Fluidized-bed bioreactors - Biotechnology Progress (ACS Publications)

Biotechnol. frog. 1995, 1 1, 479-497

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REVIEW Fluidized-Bed Bioreactors? Francesc Gbdia* and Carles Sola Unitat d’Enginyeria Quimica, Universitat Autbnoma de Barcelona, Bellaterra, 08193 Barcelona, Spain

Fluidized-bed reactors present a number of advantages that make them a n attractive alternative in processes involving biocatalysts. However, fluidized-bed bioreactors are also realtively complex, basically for two reasons. First, their use requires the biocatalyst, commonly cells or enzymes, to be immobilized into or onto a solid support. Second, the hydrodynamic characterization is difficult, especially in those systems where three phases (gas-liquid-solid) are involved. The mathematical model of a fluidized-bed bioreactor needs to take into account those hydrodynamic aspects that will determine the flux model in the reactor. Moreover, the description of other aspects is also required: the mechanisms of transport between the different phases, the kinetic equations for the phenomena taking place in the biocatalytic particles, such as cell growth, product formation, substrate consumption, enzyme deactivation, and the mass balance equations in the reactor. In addition to these aspects, the application of fluidized-bed bioreactors to different kind of processes is also discussed. The potential of this type of bioreactor is also emphasized from the point of view of the different number of possible modifications in the design both of the bioreactor and the biocatalyst particles, in order to enhance its operation.

Contents 1. Introduction 2. Basic Hydrodynamic Aspects of a

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Fluidized-BedBioreactor 3. Introducing Changes in Biocatalyst

484 Particles and Bioreactor Configuration To Modify the Fluidized-Bed Hydrodynamics and Its Operation 4. Developing a Model for a 487 Fluidized-BedBioreactor Reaction and Diffusion within the 487 Biocatalyst Particles Flux Model in the Bioreactor 489 Mass Balance Equations 489 Transport Phenomena between 490 Phases 5. Applications of Fluidized-Bed 492 Bioreactors 6. Conclusions 492 ~~

1. Introduction Fluidized-bed bioreactors have received sustained attention due to a number of advantages associated to their use. However, their full implementation at the production scale has been quite limited up to now, except for biological wastewater treatment, very probably because of the complexity associated to their operation. In this paper, a number of important issues for the characterization, design, and operation of fluidized-bed bioreactors are discussed, and a scope of their application to various +

Dedicated to Prof. J. Klein on the occasion of his 60th birthday.

kind of processes is given. However, the applications in the field of wastewater treatment have not been included. These reactors have been widely discussed as part of an exellent series of papers on fluidized-bed bioreactors (Andrews, 1982;Andrews and Przezdziecki, 1986;Andrews, 1988) and also by Cooper and Atkinson (1981). The fundamentals of the fluidization phenomena are very comprehensively covered in the chemical engineering literature (Davidson and Harrison, 1971; Kunii and Levenspiel, 1977). A recent book deserves special mention as well due to the effort made in the classification and exhaustive analysis of the many different types of fluidized-bed reactors, from either their fundamentals or applications (Fan, 1989). Most of the fluidized-bed reactors developed for biological processes involving cells as biocatalysts include three phases: solid, liquid, and gas. A classification of the basic types of fluidized-bed bioreactors, according to Muroyama and Fan (19851,is given in Figure 1. This work will focus mainly on the more extensively used configuration, the cocurrent up-flow reactor, with liquid as the continuous phase, and other more unusual configurations, like the inverse three-phase fluidized-bed or the gas-solid fluidized-bed, will not be adressed directly. The solid phase consists of immobilized cell particles. Gas is present either because of the aeration requirements of the cells or as a product of their metabolism. In some cases, due to the low reaction rates, high liquid residence times are needed for the completion of the reaction, and therefore, the drag force created by the low liquid flow rate in a single-pass reactor is not enough to promote fluidization of the solid particles. In other words, the superficial liquid velocity is much lower than the settling velocity of the solid particles. Usually, fluidization is obtained either by external liquid recirculation or by the gas loaded or produced in the reactor. Fluidization at

8756-7938/95/3011-0479$09.00/00 1995 American Chemical Society and American Institute of Chemical Engineers

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Francesc G-bdia, a Professor of Chemical Engineering at the Universitat Autbnoma de Barcelona, has devoted an important part of his research activity since 1982 to the use of immobilized cells systems. Research subjects in this area focus on the design and operation of packed-bed and fluidized-bed continuous bioreactors and the characterization and modification of the immobilized cells particles in order to enhance cell activity and bioreactor performance.

Carles Sola, a Professor of Chemical Engineering at the Universitat Autijnoma de Barcelona, is currently the Provost of the University. Since 1977, he has focused his research on various aspects of Biochemical engineering: enzymatic reaction engineering; fermentation technology; immobilized biocatalysts; mathematical modelization; bioprocess engineering; and design, operation, monitoring, and control of bioreactors.

relatively low liquid flow rates is also favored in tapered fluidized-bed configurations (Scott et al., 1978),where the liquid superficial velocity at the bottom of the reactor is higher due to the reduced cross-sectional area. In the case of immobilized enzymes, the usual situation is a twophase system, involving solid and liquid. As already mentioned, an intrinsic characteristic is that fluidized-bed bioreactors necessarily use immobilized biocatalysts. A differentiation between three-phase fluidized-bed and the so called air-lift bioreactors could be made on the basis that the latter have a physical internal division in two sections, one aerated and one not aerated, by means of a draft tube, and that their operation does not require the use of immobilized cells specifically. Indeed, they are often used as a free-cell culture system in which good mixing is provided by the aeration system instead of mechanical agitation. Air-lift bioreactors have been the object of relevant specific analysis (Chisti, 1989; Siege1 and Robinson, 1992) and will not be discussed here, although they can be included within a more generalized concept of fluidized-beds, under the denomination of draft-tube fluidized-beds (Fan, 1989). Basically, the particles used in fluidized-bed bioreactors can be of three different types: (a) inert cores on

