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Chemical Reaction Engineering—Boston Downloaded from pubs.acs.org by SWINBURNE UNIV OF TECHNOLOGY on 11/26/18. For personal use only.
Considerations of Macromixing and Micromixing in Semi-Batch Stirred Bioreactors R.
K. BAJPAI* and M . REUSS
Technische Universität and Institut für Gärungsgewerbe und Biotechnologie, Seestrasse 13, D-1000 Berlin-65, Federal Republic of Germany
Simulations have been carried out to investigate the interactions of micro- and macromixing in stirred fermentors operated in semi-batch manner by considering the extremes of segregation in the macromixer of a two-environment model. Results suggest that the reactors with internal or external recycle, those with circulation time distribution (CTD) corresponding to a large number (N) of continuous stirred tank reactors in series, subject themselves to a more reliable scale-up. Particularly for highly viscous non-Newtonian fermentation broths, such reactors are shown to be better than those typified by smaller N.
Mixing i n r e a c t o r s i s c h a r a c t e r i z e d by two components, macromixing and micromixing. While macromixing i s e a s i l y measured and i t s importance i n the design and o p e r a t i o n o f r e a c t o r s i s undoubtably r e c o g n i z e d , micromixing presents even these days a r a t h e r a b s t r a c t s i t u a t i o n . Although the b a s i c concepts o f micromixing were developed and worked out more than two decades ago, i t s t i l l r e p r e s e n t s a very s p e c i a l i z e d domain. P a r t i c u l a r l y , i t s s i g n i f i c a n c e f o r s c a l e - u p o f r e a c t o r s remains to be f u l l y v i s u a l i z e d . The present work i s an attempt to i n v e s t i g a t e the i n t e r a c t i o n s between micro- and macromixings i n s t i r r e d r e a c t o r s i n v o l v i n g biochemical r e a c t i o n s and t h e i r i m p l i c a t i o n s with regards to the s c a l e - u p o f these r e a c t o r s . Importance o f mixing i n flow r e a c t o r s having biochemical r e a c t i o n s has been s t u d i e d i n the past (1.-4). The r e s u l t s o f these s t u d i e s , are however, not a p p l i c a b l e to fermentation systems operated i n batch or semi-batch manner and very few p u b l i c a t i o n s have addressed themselves to such systems {2). On the o t h e r hand, fermentations are most commonly c a r r i e d out i n batch or semi-batch systems i n which the r o l e o f mixing towards performances a t d i f f e r e n t s c a l e s o f o p e r a t i o n s i s not w e l l understood. P o s s i b l e reasons f o r t h i s l a c k o f i n t e r e s t have been a presumption o f p e r f e c t mixing i n non-flowing r e a c t o r s and the 1
Current address: University of Missouri, Department of Chemical Engineering, Columbia, MO 65211. 0097-6156/82/0196-0555$06.00/0 © 1982 American Chemical Society
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d i f f i c u l t i e s o f measurement even o f macromixing i n such systems. Recent advances by Bryant and o t h e r s (!5, 6) i n measurements o f c i r c u l a t i o n time d i s t r i b u t i o n s , CTD, t a k i n g advantage o f the r e c i r c u l a t i n g nature o f f l u i d flow i n s t i r r e d v e s s e l s , permit a c o u p l i n g o f mixing and r e a c t i o n k i n e t i c s i n these systems. In some of our p u b l i c a t i o n s (7_, 8, 9 ) , we have presented a scheme f o r such a c o u p l i n g i n which a case o f complete s e g r e g a t i o n (no micromixing) i n the r e c i r c u l a t i n g flows has been c o n s i d e r e d . In the present paper, the treatment has been extended to compare the i n f l u e n c e of the l i m i t s o f micromixing ( i . e . maximum mixedness and complete s e g r e g a t i o n ) corresponding to d i f f e r e n t CTDs upon the observed gross k i n e t i c s . Two Environment R e c i r c u l a t i o n Model Consider a s t i r r e d tank r e a c t o r having o n l y one a g i t a t o r . Due to the movement o f a g i t a t o r b l a d e s , l i q u i d i n i t s v i c i n i t y i s pushed away from i t and the d i s p l a c e d volume i s r e p l a c e d by l i q u i d from o t h e r p a r t s o f the s t i r r e d v e s s e l . As a r e s u l t o f continued a g i t a t i o n , a s i t u a t i o n i s c r e a t e d i n which l i q u i d i s c o n t i n u o u s l y r e c i r c u l a t e d from the i m p e l l e r to the bulk, o n l y to r e t u r n back to i t a f t e r some time. Since up to 70% o f energy i n t r o d u c e d i n t o the l i q u i d by the a g i t a t o r i s d i s s i p a t e d i n the c l o s e v i c i n i t y o f i m p e l l e r (10, 11), the system can be d i v i d e d i n t o two compartments: one c o n s i s t i n g o f the immediate s u r roundings o f the i m p e l l e r , known as the