The agitation system in the bioreactor provides the liquid motion that enables many different tasks to be fulfilled. An example of a typical stirred bioreactor is shown in diagrammatic form in Fig. 5.1. It is important to understand the interaction between the fluid motion, the agitator speed, and the power input into the bioreactor and these tasks. It is also necessary to know how a change of scale affects these relationships. Many of these aspects can be studied without carrying out a specific bioprocess and these physical aspects most relevant to bacterial fermentations are listed in Table 5.1. Table 5.2 sets out those aspects that are specific to the organism being grown and will usually be different for each case. The more important of these aspects with respect to scale-up are discussed later.
The physical aspects in Table 5.1 have been discussed extensively for conditions relevant to a wide range of organisms elsewhere (Nienow,
TABLE 5.1 Physical aspects of the agitation/agitator requiring consideration (Nienow, 1998)
Unaerated power draw (or mean specific energy dissipation rate ex W/kg) Aerated power draw (or aerated (§T)g W/kg) Flow close to the agitator-single phase and air-liquid Variation in local specific energy dissipation rates ex W/kg Air dispersion capability Bulk fluid- and air-phase mixing
TABLE 5.2 Biological aspects that are system specific (Nienow, 1998) Growth and productivity
Nutrient and other additive requirements including oxygen CO2 evolution and RQ Sensitivity to O2 and CO2 concentration pH range and sensitivity Operating temperature range Shear sensitivity
1996,1998; Nienow and Bujalski, 2004). Here, their relevance to microbial fermentations for which the viscosity essentially does not go much higher than that of water is discussed, for example bacteria and yeast. Thus, viscous polysaccharide and filamentous systems are excluded from consideration in this chapter. With such low viscosities, the flow in the fermenter is turbulent from a 5-liter bench bioreactor to the largest scale, that is Reynolds number, Re = pLND2/m > ^104 where pL is the growth medium density (kg/m3), m is its viscosity (Pa s), D is the impeller diameter (m), and N is its speed (rev/s). For scale-up purposes, as long as the flow is turbulent, the actual value of the Reynolds number does not matter and turbulent flow theories can be used to analyze the fluid mechanics in the bioreactors across the scales. The topics listed in Table 5.1 will be considered first for such flows.
1. Mass transfer of oxygen into the broth and carbon dioxide out
The transfer of oxygen into a fermentation broth has been studied since the 1940s when ''submerged fermentations'' were first established. The topic was reviewed by Nienow (2003). The overall oxygen demand of the cells throughout the batch or fed-batch fermentation must be met by the oxygen transfer rate and the demand increases as long as the number of cells is increasing. Roughly, for every mole of O2 utilized, 1 mole of CO2 is produced, that is the respiratory quotient, RQ « 1 (Nienow, 2006). Thus, a maximum oxygen transfer rate must be achievable and this rate depends on the mass transfer coefficient, kLa (1/s), and the driving force for mass transfer, AC, since
The value of kLa is similar for both O2 transfer from air to the broth and CO2 from it. For oxygen transfer, the driving force conceptually is the difference between the oxygen concentration in the air bubbles and that in the broth, which must always be held above the critical dO2 value throughout the fermenter for the duration of the process. In a similar way, the dCO2 must be kept below that which will lead to a reduction in fermentation rate or productivity.
It has been shown many times (Nienow, 2003) that in low-viscosity systems, kLa is only dependent on two parameters. These are, first, the total mean specific energy dissipation rate imposed on the system (eT)g (W/kg) and, second, vs (m/s), the superficial air velocity [=(vvm/60) (volume of broth)/(X-sectional area of the bioreactor]. (eT)g and vs together must be sufficient to produce the necessary kLa where kLa = A(ex)g (vs)b (5.2)
This equation applies independently of the impeller type and scale, and a and b are usually about 0.5 ± 0.1 whatever the liquid. On the other hand, A is extremely sensitive to growth medium composition (Nienow, 2003) and the addition of antifoam which lowers kLa or salts which increase it may lead to a 20-fold difference in kLa for the same values of (eT)g and vs. Typical values of (eT)g are up to ^5 W/kg and for the airflow rate about 1 volume of air per volume of growth medium (vvm). Since the value of kLa is similar for both O2 and CO2 transfer, provided scale-up is undertaken at constant vvm (or close to it), the driving force for transfer in of O2 and transfer out of CO2 will remain essentially the same across the scales. In this case, since vvm scales with fermenter volume and vs scales with its cross-sectional area, vs increases. There is some debate as to whether (eT)g should include a contribution from the sparged air [~vs g where g is the acceleration due to gravity (9.81 m2/s)], which only becomes significant on scale-up at constant vvm. This approach should also eliminate problems with high dCO2 on scale-up (Nienow, 2006).
The oxygen uptake rate (OUR, in mol O2/m3/s) largely determines the metabolic heat release Q (W/m3) (RQ « 1) which is proportional to it (Van't Riet and Tramper, 1991), that is
This cooling load has to be removed by heat transfer at an equivalent rate given by:
where U is the overall heat transfer coefficient (which is hardly affected by the agitation conditions), AO is the difference between the temperature of the cooling water and the broth temperature (it being critical to control the latter), and A is the heat transfer area available. At the commercial scale, heat transfer is often a problem as Q scales with the volume of the reactor, that is, for geometrically similar systems with T3 (bioreactor diameter, T m) while cooling surface area scales with T2. Hence, on the large scale for such systems, cooling coils are often required and sometimes cooling baffles. The inability to meet the cooling requirements at the large scale [especially, e.g., in high cell density (>50 g/liter dry cell weight) fed-batch fermentations] is a very serious problem because it is extremely expensive to resolve.
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