which a biofilm is created by cells attachment or, in the case of enzymes, by adsorption or covalent binding immobilization; (b) porous particles in which the biocatalysts are entrapped; (c) cell agregates obtained by selfimmobilization, due to the ability of some cell strains to form flocs, pellets, or agregates. In comparison to conventional mechanically stirred bioreactors, fluidized-bed bioreactors provide a much lower attrition of the solid particles, and almost any kind of immobilized biocatalysts preparations can be used without physical disruption. Biocatalyst concentration can be significatively higher because of immobilization, and typical wash-out limitations found in the case of free cells are overcome. Moreover, depending on the operational conditions, liquid flow in the fluidized-bed bioreactors can approach plug flow, this being a kinetic advantage with respect to completely mixed systems for reactions presenting product inhibition. In comparison to packed-bed reactors, fluidized-bed bioreactors can be operated with smaller size particles, without the drawbacks of clogging, high liquid pressure drop, creation of preferential flow paths, or particle compression due to bed weight. Moreover, the smaller particle size minimizes the internal diffusional resistances and the higher level of mixing enhances external mass and heat transfer from liquid to solid phase. On the other hand, fluidized-bed bioreactors present higher axial dispersions than packed-bed. In the limit, fluidizedbed with high liquid recirculation approaches a complete mixed regime. This implies that reaction kinetics are an important factor to consider in the analysis and design of fluidized-bed bioreactors. Configurations favoring liquid mixing will be more appropriate for substrateinhibited reactions, and, opposite, configurations approaching plug flow will be more indicated for productinhibited reactions. Another advantage of fluidized-bed bioreactors is the ease of separation of the gas produced in most transformation involving cells (i.e., COa), or the feed of a gas stream to the reactor, for example, for aeration purposes. Also, fluidized-bed reactors make the biocatalyst replacement easy, without disruption of the operation, enabling then to control the overall activity of the reactor, for example, replacing particles with deactivated enzyme or removing excesses of biomass from biofilms. On the other hand, solids attrition is higher in fluidized-bed than in packed-bed bioreactors. From the productivity point of view, the different advantages of fluidized-bed, especially from the mass transfer point of view, make it possible to obtain higher levels of overall productivity than in packed-bed reactors, in spite of the fact that the fraction of immobilized biocatalyst particles is lower for a fluidized bed (Klein and Kressdorf, 1983). Fluidized-bed offers more possibilities of designing enzyme and immobilized cell particles and operation strategies in order to enhance the bioreactor performance, for example, in terms of overall productivity, biocatalytic stability, or product separation, as will be further discussed. An intrinsic characteristic that makes fluidized-bed bioreactors more complex than packed-bed bioreactors is their hydrodynamic stability, especially taking into account that the properties of the biocatalyst particles change considerably during the operation time. In fact, the nature of the particles (for example, their density and size, or their evolution with time, especially important in some kind of immobilized cells), the liquid and gas flow rates employed, and the type of reaction kinetics, as well as the kinetics of cell growth or enzyme deactivation, influence one another and have a direct effect on the reactor design and performance. A very interesting

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discussion of this interrelationship, often overlooked, is given by Andrews and Przezdziecki (1986). Another aspect that contributes to the complexity of a fluidized-bed bioreactor, in particular when immobilized cells are used, appears from the fact that the characterization of the cell behavior must be known, both at the kinetic level and at the physiological and genetic levels, and its relationship with the diffusional restrictions in the particles and the possible direct effects associated to the immobilization itself, must be well understood and correctly described, in order to build appropriate reliable models of these systems to be used in reactor design, control, and scaling-up. These aspects have received much interest in the available literature, but quite often the results published are contradictory. Wide information on the physiology of immobilized cells can be obtained from De Bont et al. (1990). The growth pattern and intrinsic kinetics of immobilized cells have been shown to differ substantially from those of free cells by some authors (Doran and Bailey, 1986; Galazzo and Bailey, 1990; Hilge-Rotman and Rehm, 19901, as some others report that no substantial changes could be observed (Veelken and Pape, 1984; Senac and HahnHagerdal, 1991;Vives et al., 1993). In other cases (Taipa et al., 1993), the different metabolic behavior of immobilized cells with respect to free cells has been explained by changes in the intracellular pH due to the interaction with the immobilization matrix. However, the experiments reported in each case are performed at very different conditions and it is therefore difficult to obtain clear conclusions. Also, in the case of selfimmobilization, like pellet formation by different microorganisms producing antibiotics, the effect of the morphology on the antibiotic production is critical to generate the best conditions to trigger the secondary metabolism of the cells (Smith et al., 1990; Braun and Vecht-Lifshitz, 1991). Although the description of the behavior of the immobilized cells and how it is affected by operational conditions is not the object of the present paper, it is very important to adress this point, as any optimized fluidizedbed bioreactor operation will require this kind of fundamental knowledge about the biocatalyst. In the case of immobilized enzymes, although the situation is less complicated because the absence of growth, the determination of the intrinsic kinetic properties (Hoojimans et al., 1992) and the effects of the immobilization procedure and the microenvironment in the particle on the catalytic activity of the enzyme are also a necessary step to develop accurate models useful to design and operate a fluidized-bed. The content of the present review is divided in four main sections. The first section focuses on basic hydro-

dynamic aspects of fluidized-bedbioreactors. The second section concentrates on modifications that different authors have proposed, either in the bioreactor or in the biocatalytic particles, in order to enhance the stability and operation of the reactor. The development of a mathematical model of fluidized-bed bioreactors is the objective ot the third section. Finally, different applications are discussed in the last section. The review concerns liquid-solid and gas-liquid-solid fluidized-bed reactors. In general, three-phase systems are more extensively discussed because they are more generally used and are more complex. Additionally, the particularities of two-phase systems are addressed specifically at different points of the discussion.

2. Basic Hydrodynamic Aspects of a Fluidized-Bed Bioreactor An accurate knowledge of the hydrodynamic aspects of a three-phase fluidized-bed bioreactor, the characterization of the type of flow, the degree of mixing, and the heat and mass transfer coefficients are most critical in order to assure its reliable design and operation. The complexity of the hydrodynamic behavior of these bioreactors is a consequence of the high number of factors involved. In addition to the references already mentioned in the introduction (Davidson and Harrison, 1971; Kunii and Levenspiel, 1977; Fan, 1989), there are a series of very interesting studies performed to characterize systematically the hydrodynamics of three-phase fluidizedbed bioreactors, using in most cases sophisticated experimental techniques and mathematical tools, that constitute an advanced reference material for a detailed description of the different phenomena taking place during fluidization (Muroyama and Fan, 1985; Fan et al., 1990b; Fan and Tsuchiya, 1990; Tsuchiya et al., 1992; Tzeng et al., 1993; Hallow et al., 1993; Yashima et al., 1992; Tang and Fan, 1990a). One aspect that should be emphasized is that most of the biocatalyst particles have densities quite close to those of the reaction media, usually on the order of 1030-1200kg/m3. This fact should be taken into account when the results of some of these works are examined and extrapolated to explain the behavior of a bioreactor, as quite often they are based on systems like glass beads-water-air, and only some of the most recent ones incorporate the analysis of systems with low-density particles. Therefore, these basic studies, which are very much detailed and provide interesting methodologies, give qualitative trends that can be applied to this case of bioreactors, but the use of quantitative information, such as holdup correlations (revised by Muroyama and Fan (1985)), should be experimentally checked for each case. In a three-phase fluidized-bed, three different sections can be distinguished: the gas-liquid distribution section, in the bottom, the fluidized-bed central section, and the gas disengagement section a t the top. In the central section, the volumetric fractions occupied by gas, liquid, and solids have the following relationship:

Also, the overall holdup for each phase is

The different phase holdup and the total axial pressure gradient have the following relationship:

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(3) In this equation, it should be noticed that the term corresponding to the gas phase is usually much smaller than the rest. The evaluation of the gas and liquid phase holdups, therefore, can be done by measuring experimentally the pressure fluctuation (Zheng et al., 1988) and using the previous equations, provided that solid holdup is known, for example, from the measurement of the bed expansion at a given fluidization state. However, pressure fluctuations are usually small in laboratory scale bioreactors. Other experimental techniques have been used, such as conductivity (Davison, 1989; Begowich and Watson, 1978; UribeSalas et al., 19941, capacitance, fluid isolation, radioactive tracers, electrical resistance, optical probes, etc. (Muroyama and Fan, 1985). In the three-phase fluidized-bed, with cocurrent upflow circulation of liquid and gas, the type of flow pattern will be dictated very much by the value and the ratio of the liquid and gas superficial velocities in the reactor (Muroyama and Fan, 1985; Zheng et al., 1988). Three main regimes are possible: (a) the dispersed flow regime will occur at high ratios of the liquid velocity to the gas velocity, and it is characterized by the homogeneous dispersion of small gas bubbles in the liquid; (b) the coalesced bubble flow regime will happen at increased gas flow rates, and it is characterized by the formation of bigger bubbles as a result of the coalescence of smaller ones; the coalesced bubbles have a nonuniform distribution in the liquid; (c) the slug flow regime is the consequence of a further increase of gas flow rates and occurs at high ratios of the gas to the liquid velocity, being characterized by the formation of big gas bubbles, that in small diameter bioreactors tend to occupy completely their cross-sectional area. Slug formation breaks the bed continuity and causes great instability. Figure 2 gives an example of experimental data represented in a fluidization chart, showing these different regimes. If the gas flow rate is increased dramatically, it will become eventually the continuous phase in the bioreactor. The liquid flow pattern in the bioreactor, that has to be well characterized in order to build a representative model of the bioreactor performance, is directly influenced by the degree of mixing associated with these different regimes, as well as by other factors, such as internal gas generation, bead size distribution, and external liquid recirculation. Basically, the flow will approach plug flow in systems with high velocity in the liquid phase (Ching and Ho, 1984; Kim et al.,1972). Quite often, the bioreactors will experience different degrees of mixing, and complete mixed flow can be observed in fluidized-bed bioreactors. Gommers et al. (1986) studied the influence of the gas phase on the liquid and solid mixing in a fluidized-bed bioreactor, taking two extreme situations: a reactor operating without gas and a reactor to which gas was introduced artificially from the bottom. They showed that the gas phase greatly influences the degree of liquid mixing in the reactor and that this effect increases sharply with the bed diameter, according also to some previous work (Epstein, 1981). In contradiction, Begovich and Watson (1978) did not find any effects of bed height and column diameter on the hydrodynamic of a fluidized-bed with glass beads. Regarding the solid particles, they conclude that solids follow the streamlines of the liquid flow in the bioreactor, as long as the particles are neither too large nor too heavy. The approach followed by Gommers et al. (1986) allows us to have a good understanding of how different factors affect the overall bioreactor behavior. However, in a fluidized-bed

fermenter, with a certain component of plug flow in the liquid phase, the gas holdup will increase with the axial distance, in proportion to the substrate consumed up to a given fermenter height. Davison (1989) has experimentally observed this situation by means of nonintrusive conductivity measurements made at different heights of a fluidized-bed fermenter with Zymomonas mobilis, immobilized in carrageenan beads converting glucose into ethanol. Also, it was shown that axial dispersion increases with bed height and that it was more pronounced at higher gas flow rates. Measurements in this work were made both in a simulated three-phase fluidized-bed with a gas injection at the bottom and in a real fermenting reactor, where gas was generated by the immobilized cells. The gas flow rate had a critical influence in the type of flow regime observed in the reactor: dispersed bubble flow a t low gas flow rates and coalesced bubble flow at high gas flow rates. An interesting result of this work, that gives an example of the general remarks made at the beginning of this chapter, is presented in Figure 3: the effect of gas flow rate on liquid dispersion in the bioreactor (which is inversely proportional to the Peclet number) is plotted using the experimental data and the dotted curves corresponding to three different correlations obtained previously in nonbiological systems, using particles much heavier than carrageenan beads. It can be seen that, although the general trend is similar, the correlations do not predict accurately the experimental results in this case. Brohan and McLoughlin (1984) studied the effect of superficial liquid velocity in a fluidized-bed bioreactor with Saccharomyces carlsbergensis flocs, using three different systems: glass beads, inactivated flocs, and metabolically active flocs. The degree of dispersion that the liquid in the fermenter exhibited with increasing liquid velocity was markedly higher in the latter case, indicating that the COz gas produced in the fermentation had a critical contribution to the internal mixing degree in the reactor. When liquid recirculation is used to promote fluidization because of the slow reaction rate and the high liquid residence time required, the plug flow is usually disrupted and completely mixed flow is usually achieved. There are other additional factors that should be considered to perform the analysis of the hydrodynamics of a fluidized-bed bioreactor, basically the properties of the solid particles and the properties of the liquid phase. In general terms, the weight and size of the solid particles will directly influence the liquid and gas flow rates required for bed fluidization. If the liquid residence time is fixed by criteria of substrate conversion, for example, then the heavier particles will require higher LID ratios to increase liquid superficial velocity and enhance fluidization. In a three-phase reactor, the solid particles can also interact directly with the gas phase. Lee and Buckley (1981) showed that dense particles can penetrate and divide gas bubbles, thus causing phenomena opposed to coalescence. Also, the size and shape of the particles can have direct influence in coalescence and disruption of the gas bubbles (Sinha et al., 1986; Henriksen and Ostergaard, 1974). Small particles can, in general, favor coalescence, as big particles can more easily break gas bubbles into smaller ones. Regarding the liquid properties, density, viscosity, and surface tension influence fluidization. The influence of density is quite direct, as it will change the sedimentation velocity of the solid particles. Viscosity can have a significative influence of the coalescence of gas bubbles. High-viscosity liquids will promote coalescence even at low gas flow rates (Shah et al., 1982), as low viscosity will enhance bubble disruption (Schumpe and Deckwer, 1987). Low liquid surface ten-

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sion prevents gas bubble coalescence (Shah, 1985). Bejar et al. (1992) studied the transition from dispersed flow regime, thus stable fluidization, into coalesced flow and slug formation, thus unstable fluidization, as a function of different physical properties of the reaction system, in addition to the gas flow rate used in the fermenter and the gas generated by fermentation. Their study focuses on the difference between solid and liquid densities, the liquid viscosity, and surface tension and has been developed in two different fluidized-bed reactors with Saccharomyces cerevisiae cells entrapped in calcium alginate beads. The experimental results obtained are plotted in a fluidization chart (Figure 4) as a function of two moduli on the basis of the physical properties:

Two different zones can be distinguished in the chart, corresponding to stable and unstable fluidization. Moreover, the same approach could be extended to data from another fluidized-bed bioreactor working with Zymomonas mobilis immobilized in carrageenan beads, showing good agreement (Davison et al., 1994). One important factor to consider is that the physical properties influencing the type of fluidization regime often change during the operation of the fermenter. For example, the particle density may change because cells grow and accumulate to some extent inside the beads or form biofilms. Also, liquid density may decrease because more substrate is being consumed. In consequence,the difference between both densities, which usually are quite close, can suffer very significant changes in terms of relative value. This situation is of special relevance at the beginning of the reactor operation, where this dynamic behavior and its influence on the reactor hydrodynamics should be well defined to assure a successful operation. Finally, some aspects directly related to the physical construction of the bioreactor need also to be considered, as they can greatly influence the fluidized-bed operation. The LID ratio is very important from this point of view: high values will tend to favor plug flow liquid circulation, but gas bubble coalescence and slug formation will be more possible, as low values will introduce more backmixing in the bioreactor but will have low wall effects. Moreover, small construction details, very often not adressed, can have important consequences in the reactor performance. Asif et al. (1991) have shown the effect of the gas distributor on the bed hydrodynamics, in an

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experimental system based on water as the fluidizing medium and polystyrene beads as the solid phase. Typical pulse tracer injection and the dispersion model, that will be further discussed in section 4, were used to quantify the effect of different distributor properies. The results showed pronounced effects due to the formation of dead zones in the distributor region, when the pressure drop at the distributor and the density of wholes were low, and also for low liquid superficial velocities. The quantification of these effects allowed design guidelines to be given for a correct distributor operation. Del Pozo et al. (1992) did an analysis of the effects on column inclination of the performance of three-phase fluidizedbeds. Interestingly, they showed that even small variations of the inclination angle, such as 1.5", can have a significant influence in the mass transfer coefficients in the bioreactor, that can be increased up to 30% or decreased up to 20%.