i m p e l l e r r e g i o n , and the other c o n s i s t i n g o f the r e s t of l i q u i d volume i n the v e s s e l , known as macromixer. Due to the very high energy d i s s i p a t i o n r a t e i n the i m p e l l e r r e g i o n , f l u i d passing through i t can be c o n s i d e r e d to be completely micromixed. T h i s r e g i o n i s , t h e r e f o r e , known as micromixer a l s o . Such a two environment model was f i r s t proposed by Manning et^ a/L (12) f o r s t i r r e d chemical r e a c t o r s . The volume o f micromixer i s assumed to be n e g l i g i b l e as compared to t h a t o f macromixer. F l u i d r e c i r c u l a t i n g through the macromixer has i n a c t u a l p r a c t i c e a d i s t r i b u t i o n o f c i r c u l a t i o n times (CTD) which can be measured d i r e c t l y by using the methods proposed by Bryant and Sadeghzadeh (5) and by Mukataka e t a l . (6) o r i n d i r e c t l y by the method used by Khang and Levenspiel~TjL3J· As o n l y a small p a r t o f the introduced energy i s d i s s i p a t e d i n the macromixer, the extent o f s e g r e g a t i o n between d i f f e r e n t f l u i d elements moving through i t i s u n c e r t a i n . Corresponding to each CTD, t h i s may take values c o n s t r a i n e d by the extremes o f complete s e g r e g a t i o n and maximum mixedness. The two environment model with i t s extreme cases has been s c h e m a t i c a l l y presented i n F i g u r e 1 f o r the case o f oxygen supply to v i s c o u s non-Newtonian fermentation broths. The case o f maximum mixedness corresponding to a given CTD has been simulated using a s t i r r e d - t a n k s - i n - s e r i e s c o n f i g u r a t i o n , each tank o f which has a zero degree o f s e g r e g a t i o n . Volumes of a l l the tanks have been assumed to be e q u a l . To be e x a c t , such a
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I I "ο §
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I s i °
•5.5
•s'i .s
s •2.
! §
I I .δ
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r e p r e s e n t a t i o n corresponds only to the case of 'sequential mixedness' because molecular d i f f u s i o n i s not p o s s i b l e between any two maximally-mixed s t i r r e d t a n k s , where as i n case of 'maximum mixedness' molecules having same l i f e expectation from any part of the e n t i r e system should be able to mix w i t h each other i n f i n i t e l y f a s t . However, due to r e c y c l i n g nature of systems under c o n s i d e r a t i o n here, i t i s most convenient to use such a c o n f i g u r a t i o n to represent the second extreme of mixedness. The case of complete segregation corresponding to any given CTD has been simulated using a d i s c r e t e s i m u l a t i o n procedure suggested by Bajpai and Reuss ( 7 ) . In t h i s c a s e , the f l u i d volume i n the macromixer i s d i v i d e d i n t o a number o f l i q u i d e l e ments of d i f f e r e n t ages, each of which c o n t r i b u t e s to the r e c i r c u l a t i n g stream according to the CTD. A l l these elements i n the macromixer remain completely segregated from each o t h e r . The methodology of s i m u l a t i o n i s discussed i n the o r i g i n a l p u b l i cation (7). For very f a s t k i n e t i c s l i k e t h a t of oxygen uptake by microorganisms, a q u a s i - s t e a d y s t a t e may be assumed. This assumption r e s u l t s i n a s i g n i f i c a n t ease of computations and has been d i s c u s s e d by Reuss and Bajpai ( 8 ) . Results S i m u l a t i o n s were c a r r i e d out f o r the case of simultaneous d i f f u s i o n and uptake of oxygen i n a viscous fermentation b r o t h . I t i s assumed t h a t oxygen t r a n s f e r takes place o n l y i n the v i c i n i t y of the i m p e l l e r , hence only i n the micromixer. A man date f o r such a handling of oxygen-uptake k i n e t i c s has been presented by B a j p a i and Reuss (8) and by Reuss e t a]_. ( 9 ) . Average oxygen uptake r a t e i n a h y p o t h e t i c a l clump of m i c r o b i a l mass i n which d i f f u s i o n and simultaneous consumption of oxygen takes place i s given by
= (-r) = η Q
%
max
(1)
fl
C
0
2
+
K
M
where η i s the e f f e c t i v e n e s s f a c t o r . For the case of M i c h a e l i s Menten type of k i n e t i c s and s p h e r i c a l geometry, a pseudoanal y t i c a l s o l u t i o n was proposed by Atkinson and Rahman (14) of the f o l l o w i n g type f o r η : tanh φ η = 1 1 =
Ψ
Ψ (
φ tanh φ φ
- 1 )
f o r Ψ1
tanh Ψ 1 (
tanh Ψ
(2)
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Stirred
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where φ i s 'Thiele modulus' and Ψ i s a 'general modulus' r e l a t e d to T h i e l e modulus and other operating parameters as
Ψ
=
— *
(3) %
+
*"J
%
/
K
m
"
1
π
(
1
+
%
/
Κ
μ
)
