4. SCALE-UP OF BIOREACTOR SYSTEMS

1. 4. SCALE-UP OF BIOREACTOR SYSTEMS

2. 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.

3.  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.

4. 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.

5. Volume (VL)  = Lab Scale Bioreactor VL1 = Pilot Scale Bioreactor VL2  = Large Scale Bioreactor VL3

6. 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.

7. 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

8.  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.

9.  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.

10.  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.

11.  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.

12. FIG. 4.3 HypotheticalYX/S vs. R data for different bioreactor volumes, if R were an “ideal” scale-up criterion.

13.  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.

14. 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.

15. FIG. 4.4 Independent Variables for a Bioreactor System.

16.  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.

17.  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

18. 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

19. For a given fermentation broth of density  and viscosity  P  n3Di5…………………(4.2) Also Pg/P = f (Na)

20. 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).

21. 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

22. 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).

23. 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.

24. 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)

25. 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.

26. 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 = (2R)(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)

27. 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.

28. 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)

29. 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

30. 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

31. 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.

32. 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.

33. At steady-state: QO2 X = KLa (CL* - CL) Which means that as KLa increases, X increases for given CL level and QO2.

34. Scale-up Examples: See Figures 4.5 and 4.6

35. 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].

36. 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].

37. 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].

38. 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].

39. 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].

40. 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.

41. 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].

42. 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].

43. 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.

44. 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)

45.  For aerobic fermentations, it is equally important to satisfy both criterion (4.10) and the oxygen supply requirements.

46. 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).

47. 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.

48.  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.

49. 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.

50.  Volumetric scale-up ratio = V2/V1 = 10,000/80 = 125  Impeller diameter scale-up ratio = Di2/Di1 = 5