3. Introducing Changes in Biocatalyst Particles and Bioreactor Configuration To Modify the Fluidized-Bed Hydrodynamics and Its Operation There are different ways that have been proposed in order to improve the operation and stability of fluidizedbed bioreactors, basically introducing new concepts in the design of either the bioreactor or the biocatalysts particles. Although in principle the focus in most cases is on hydrodynamic aspects, their connection to the overall reactor performance is evident (type of flow regimes, mass transfer coefficients, phase holdups, etc., will dictate very much of the reactor performance, in addition to the reaction kinetics and operation conditions). Moreover, some of these new concepts could directly introduce new advantages from the kinetic point of view, for example, designing systems that allow the in-situ separation of inhibitory products or also influence the time evolution of the biocatalyst concentration and activity, especially in the case of cells. Andrews and Przezdziecki (1986)adressed very clearly the importance of selecting the right particles in order

to correctly design fluidized-bed fermenters, basically involving yeast flocs or biofilms growing on inert particles. The size and density of the biocatalyst particles are the only free variables for a given kinetic behavior, liquid flow rate, inlet substrate concentration, and desired conversion. Once they are fured, the superficial liquid velocity to keep the bed fluidized is also fixed. In turn, superficial liquid velocity and liquid flow rate will fur bead diameter, as superficial liquid velocity and residence time will fur bed height. However, liquid recirculation and the effect of gas evolution, which previously has been shown to be an important factor in fermentation systems, are not considered in their discussion. The analysis is also made from the point of view of how a given support for a biofilm will influence the overall bioreactor productivity, in terms of generating a biofilm with an optimal width that maximizes its effectiveness. Important aspects to consider in this selection are that too heavy particles will need reactors with a height to diameter ratio too high and that lower density particles will enhance bed stratification, which can be of interest in some applications. Bed stratification is one of the extremes in solids mixing in a fluidized-bed bioreactor, the other being complete mixing. In the stratification conditions, the movement of the solid particles in the bed is very limited and they are ordered by decreasing settling velocities, from the bottom to the top of the bed. One of the consequences of this situation is that, in liquid plug flow regimes, the particles at different reactor heights will experience different environments. In the case of cells growing as biofilms, typically the particles at the bottom of the bed will provide better conditions for cell growth (for example, substrate availability), and as a consequence, they will decrease their overall density; therefore, they will migrate to the upper part of the reador. Excess biofilm could be regulated by solids attrition within the system (Chang et al., 1991) or may need an external treatment of the particles to remove it before reintroducing the particles into the reactor. In the case of immobilized cells particles obtained by

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entrapment, like the widely used calcium alginate and carrageenan beads, their density can be modified by the addition of an inert solid powder. Depending on the particular type of cells, kinetics, liquid flow rate, gas evolution in the bioreactor, etc., the density could need to be increased or decreased in order to make fluidization easier. Davison and Scott (1988) added iron oxide to the preparation of immobilized Zymomonas mobilis in carrageenan in order to prevent their washout from the reactor as a consequence of the gas accumulation inside the beads due to the fast fermentation rate of the cells. On the other hand, Vorlop et al. (1993) demonstrate the possibility of controlling the final density of calcium alginate beads entrapping Saccharomyces cerevisiae cells at low values (very close to medium densities) by means of the addition of microporous glass particles with very low density. By this strategy, satisfactory fluidization of these particles, avoiding slug formation and bed unstability, could be obtained without the need for liquid recirculation and with only moderate gas flow rates. A very relevant example of how the particle formulation and their dynamic evolution interact with fluidizedbed operation can be found in the production of antibiotics by mycelial microorganisms that can grow in pellet form, thus becoming self-immobilized, such as penicillin production by Penicilium chrysogenum (Kim et al., 1986; Oh et al., 1988). Antibiotics are secondary metabolites and therefore can be produced a t low growth rates, that in turn can be achieved by limitation of a key compound for cell growth, for example, phosphate. The use of a nutrient regulation for the control of the bioreactor operation is not straightforward, especially regarding the fact that the levels reached are usually undetectable. If limitation is not reached, mycelial growth will be promoted and penicillin production arrested, the particles (pellets) will become bigger in size and less dense, and the medium will become more viscous, due to the generation of free mycelia by the attrition in the bioreactor. As a consequence, liquid mixing is very poor, as well as mass transfer, oxygen supply by aeration is very limited, and the hydrodynamics of the reactor are bad. When nutrient limitation is reached, mycelial pellets remain relatively stable and continuous production of the antibiotic during extended time periods is then possible. The inverse fluidized-bed is a bioreactor concept that incorporates the control of the number of cells, preferentially growing as biofilms on an inert support, by providing a physical way to increase the attrition and erode the biofilm (Ramsay et al., 1991). The bioreactor is divided into two sections by an internal draft tube. The external annular section consists of the inverse fluidizedbed. The support particles should be lighter than the reaction medium and become heavier with the biofilmgrowing process. Biofilm growth and liquid circulation are responsible for the inverse fluidization phenomena. Eventually, the densest particles will reach the internal tube and then circulate upward. Placing a shearing device inside this tube allows the biofilm to erode and, therefore, control its thickness. Bramble et al. (1990) have reported on the development and operation of a magnetically stabilized fluidized-bed. This concept is based on the addition of a magnetic material inside the biocatalysts beads (in the reported experiments, magnetite was added to calcium alginate beads entrapping Coffea arubica cells) and the inclusion of the whole reactor inside a group of coils that generate a magnetic field. In this way, magnetic beads can be stabilized in the reactor, so the typical solid mixing, happening often in fluidized-beds, can be avoided. Also, a selective removal of beads that have spent a given time

