DEFINITION OF SCALE-UP: Study of problems associated with the transfer of experimental data from laboratory and pilot-plant equipment to large scale industrial equipment.
The “ideal” scale-up criterion is that parameter which has the same numerical value as the volumes of the geometrically similar bioreactors increase in size.
First scale-up criterion is the Preservation of Geometrical Similarity: HL1/Dt1 = HL2/Dt2 =….. = HL3/Dt3…....(4.1) FIG. 4.1 Geometric Scale-up of Bioreactors.
Volume (VL) = Lab Scale Bioreactor VL1 = Pilot Scale Bioreactor VL2 = Large Scale Bioreactor VL3
EXAMPLE No.1 FOR SCALE-UP For a given Medium Composition Temperature pH We want to maximize the cell yield factor YX/S. We start with a 10 L Laboratory scale bioreactor unit and we perform optimization experiments at different volumetric rates of oxygen supply, R.
Where: R = KLa (CL* - CL) = (moles O2)/(L)(hr) YX/S = Cell to substrate yield Factor based on glucose = (g CDW yeast cells)/ (g glucose used) Using the 10 L laboratory scale bioreactor we carry out experiments and we get the following hypothetical results shown in Fig. 4.2
QUESTION: When we scale-up to 50,000 L bioreactor system, are we going to get the same YX/S vs. R relationship? FIG. 4.2 10 L Bioreactor Hypothetical Fermentation Results for Yeast Aerobic Growth. Yeast Cell Yield vs. Rate of Oxygen Transfer.
It depends on what scale-up criteria we use when we go from 10 L to 50,000 L bioreactor systems. If the volumetric rate of oxygen transfer R were a true scale-up criterion, then the relationship between YX/S vs. R shown in Fig. 4.1 for the 10 L bioreactor should be exactly the same for any bioreactor size.
For example, if experiments were done with bioreactors of 10 L, 1,000 L, 10,000 L, 50,000 L or more, and the yield YX/S was measured at different R, then the YX/S vs. R data for each bioreactor volume should be the same and independent of bioreactor volume.
This would have been true only if R were a true scale-up criterion. This hypothetical situation is shown in Fig. 4.3, where the data are the same for different bioreactor volumes.
FIG. 4.3 HypotheticalYX/S vs. R data for different bioreactor volumes, if R were an “ideal” scale-up criterion.
In reality scale-up of laboratory and pilot- plant data to commercial size industrial bioreactors is very difficult and complicated. No actual data or correlation exist for scale- up.
Different people use different scale-up criteria to design commercial size bioreactor systems. Also in industry there are a lot of trade secrets on scale-up of bioreactors, and very few published results exist in the literature.
Scale-up criterion in general are a function of independent variables n, Di, DT, HL, Qg, , . Several people used several different scale-up criteria. Once a criteria is selected, then you make sure that the numerical value of this scale-up criterion is the same for the small and large size bioreactor.
Scale-up criterion small bioreactor = Scale- up criterion large bioreactor. Example: if we select the volumetric mass transfer coefficient KLa to be the scale-up criterion, then we make sure that when we scale-up we have: (KLa) small bioreactor = (KLa) large bioreactor
Different Important DEPENDENT variables used in scale-up. 1) Agitation Power, P or Pg From the Np vs. NRe figure, at turbulent flow conditions: Np = constant = Pgc/n3Di5
For a given fermentation broth of density and viscosity P n3Di5…………………(4.2) Also Pg/P = f (Na)
2) Rate of Liquid Pumping by the Impeller, RL • An Impeller serves a dual function of pumping around of liquid inside the bioreactor vessel, and local turbulent micromixing. Consider an impeller of diameter Di at a rotational speed n (min-1).
During one revolution the impeller “pumps” around a liquid of volume VL, which is proportional to the third power of the impeller diameter Di, i.e. the liquid volume, VL “swept” by the impeller. VL Di3
Therefore the rate RL at which the impeller pumps around the liquid is proportional to n .VL RL n Di3……………………….(4.3) Where: RL = (m3 liquid pumped)/(min).
Therefore, if for a given rotational speed n, the impeller diameter Di is increased by a factor of two, then the liquid pumping rate within the vessel, RL, will increase by a factor of 23. i.e. 8 times more. This demonstrates the powerful effect of impeller diameter on the liquid pumping rate, and how this affects the bulk mixing within the bioreactor vessel.
3. Un-gassed Power Per Unit Liquid Liquid Volume Delivered by the Impeller (P/VL). For turbulent mixing conditions according to Eq. 4.2: P n3 Di5 Also VL Di3 Therefore, P/VL n3 Di3…………(4.4)
For example, if the values of n and Di are increased by a factor of 2 each, then the un- gassed power per unit liquid volume is increased by a factor of (23)(22) = 32 more. This shows the powerful effect of increasing both n and Di.
4. Impeller Tip Velocity, Vt The peripheral tip velocity, Vt, of the impeller diameter Di, and the rotational speed n (s-1), is given by: Vt = (2R)(n) = (Di)(n) Where: Vt = impeller tip velocity (m/s) The tip velocity of the impeller represents the maximum velocity. Vt n Di…………………………(4.6)
At the tip of the rotating impeller of diameter Di we have maximum shear rate, (s-1). Shear rate = du/dx = (m/s)/(m) = s-1 and x is the distance away from the tip of the impeller. In order to calculate the exact value of shear rate, , we need to know the liquid velocity profile distribution close to the impeller tip.
