interfacial area and, hence, the volumetric mass transfer coefficient (Kobayashi et al., 1990).

Draft tube fluidized bed bioreactors have been very successful at increasing mass transfer rates, with increases in kla on the order of 1.5 to 3 times higher than fluidized beds without draft tubes (Karamanev et al., 1992). It has been suggested that the addition of the draft tube increases the bubble rise velocity through the increased liquid velocity within the draft tube, thereby decreasing the likelihood of bubble coalescence at the base of the reactor. The decrease in time for mass transfer appears to be offset by the larger available interfacial area for mass transfer; furthermore, many of the resulting small bubbles are entrained in the annular flow, providing additional retention time for mass transfer (Karamanev et al., 1992).

The use of floating bubble breakers has been used to increase the volumetric mass transfer coefficient in a three-phase fluidized bed of glass beads (Kang et al., 1991); perhaps a similar strategy would prove effective for a bed of low density beads. Static mixers have been shown to increase kla for otherwise constant process conditions by increasing the gas holdup and, therefore, the interfacial area (Potthoff and Bohnet, 1993).

Paz et al., (1993) have modified the density of calcium alginate beads by adding α-alumina to the gel in an attempt to produce beads that were more effective at breaking up bubbles in a three-phase fluidized bed bioreactor than were normal density calcium alginate beads, thereby causing an increase in interfacial area. Production of acetic acid by alginate plus alumina entrapped Acetobacter sp. cells was more than 2.5 times that of cells trapped only in alginate; the measured volumetric mass transfer coefficient was over three times greater.

Understanding the effect of reactor diameter on the volumetric mass transfer coefficient is critical to successful scale up. In studies of a threephase fluidized bed bioreactor using soft polyurethane particles, Karamanev et al. (1992) found that for a classical fluidized bed bioreactor, kla could either increase or decrease with a change in reactor diameter, depending on solids holdup, but for a draft tube fluidized bed bioreactor, kla always increased with increased reactor diameter.

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Tang and Fan (1990) recommended basing volumetric mass transfer coefficient determinations on the entire axial concentration profile, thereby avoiding errors caused by end effects. Kang et al. (1991) further demonstrated the applicability of this method, successfully adopting the axial dispersion model for determination of the volumetric oxygen transfer coefficient in a three-phase fluidized bed of glass beads plus floating bubble breakers. Perhaps some of the discrepancies and contradictions seen in the various studies cited above could be explained by applying this approach to the various experimental systems.

Intraparticle Mass Transfer. One way biofilm growth alters bioreactor performance is by changing the effectiveness factor, defined as the actual substrate conversion divided by the maximum possible conversion in the volume occupied by the particle without mass transfer limitation. An optimal biofilm thickness exists for a given particle, above or below which the particle effectiveness factor and reactor productivity decrease. As the particle size increases, the maximum effectiveness factor possible decreases (Andrews and Przezdziecki, 1986). If sufficient kinetic and physical data are available, the optimal biofilm thickness for optimal effectiveness can be determined through various models for a given particle size (Andrews, 1988; Ruggeri et al., 1994), and biofilm erosion can be controlled to maintain this thickness. The determination of the effectiveness factor for various sized particles with changing biofilm thickness is well-described in the literature (Fan, 1989; Andrews, 1988)

Use of bioflocs rather than supported film particles will maximize the effectiveness factor for a given particle, but uneven growth of flocs can cause severe stratification in the bed. If stratification can be overcome by methods such as the use of a tapered bed to control porosity; the removal, breaking up, and recycle of biomass at the bottom of the bed; or, ideally, the use of microbial strains or species that will stop growing at a desirable floc size, such as a Zymomonas mobilis strain that stops growing at one millimeter in diameter (Scott, 1983), the use of bioflocs rather than support particles can improve reactor productivity.

5.7Modeling

The complexity of the three-phase fluidized bed bioreactor is gradually coming under control as more sophisticated models become available. The chief need is for a model that integrates the microbial kinetics with the

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mental validation of their simulation results, and all of these modeled the phenol degradation process (Worden and Donaldson, 1987; Wisecarver and Fan, 1989). Development of integrated models for other biofluidization applications would be beneficial to future industrial developments.

Few models include the effects of in situ gas formation on the fluidization properties of the reactors; this improvement, along with improvements in other areas, such as inclusion of improved structured models of microbial kinetics or inclusion of maintenance energy requirements or the effects of suspended cells on the reaction rate, might produce more accurate models, though it is unclear at this point whether the increased complexity would be justified.

5.8Scale Up

As mentioned previously, the design of a three-phase fluidized bed bioreactor is complex, even more so than the design of a nonbiological three-phase fluidized bed reactor. Scale-up to commercial size is relatively common for wastewater treatment, but because of the increased constraints in biosynthetic processes, fewer examples exist for these. Several are listed in Table 21. As process development techniques continue to improve as a result of advances in the understanding of engineering fundamentals, computing power, and analytical methods, the daunting task of designing a commercial scale three-phase fluidized bed bioreactor becomes less intimidating and is expected to be undertaken more frequently in the future. The traditional, linear scale-up approach, proceeding from kinetic studies at lab scale, determining pilot plant specific correlations in small pilot plants, building a large demonstration unit based on pilot plant experiments then developing a model specific to the large demonstration unit, and, finally, building the commercial reactor and only then tuning the correlations for the final plant, is being replaced by a more interactive approach, in which a unified model that considers kinetics, thermodynamics, hydrodynamics, and hardware is reconciled to data at all scales. Not only does this allow more confidence in the final design, it also results in a better understanding of the process (Tarmy and Coulaloglou, 1992).

An example of the application of a unified model to the design of a three-phase, fluidized bed bioreactor is the scale down, scale up procedure. A model of the full scale reactor is developed, then is used to design

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a scaled-down laboratory reactor. The laboratory reactor is built and used for a series of experiments, the data from which are used to validate the model. If the model is validated, it can then be used as the basis for a full scale design. Schoutens et al. (1986a, 1986b, 1986c) used this approach to show that a fluidized bed reactor was the preferred design for the production of butanol and isopropanol by Clostridium spp. immobilized in calcium alginate beads (Schoutens et al., 1986a). The model, developed for a 50-65 m3 reactor, was shown to be accurate in predicting the results in 10-15 dm3 reactors, thereby confirming its reliability for large scale design, according to the authors (Schoutens et al., 1986c).

Table 21. Examples of Pilot and Large Scale Applications of Three-Phase Biofluidization to Fermentation Processes

Another, more traditional, approach to scale-up is application of similarity through dimensional analysis. One comparison of several such design criteria (biological, dynamic, and geometric) for biological fluidized bed reactors found that of the parameters tested, the sludge retention time (STR), the Peclet number, and the particle Reynolds number were most suitable for scale-up (Ozturk et al., 1994). Because of constraints on particle size and material, and fluid viscosity, it is difficult to maintain similarity in all relevant dynamic similarity criteria simultaneously. Conservative measures, such as using low estimates of such values as the overall mass transfer coefficient (Ryhiner et al., 1988), are suggested, in any case.