485

in the bioreactor could be achieved. As a consequence, the potential of this system is relevant for those applications where the solids residence time in the reactor needs to be carefully controlled and also when solids attrition needs to be avoided. Pieters et al. (1992) have discussed the advantages of using magnetic microparticles, particularly for the hydrolysis of maltodextrin with immobilized glucoamylase. From a general point of view, the incorporation of magnetic materials in the preparation of the biocatalyst particles makes their handling, the bioreactor operation, and also their recovery from the reactor liquid easier. The operation of a fluidized-bed bioreactor with magnetic particles is enhanced by the fact that bead washout can be completely avoided by the placement of an electromagnet at the top of the bed. The control of the biocatalyst activity in the solid particles of the bioreactor is of critical importance for a proper operation, especially in the case of continuous processes. When the desired conversion involves the use of enzymes, deactivation should be taken into account. The current industrial operation of continuous enzymatic processes is based on a number of packed-bed bioreactors, each one of them operating at a different level of deactivated enzyme, and thus catalytic activity. Syncronization of the various bioreactors allows one to obtain an averaged product stream, in spite of the intrinsic timechanging conversion in each one of them. A very interesting alternative has been developed by Vos et al. (1990a,b,c): the countercurrent multistage fluidized-bed. The main characteristic of this bioreactor is the continuous transport of the solid particles of immobilized enzymes, from one stage to another, as sketched in Figure 5. By this, the overall catalytic activity of the reactor remains constant, as the exhausted enzyme is removed from the reactor bottom stage while fresh biocatalyst is added a t the top stage. A second advantage of the distribution of the reactor in compartments is the very low back-mixing of the biocatalyst and the plug-flow regime in the liquid phase. As discussed previously, this work also shows the direct influence of the bead properties (basically density and size) on reactor hydrodynamics, for example, mixing or solid stratification of the solid particles in the different stages. The hydrodynamic stability of a multistage fluidizedbed operating with low-density particles has also been described by Sisak et al. (19901, in a system containing aminoacylase immobilized on polyacrylamide beads. In a narrow column, they found slug formation, while a wider column suffered channeling and bed expansion with increasing flow rate was very irregular. These problems were overcome by providing the bioreactor with a low stirring with impellers (3.5 rpm). Conversion and operational stability were clearly improved with respect to nonstirred fluidized-bed or packed-bed systems. The effect of the bioreactor hydrodynamics on the mass transfer between different phases in the bioreactor is also a key point in the overall operation. In the case of a gasspouted three-phase fluidized-bed,with a viscous medium and low density differences between bioparticles and liquid (Karamanev et al., 19921, bubble coalescence is enhanced and the gas forms large bubbles and slugs. As a consequence, the mass transfer coefficient between gas and liquid (kla) is low and limits cell growth in the particles. Two different changes in the reactor design are studied to avoid this situation: the use of static mixers and the incorporation of an internal draft tube, in order to increase the number of small air bubbles in the reactor. As shown in Figure 6, the lzlu value is very much influenced by these changes. Kang et al. (1991) propose a different approach to enhance the volumetric

486

Biofechnol. Prog., 1995, Vol. 11, No. 5 fresh biocatalyst

podrct Out

t high

low

+

srbstrate in

flow

'T'

old biocatalyst

srbstrate in

reversed flow

m

flow stopped

l flow

Figure 5. Operation phases of a multistage fluidized-bed reactor for a deactivating biocatalyst Represented with permission from Vos et al. (1990a). Copyright 1990 Wiley. 120 0

J.0

I

o Three phase fluidized bed

100 + A A Static mixers

-

'

0 Draft tube

80

2.5

'i OJ

2.0

60

0, Y

Y

40 15 20 10

0 0

5

10

15

20

25

Gas flclw rote, I/min Figure 6. Effect of the gas flow rate on kla values for a fluidized-bed reactor, draft tube, fluidized-bed, and fluidized-bed with static mixtures Reprinted with permission from Karamanev et al. (1992). Copyright 1992 Elsivier. rate of oxygen transfer in a fluidized-bed reactor operated at the bubble coalescing regime, consisting of the use of floating bubble breakers. A different concept to enhance oxygen supply to immobilized cells within a fluidized-bed was developed by Chevalier and de la Noue (19881, consisting of the coimmobilization of algae and bacteria in carrageenan beads. Opposite, the immobilized cell particles can be engineered in order to provide anaerobic conditions in a fluidized-bed,introducing the co-immobilization of oxygenreducing microbial membrane fragments together with the cells (Gbdia et al., 1990). In some particular systems, such as those using animal cells, air supply through a bubble-free system is often required in order to avoid cell damage and the fluidized-bed design needs to be modified for this purpose. Hambach et al. (1992) developed a reactor integrated membrane system for bubble-free oxygenation of Chinese hamster ovary cells attached to collagen microspheres, achieving high cell densities in the bioreactor. Finally, a completely different approach to enhance the operation of a fluidized-bed changing the formulation of the biocatalysts particles consists of the integration of

reaction and product separation, which is especially helpful when the reaction is product inhibited (Freeman et al., 1993). Although the final advantage is from the kinetic point of view, the practical implementation of such integration implies changes in the bed design and hydrodynamics. Andrews and Fonta (1989) describe the operation of a fluidized-bed for the production of lactic acid based on the immobilization of Streptococcus thermophilus on monosized activated carbon. The choice of this support is made in order to adsorb the substrate at the bottom of the bed, and the product at the top of it, and in consequence reduce their inhibitory effect. The operation of the bioreactor requires, as schematized in Figure 7, the external removal of excess biomass and product desorbtion. Silbiger and Freeman (1991) have developed a continuous process for A'-hydrocortisone dehydrogenation using Arthrobacter simplex immobilized in poly(acry1amide hydrazide) beads in a fluidized-bed with enhanced substrate solubility by means of a cosolvent and a selective product recovery by adsorption onto a solid, based on the addition of microcrystalline cellulose powder. Van der Wielen et al. (1990) have shown the potential of introducing selective product removal t o

Biotechnol. Prog., 1995, Vol. 11, No. 5

487

Excessl biomass removal

Carbon with biomass xo AdsorbatespS = 0

Substrate desorbs as product adsorbs

I

T

I

I I

Desorb product

I

Biofilm grows

t

Monosized ac Iivated carbon with

Fluidized bed stratilied bY biofilm thickness

Cubslrate adsorbs

1 AdsorbatesqS = qp = 0

Figure 7. Operation diagram of a fluidized-bed bioreactor with simultaneous bioconversion and adsoptioddesorption of substrate and product Reprinted with permission from Andrews and Fonta (1989). Copyright 1989 Humana.

improve substrate conversion in enzymatic reactions, in a multistage countercurrent fluidized-bed. They propose the glucose-fructose isomerization reaction with a zeolitic adsorber as a model system and make a theoretical analysis of the reactor and a simulation of its performance to select the most appropriate operation. Davison and Scott (1992) have proposed a system based in two different types of particles with different densities. As one type of particles, containing the biocatalysts, in this particular example cells of Lactobacillus delbreuckii, remains fluidized in the bioreactor, the second type, which is heavier and contains no cells, is introduced from the top of the bioreactor and collected at the bottom. This second type of particles is selected in order to remove selectively the inhibitory product of the fermentation, such as lactic acid. By this system, 4-fold lactic acid productivities have been obtained (Davison and Thompson, 19921, although the bioreactor design and operation is somewhat more complex. The same objective can also be accomplished by introducing changes in the bioreactor design. Busche and Allen (1989) propose the use of a pervaporation membrane modulus removing selectively the inhibitory products, coupled to a fluidized-bed reactor for acetone-butanol fermentation.