5. Impeller Reynolds Number, NRe. The Reynolds number based on impeller diameter is given by: NRe = n Di2/. Therefore, for a given fermentation broth of given constant physical properties and , we have: NRe n Di2…………………………….(4.7)
In general, the choice of scale-up criterion depends on two considerations: a) Nature of the fermentation and morphology of the microorganism. aerobic anaerobic fungi single cell microorganisms mammalian cells plant cells exothermic fermentation Thermophilic microorganisms viscous or non-viscous fermentation broth Newtonian or non-Newtonian broth
During scale-up, what is the objective parameter of fermentation we wish to optimize (maximize). yield of product or biomass cell concentration product concentration product activity volumetric bioreactor productivity
4.1 SCALE-UP CRITERIA USED • Different scale-up criteria have been used depending on the type of fermentation and the objective of optimization. • The first assumption is geometric similarity between bioreactor vessels of different sizes as shown in Eq. 4.1. • However, in some scale-up cases geometric similarity is not preserved. This makes scale- up much more complex.
Volumetric Mass Transfer Coefficient, KLa (KLa)1 = (KLa)2…...........………...(4.8) Where: 1 = small scale bioreactor 2 = large scale bioreactor This criterion is usually applied to aerobic systems where oxygen concentration is most important and affects metabolism of the microbial cell.
At steady-state: QO2 X = KLa (CL* - CL) Which means that as KLa increases, X increases for given CL level and QO2.
FIG. 4.5 The effect of sulfite oxidation values on the yield of baker’s yeast. [Adopted from S. Aiba, A.E. Humphrey and N.F. Millis. “Scale-up”. In Biochemical Engineering, 2nd Ed., Academic Press, Inc., New York (1973) 205].
FIG. 4.6 The effect of sulfite oxidation value on the yield of ustilagic acid. [Adopted from S. Aiba, A.E. Humphrey and N.F. Millis. “Scale-up”. In Biochemical Engineering, 2nd Ed., Academic Press, Inc., New York (1973) 206].
FIG. 4.7 Comparison of the yields of streptomycin at different mass transfer coefficients of oxygen applying in vessels of different sizes. [Adopted from S. Aiba, A.E. Humphrey and N.F. Millis. “Scale-up”. In Biochemical Engineering, 2nd Ed., Academic Press, Inc., New York (1973) 206].
FIG. 4.8 Comparison of the yields of penicillin at different mass transfer coefficients of oxygen applying in vessels of different sizes. [Adopted from S. Aiba, A.E. Humphrey and N.F. Millis. “Scale-up”. In Biochemical Engineering, 2nd Ed., Academic Press, Inc., New York (1973) 207].
FIG. 4.9 Yield of vitamin B12 in different sized fermentors with different values of mass-transfer coefficient. [Adopted from S. Aiba, A.E. Humphrey and N.F. Millis. “Scale-up”. In Biochemical Engineering, 2nd Ed., Academic Press, Inc., New York (1973) 207].
2. Power Per Unit Liquid Volume, (P/VL) (P/VL)1 = (P/VL)2…..........………...(4.9) Where: 1 = small scale 2 = large scale • The majority of aerobic fermentor systems have been scaled-up on the KLa basis and very few on the P/VL basis. Example: See Figures 7.3 and 7.4.
FIG. 7.3 Effect of different values of power input on the yield of penicillin with different fermentation conditions. [Adopted from S. Aiba, A.E. Humphrey and N.F. Millis. “Scale-up”. In Biochemical Engineering, 2nd Ed., Academic Press, Inc., New York (1973) 203].
FIG. 7.4 Effect of different values of power input on the yield of novobiocin in fermentors fitted with different-sized impellers. [Adopted from S. Aiba, A.E. Humphrey and N.F. Millis. “Scale-up”. In Biochemical Engineering, 2nd Ed., Academic Press, Inc., New York (1973) 203].
3. Tip Velocity of the Impeller, Vt This scale-up criterion is used for shear sensitive fermentations where a maximum shear rate is allowed to prevent possible irreversible shear damage to the cells growing inside the bioreactor. In some cases where the cells have a tendency to form dense flocks, it is necessary to provide at least the minimum shear rate required to break-up these flocks.
This is true in some fungal fermentations where the mycelia of these fungi have a tendency to form hard flocks if the shear rate is below the minimal required to prevent flock formation. The scale-up criterion for equal impeller tip velocity is shown in Equ. 4.10. (n Di)1 = (n Di)2 ..……………(4.10)
For aerobic fermentations, it is equally important to satisfy both criterion (4.10) and the oxygen supply requirements.
4. Aeration Number, Na • If we apply this scale-up criterion, it means that the aeration numbers for the small and large size bioreactor vessels is the same. (Na)1 = (Na)2…………………….(4.11) The aeration number is given by: Na = Q/(n Di3) = Q/(n Di)(Di2) which means that Na is also a function of the tip velocity Vt (i.e. n Di term).
5. Impeller Reynolds Number, NRe • This criterion is used sometimes when the heat transfer rate from the fermentation broth to the cooling coils inside the bioreactor vessel is of paramount importance. • This is especially important for thermophilic microorganisms. The heat transfer coefficient is a function of impeller Reynolds number.
For this scale-up criterion the impeller Reynolds numbers must be equal for the small and large scale bioreactor (NRe)1 = (NRe)2 ………………….(4.12) There are empirical correlations for the heat transfer coefficient h as a function of Reynolds number in stirred tank vessels.
4.2 EXAMPLES OF SCALE-UP BY S.Y. OLDSHUE Oldshue worked out relationships between properties for scale-up from 80 L to 10,000 L bioreactor, which was not aerated but agitated with a six blade turbine impeller. Standard geometry vessel was used and geometric similarity was applied.
Volumetric scale-up ratio = V2/V1 = 10,000/80 = 125 Impeller diameter scale-up ratio = Di2/Di1 = 5