4. Developing a Model for a Fluidized-Bed Bioreactor The development of a reliable model is of critical importance for the successful design, scale-up, operation, and control of fluidized-bed bioreactors, due to their complexity and the high number of phenomena taking place that need to be correctly described. In order to build such a model, the following main blocks need to be developed: (1)intrinsic reaction kinetics and diffusion in the biocatalyst particles, (2) a flux model in the bioreactor, (3) mass balance equations for the species taking part in the reaction (substrate, product), and (4) transport phenomena between different phases (gasliquid, liquid-solid). The analysis that will follow has been constrained to the pseudo-steady-state performance of the bioreactor, which is often the most interesting situation from the operational point of view. The modelization of the transient response of a fluidized-bed reactor exposed t o step changes in its operation has been

described by several authors (Tang et al., 1987; Worden and Donaldson, 1987; Farag et al., 1989; Papathanasiou et al., 1988). Also, isothermal operation is assumed. Although this is a generally accepted condition, because of the low velocity of most biological reactions and because the mild operation temperatures cause no limitation in heat transfer, the process taking place is very complex, as a consequence of the interaction between gas, liquid, and solid phases (Kumar et al., 1993; Kim and Laurent, 1991; Fan, 1989), and should be taken into consideration especially in the case of large-scale bioreactors. Finally, the description that follows concentrates mainly in the liquid phase and solid biocatalytic particles, and some examples of how to treat a compound present in the gas phase, as oxygen, are also considered. Reaction and Diffusion with the Biocatalyst Particles. In a three-phase fluidized bed bioreactor, reaction ta,kes place in the solid particles, either biofilms or beads, simultaneously to the physical diffusion of substrates and products, which follows Fick's law. Moreover, substrates and products are also transported between the solid particles and the surrounding liquid. This external mass transfer is usually modeled by means of a hypothetical liquid film that creates the resistance to the transport. Finally, partitioning phenomena between the particles and the liquid can also happen as a result of the material properties. This situation is sketched in Figure 8. It is important to emphasize a point that has already been discussed: the kinetic equation used in the model should be representative of the intrinsic behavior of the immobilized biocatalyst, that is, free of any mass transfer limitation. The behavior of free and immobilized biocatalysts can be intrinsically different as a consequence of the immobilization itself. However, many authors use the kinetic equations and parameters corresponding to the free biocatalyst as a first approximation, when the kinetic data for the immobilized preparation are not available. Figure 9 illustrates the different rates and kinetic parameters that can be defined (Engasser and Horvath, 1976). In the case of cells, another aspect that needs to be considered is that cells slowly grow and die inside the solid particles and, as consequence cell distribution and activity, will strictly change along the operation of a

Biotechnol. Prog., 1995,Vol. 11, No. 5

488

reaction taking place. The boundary conditions for these equations are, usually, those corresponding to the center of the bead:

-ds =0 dr

and -dP =0 dr

ut r = O

(7)

and the equality of substrate and product fluxes by external mass transfer and internal diffusion at the surface of the bead:

ds

k,,(S, - S,,,) = Dsdr Ir=R

Sf

S(r)

Figure 8. Inter- and intraparticle mass transfer of a single porous spherical bead Reprinted with permission from Kiesser et al. (1990). Copyright 1990 VCH.

If the concentrations of the compounds are different on both sides of the external surface of the beads due to the partition effects, this should be taken into account by substituting in the first terms of these equations, p&’,,, for S s u r and j3pPsur for P,,,, where ps and pp are the partition coefficients for the substrate and the product. Also, if the effects of external mass transfer can be neglected, which is quite possible due to the good mixing in the bioreactor, then the second set of boundary conditions can be reduced to

S = S f and P = P f ut r = R

EFfLCflVE RATE AN0 KINETIC PARAYCTCRI

Figure 9. Schematic illustration of the different rates and kinetic parameters for an immobilized enzyme Reprinted with permission from Engasser and Horvarth (1976). Copyright 1976 Academic Press. bioreactor, as discussed by several authors (de Gooijer et al., 1991; Monbouquette et al., 1990; Wolffberg and Sheintuch, 1993). However, for most practical applications, a pseudo-stationary state regarding the concentration of active cells is often adopted. In the case of deactivating enzymes, the kinetic equation describing enzyme deactivation has to be incorporated into the model, together with the equations corresponding to the reaction kinetics. For steady-state conditions, the mass balance for substrate and product (S and P)within a spherical bead, with simultaneous diffusion and reaction, gives the following equations:

(10)

The solution of this system of equations usually requires numerical calculation, due to the nonlinear form of most kinetic equations, and it is easier if dimensionless variables and parameters are adopted (Gbdia et al., 1987; Tong and Fan, 1988). In addition to the intrinsic kinetic equation and its corresponding parameters, the value of the mass external coefficients, K,, and kmp, and the effective diffusion coefficients must be known. External mass transfer coefficients can be estimated with reasonable accuracy from correlations, such as that given by Tourni6 et al. (1979):

Sh = 0.245Ga0.323Mv0.3Sco~4

(11)

in terms of dimensionless moduli, defined in the nomenclature section, among which the Sherwood number (Sh) is directly related to the external mass transfer coefficient or that of Nelson and Galloway (Wen (Sh = K, d&) and Fane, 1982):

1- E , 113

tanh

5

with

(13) (5)

Arters and Fan (1990) studied the effect of the experimental methodology on the estimation of solid-liquid mass transfer coefficients. They also proposed the following equation: where u(S,P) is defined as the rate of product formation or substrate depletion and will be given by a kinetic equation and parameters describing the evolution of the

Sh - Sho

ShO

Nu = 0.237(-)Mv4

0.144

(14)

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Biotechnol. Prog., 1995, Vol. 11, No. 5

Internal effective diffusion coefficients can be estimated by means of equations such as the proposed by Satterfield et al. (1973): DMMEp

De, = -

(15)

Zf

or Bailey and Ollis (1986): (16) that depend of parameters describing the physical nature of the porous particles, such as the porosity, the pore diameter, and the tortuosity factor. Better, effective diffusion coefficients can be determined experimentally, especially when these physical characteristics are not well known or when the effect of other factors such as cell concentration on the value of the coefficients cannot be predicted. Westrin and Axelsson (1991) have discussed extensively the various experimental techniques that can be used to determine the effective diffusion coefficients. In the case of the widely used calcium alginate beads, a number of authors report the use of the coefficients corresponding to water, while the presence of cells and other factors can cause significant changes in them (Scott et al., 1989; Estap6 et al., 1992; Fan et al., 1990a). From the numerical solution of the previous equations, the effectiveness factor of the biocatalyst particles can be evaluated. The effectiveness factor is defined as the ratio of the actual reaction rate for the whole particle to the reaction rate evaluated in the case that all the bead would have the concentrations found at the surface, that is, in absence of limitations by diffusion:

v

v = - vsur

which will have a flux pattern between perfectly mixed and plug flow. The determination of the real liquid flux model in the bioreactor is a necessary step in order to apply the mass balance equations for the species taking part in the reaction. Stimulus-response techniques are commonly used for such a purpose, being based on the introduction of an inert tracer at the reactor inlet and the analysis of the curve of response obtained at the outlet, which reflects the type of flux (Levenspiel, 1979). The models that describe the liquid flux in a real reactor can be (a) axial dispersion models, in which axial dispersion is superimposed on the liquid convective flux, (b) tank-in-series models, in which the bioreactor is considered as a series of CSTR reactors of the same volume, or (c) compartimented models, in which the flux model in the bioreactor is described as the combination of different ideal compartments. Descriptions of the different models, possible tracers to use, and general methodology for the determination of the model parameters are given by various authors (Swaine and Dauglis, 1988; Nauman and Buffham, 1983). In the case of fluidized-bed bioreactors, especially when fermentation gas is produced, some interesting contributions have been proposed, such as the consideration of a variable dispersion coefficient, which increases its value in proportion to the fermentation gas generated up to a given point in the reactor (Petersen and Davison, 1991). Also, some correlations can be used in order to estimate the axial dispersion coefficient when experimental data are not available (Vos et al., 1990a). Mass Balance Equations. The mass balance equations to be used in the bioreactor model are dictated by the type of flux pattern. In the case of plug flow with axial dispersion, the mass balance equation corresponding to the substrate, for example, is given by d2S, E$-

(17)

where uBUrcan be evaluated using the kinetic equation, u(S,P), and the substrate and product concentrations at the surface and v in the particle can be evaluated taking into account that, in steady-state operation, the rate of reaction, for example, as product formation, must be equal to the rate of diffusion outside the beads:

&2

dSf - u- - E,V = 0

'dz

(19)

with the following boundary conditions at the entry and exit sections of the fluidized bed:

(21)

The value of the effectiveness factor will approach unity in the absence of concentration gradients inside the particles, that is, when diffusion takes place at a higher velocity than reaction. Therefore, the rate of conversion by the immobilized biocatalysts will be reaction controlled. On the other hand, when diffision takes place at a lower velocity than reaction, the diffision rate will become controlling. As a consequence, there will be internal gradients of substrate and product concentrations: the substrate concentration will be greater at the bead surface than at the center, and product concentration will be greater at the bead center than at its surface. For most of the reactions, the effectiveness factor will be considerably lower than unity in this case. However, for some particular reaction kinetics, such as substrate inhibition, the effectiveness factor can be greater than unity when diffusion limitations are important. Flux Model in the Bioreactor. The hydrodynamic conditions of the bioreactor at a given operation condition will generate a given level of mixing in the liquid phase,

When the bioreactor is perfectly mixed, or when its flow pattern can be described by the tanks-in-series model, the mass balance equations to use (either for the whole reactor or for each one of the tanks in the series) for substrates and products are

+

F(S, - Sf) VE,V= 0

(22)

F(Pf- P,) - UE,V= 0

(23)

Clearly, the use of these equations needs the previous determination of various factors, but especially the holdup of the different phases. As discussed previously in the second section of this work, there are several techniques that can be used to determine experimentally these data. Also, different correlations can be used to estimate them, in particular the Richardson and Zaki equation for solid-liquid systems and the drift-flux model for the three-phase systems (Bajpai et al., 1990). In the case of solid holdups, the fact that solid particles can be nonuniformly distributed along the axial length of the reactor (Tang and Fan, 1989)has to be considered

Biotechnol. frog., 1995, Vol. 11, No. 5

490 5 -

I I

I

I

-

Ill

1

I

1

I

I 1 1 ' 1

-5-

-

prforaled plate oil-shale particles

Koae et a1 (1984) K - K : Transition

CI c

'in

v

0

.x Transitional state

-3

-

-

5 -

-

3 -

0.2

'

I

l r l r '

0.5

1

I

I

2

1

I I Illl

5 U,

10

1

1

1

I l l l L

so

20

roo

(cm/s)

Figure 10. Variaition of klu with the superficial gas velocity in various three-phase fluidization systems Reprinted with permission from Fam (1989). Copyright 1989 Butterworths. in those cases where the approximation of a uniform holdup would introduce a too high deviation of the model. Transport Phenomena between Phases. In a fluidized-bed, with two or three different phases involved, the transport phenomena between them can play a key role in the definition of the overall operation. The two most common interphases are solid-liquid and gasliquid. The transport of substrates and products between the liquid phase and the solid particles has already been discussed in terms of film resistance and the associated coefficients, k,, and kmp. The transport between gas and liquid phases is especially relevant in the case of oxygen transfer from air to the liquid phase. The corresponding coefficient, Kla,has been studied extensively, and an important number of correlations for reactors such as air-lift and three-phase fluidized-beds have been developed (Chisti, 1989; Tang and Fan, 1990b; Schumpe and Deckwer, 1987). It has to be pointed out the wide range of kla values that can be found in different types of fluidized-bed reactors and the number of factors influencing them, such as gas holdup, gas velocity, or liquid properties. Figure 10 illustrates this situation and the complexity of kla estimation. The mass balance equations in the previous point have to be modified when the compound studied is transferred from the gas phase, as oxygen. As an example, the equation corresponding to a perfectly mixed liquid flow

would be in this case

+

+

F(S, - Sf) UE,V kla(Si - Sf)V = 0

(24)

where Si is the concentration of the compound which is transferred from gas to liquid at the gas-liquid interface, which is given by its partial pressure in the gas phase and the Henry's constant:

s.'= P8H

(25)

Also, the evolution of the partial pressure of a compound in the gas phase, as oxygen, will be given by the corresponding mass balance equation, equivalent to the equations presented previously for the liquid phase. As an example, the mass balance equation for a compound in the gas phase and plug flow would be (26) The methodology discussed here has to be adapted to each particular biocatalyst and bioreactor when the model is developed. Some very complete examples, including enzymes and cells, have been previously reported (Rottenbacher et al., 1987; Ching and Chu, 1988; Sun and Furusaki, 1990; Petersen and Davison, 1991;

491

Biotechnol. Prog., 1995, Vol. 11, No. 5

L A _------

----------

--e

0:0 Dimrnrionlrrr Arlrl porilion

0.4

0.8

10

Dimrnrionkrr kid position

Figure 11. Results of the mathematical model for a tapered fluidized-bed producing ethanol from glucose with zymomonas mobilis cells immobilized in carrageenan beads. Internal concentration profiles with the dimensionless fermenter height: experimental values (points) and values predicted by the model (solid lines). Dotted lines represent the calculated COP flow rate produced by fermentation Reprinted with permission from Petersen and Davison (1991). Copyright 1991 Humana.

Figure 12. Simulation results obtained with a mathematical model describing acetic acid production with immobilized and free Acetobacter aceti in a fluidized-bed. Concentrations of dissolved oxygen, C D O and ~ , free cells, C,1 (left), and production rates by gel entrapped, Pk,and suspended cells, Pi1 (right), for different values of the gel bead radius: 1,0.1 mm; 2,0.4 mm; 3, 1.22 mm; 4, 2.5 mm Reprinted with permission from Sun and Furusaki (1990). Copyright 1990 Elsivier.

Kiesser et al., 1990; Qureshi and Maddox, 1990; Tong and Fan, 1988; Vos et al., 1990a). Tong and Fan (1988) developed a model for a multistage fluidized-bed fermentor converting glucose to ethanol by Saccharomyces carlbergensis immobilized in calcium alginate. They used a kinetic equation including ethanol inhibition, in which the corresponding kinetic parameters had been previously determined in free-cell batch experiments. To describe internal diffusion, they used the value of the effective diffusion in water for ethanol and glucose (10 x and 6.4 x cm2/s, respectively). They calculated the external mass transfer coefficients using eq 14 and considered a completely mixed flow in each individual stage. The model could predict the experimental results with 15%deviation and was used to simulate the effect of different transport resistances and liquid flow rates on the reactor performance. Petersen and Davison (1991) studied ethanol fermentation using Zymomonas mobilis cells immobilized in carrageenan and a tapered fluidized-bed. As in the

previous case, the effective diffusion coefficients for glucose and ethanol were taken as those in water. The reactor hydrodynamics were described by the dispersed plug-flow model, with the particularity that the axial dispersion coefficient changed along the fermenter height as a function of the amount of COz generated by fermentation at a given point. Previously, the authors had determined that fermentation gas evolution was the main cause for axial dispersion. Taking into account as well the fact that the cross-sectional area changes with the fermenter height for a tapered configuration, the mass balance equation (eq 19) becomes in this case

where 8 is the angle of inclination of the tapered bed, r,

Biotechnol. Prog., 1995, Vol. 11, No. 5

492

/6.0 0

a2

0.1

0.3

J 0 2 3

Cs(-)

1

R tmm) Figure 13. Simulation results obtained with a mathematical model describing acetic acid production with immobilized and free Acetobacter aceti in a fluidized-bed. Productivity of acetic acid as a function of the solid holdup for different dilution rates and a constant bead size of R = 1.22 mm (left). Productivity of acetic acid as a function of bead size for different dilution rates and bead sizes and a constant solids holdup of 0.16 (right). Reprinted with permission from Sun and Furusaki (1990). Copyright 1990 Elsivier.

is the radius of the bed a t a given height,

E =E,

+ a(1- e-yCo2)

(28)

indicates how the axial dispersion coefficient changes with COZ evolution, and Zd refers to the dimensionless reactor height. The boundary conditions for the balance equation are now

and

(30) The use of this mathematical model gave very good results in the description of the internal concentration profiles in the fermenter, as shown in Figure 11. Sun and Furusaki (1990) presented a model for the acetic acid production in a fluidized-bed with Acetobacter aceti immobilized in calcium alginate beads. The model takes into account the contribution of both immobilized and free cells in the bioreactor. In this example, the role of oxygen supply to favor cell growth and acetic acid production is critical and the model is based on an oxygen transfer from gas to liquid, and diffusion of oxygen into the gel beads, that is limited to a certain depth of the bioparticles. The Ala values are affected by the size of the particles and the solid holdup in the bioreactor. The proposed model takes into account this dependence, and it is used to simulate the effects of changing dilution rates, bead diameter, or solids holdup on the productivity of acetic acid or the concentration of oxygen and free cells in the bioreactor, as shown in Figures 12 and 13.

5. Applications of Fluidized-Bed Bioreactors The potential of fluidized-bed bioreactors is made more evident by an analysis of the various types of processes in which they have been used. As an indication of this variety, Table 1 gives the main characteristics of some examples from the literature. However, it should be pointed out that, with the exception of wastewater treatment plants, the application of fluidized-bed bioreactors in a large industrial scale is very scarce, especially when it is compared to the number of reports at the laboratory scale. Nagashima et al. (1984) reported on the construction and operation of a

pilot plant with two 1 m3 fluidized beds connected in series for ethanol production using Saccharomyces cereuisiae entrapped in carrageenan beads. Stable operation for more than half a year was demonstrated. Busche et al. (1992) evaluated positively both from the economical and technical point of view the manufacture of ethanol in fluidized-bed bioreactors operating with immobilized Zymomonm mobilis cells. Aivasidis et al. (1991)reported the production of alcohol-free beer with immobilized yeast in a 50 L pilot plant fluidized-bed reactor. The production of penicillin using Penicillium chrysogenum immobilized in urethane particles was studied by Endo et al. (Fan 1989) in a 160 L pilot plant fluidized-bed. It is also important to keep in mind that, from the point of view of the overall economy of the process, although the cost reduction when changing from a more conventional reactor to a fluidized-bed can be significant, there are other factors that may have a higher impact that in turn can make the advantages of the technological change less evident or attractive. Qureshi and Maddox (1992) made an economic analysis of the production of acetonebutanol fermentation using a fluidized-bed with immobilized Clostridium acetobutylicum coupled to a pervaporation membrane for in-situ product removal. They showed that, in comparison to conventional batch fermentations with free cells, the investment cost can be drastically reduced and that the final product price can be reduced to almost one-half, making the process viable. However, they also made clear that technical improvements in the process, such as increasing membrane selectivity and flux, would have a minor economic impact with respect to factors such as the price of the substrate for the fermentation and the plant capacity. Finally, very few studies on the application of scaleup methods to fluidized-bed bioreactors can be found. Schoutens et al. (1986a,b,c)present a very complete study on the application of scale-down methodology to study the scale-up of the production of isopropyl alcoholbutanol mixtures by immobilized Clostridium sp. Rottenbacher et al. (1987) propose a model to scale-up a gassolid fluidized-bed for ethanol production, based on two parameters, the circulation time and the specific substrate supply.

6. Conclusions Fluidized-bed bioreactors have great potential in a wide range of bioprocesses, due to their intrinsic advantages and also to the possibilities that they offer to the engineers to change their design in order to enhance their performance. However, they are also more complex and need to be well characterized in order to obtain a reliable and stable performance. Three-phase hydrodynamics

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494 a n d a good knowledge of the immobilized biocatalyst behavior are the key issue t o attain successfully such a characterization a n d also to develop useful models for design, operation, control, and scale-up of fluidized-bed bioreactors.

Notation reactor cross-sectional area (m2) effective diffusion coefficient ( m s - ~ ) substrate effective diffusion coefficient ( m s - ~ ) substrate effective diffusion coefficient ( m s - ~ ) molecular diffisitivity (m2 s-l) particle diameter (m) axial dispersion coefficient (m2 s-1) liquid flow rate (m3 s) gravitational acceleration ( m s - ~ ) Galileo number ( d P 3el2g p12) Henry's constant (L a t m mol-') overall gas-liquid mass transfer coefficient for oxygen (s-1) external mass transfer coefficient for t h e substrate (m s-l) external mass transfer coefficient for the product ( m s-l) mass liquid flow rate (kg s-l) mass flow rate of C02 generated by fermentation

(kg 6-l)

S sc Sh Sho u1 ug

V U

YSP

z zd

z

mass (kg) density number (ep- el)/el gas velocity number (el (u$cJ3/(g p1) pressure (kg m-l ss2) partial pressure of a compound in t h e gas phase (atm) product concentration (kg m-3) Peclet number ( d , u f i ) biocatalyst particle coordinate (m) biocatalyst particle radius (m) Reynold's number of superficial velocity (u1d , #$ Pl) substrate concentration (kg m-3) Schmidt number DM el)) Sherwood number (km d@M) Shenvood number specific to solid-liquid fluidized systems (km d@M) superficial liquid velocity (m s-l) superficial gas velocity (m s-l) reactor volume (m3) reaction rate: product formation or substrate depletion (kg m-3 s-l) reaction yield: product formedsubstrate depleted (dimensionless) height i n t h e reactor (m) reactor dimensionless height, z/Z (dimensionless) total reactor height (m)

Greek Letters

P

partition coefficient at t h e solid particle-liquid interface (dimensionless) volumetric fraction of a phase (dimensionless) particle porosity (dimensionless) average substrate molecule diametedaverage pore diameter (dimensionless) density (kg m-3) liquid surface tension (kg s - ~ ) viscosity (kg m-l s-l) tortuosity factor (dimensionless)

particle sphericity (dimensionless) effectiveness factor (dimensionless)

48 7 Indices f g i

1 P S

sur 0

bulk phase gas gas-liquid interface liquid biocatalyst particle solid surface of t h e biocatalyst particle reactor inlet

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Abstract published in Advance ACS Abstracts, May 1, 1995.