The assumptions behind such a r e p r e s e n t a t i o n of oxygen uptake k i n e t i c s i n a v i s c o u s fermentation broth and t h e i r e x p l a n a t i o n s are given by Reuss e t al_. (9). In Figures 2 and 3 are presented the r e s u l t s of s i m u l a t i o n s of the oxygen k i n e t i c s f o r two d i f f e r e n t mean c i r c u l a t i o n t i m e s . H e r e i n , the mean oxygen uptake r a t e s i n the macromixers are p l o t t e d as f u n c t i o n s of the average d i s s o l v e d oxygen c o n c e n t r a t i o n s . The parameter i n each f i g u r e i s the number of s t i r r e d v e s s e l s - i n - s e r i e s which c o n t r i b u t e to the c i r c u l a t i o n time d i s t r i b u t i o n . For the case of plug flow ( i . e . N= °°), the two cases of complete segregation and maximum mixedness are the same. For a l l other values of N, the performance of a maximum mixed r e a c t o r improves and t h a t of a completely segregated r e a c t o r d e t e r i o r a t e s as the value of Ν decreases. For a given mean c i r c u l a t i o n t i m e , τ , the d i f f e r e n c e between the two extremes of segregation decreases as Ν i n c r e a s e s . This i n f l u e n c e of the extent of segregation i s a strong f u n c t i o n of the mean c i r c u l a t i o n time - i t being stronger with l a r g e r c i r c u l a t i o n t i m e s . S i m i l a r trends of the i n f l u e n c e of l i m i t s o f segregation were observed f o r another m i c r o b i a l system too - that of growth of bakers' y e a s t upon glucose i n v o l v i n g appearance of glucose e f f e c t . D i s c u s s i o n and Conclusions Let us see i f the trends observed by these s i m u l a t i o n s are j u s t i f i e d i n the l i g h t of our c u r r e n t knowledge of chemical r e a c t o r s . The w e l l known l i m i t cases of zero and f i r s t order k i n e t i c s i n a CSTR and a PFR suggest t h a t 1) i n case of a f i r s t order r e a c t i o n , f o r the same average c o n c e n t r a t i o n , the o v e r a l l r e a c t i o n r a t e i s same f o r PFR as w e l l as f o r CSTR extreme c a s e s . In other words av
(CSTR)
av (CSTR)
no segregation av
k C
av
complete s e g r . (4)
2) i n case of a zero order r e a c t i o n , the o v e r a l l r e a c t i o n r a t e f o r the same average d i s s o l v e d oxygen c o n c e n t r a t i o n shows the f o l l o w i n g behavior
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Figure 2. Predicted gross oxygen uptake kinetics for different reactor circulation time distributions corresponding to a mean circulation time (τ) of 10 s.
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av (CSTR)
>
no s e g r e g a t i o n
(-r)
av PFR
>
av (CSTR) complete segr.
(5)
These r e s u l t s a r e obtained by averaging the c o n c e n t r a t i o n s and r e a c t i o n r a t e values over a l l the elements o f the corresponding r e a c t o r s . For zero order k i n e t i c s , such an a n a l y s i s leads t o Figure 4 wherein r e s u l t s a r e presented f o r a PFR and a completely segregated CSTR. .The case o f completely mixed CSTR i s t r i v i a l (a h o r i z o n t a l l i n e a t the maximum r a t e up t o C >0). av A comparison o f t h i s a n a l y s i s with the r e s u l t s shown i n F i g u r e s 2 and 3 p o i n t s t o the f a c t t h a t f o r our present k i n e t i c s , the behavior i s dominated by zero order r e a c t i o n r a t e . T h i s i s understandable t o o , c o n s i d e r i n g the very low values o f (=1.28 y m o l e s / l i t e r ) used i n our s i m u l a t i o n s . P o s s i b l y f o r any reason able value o f d i s s o l v e d oxygen c o n c e n t r a t i o n , esp. i n case o f segregated c a s e s , a zero o r d e r k i n e t i c s p r e v a i l s and the high oxygen requirements r e s u l t i n a very s h o r t d u r a t i o n o f f i r s t order k i n e t i c s before the uptake r a t e drops t o i n s i g n i f i c a n t v a l u e s . For the case o f maximum mixedness, however, both the zero and the f i r s t order k i n e t i c s c o n t r o l . A l a r g e number o f i n d u s t r i a l l y important fermentations i n v o l v e molds which have a h i g h l y v i s c o u s non-Newtonian c h a r a c t e r . These broths a r e very l i k e l y to show a segregated behavior d u r i n g r e c i r c u l a t i o n s . Hence, based upon the r e s u l t s o f s i m u l a t i o n s presented above, i t can be concluded t h a t the r e a c t o r s f o r such fermentations should be designed so as t o have a CTD c o r r e sponding as c l o s e l y as p o s s i b l e t o t h a t o f a PFR. Moreover, the r e s u l t s o f F i g u r e s 2 and 3 show t h a t the u n c e r t a i n t i e s o f mix edness ( a l t e r n a t i v e l y those o f the e x t e n t o f s e g r e g a t i o n ) a r e f a r more important f o r lower values o f Ν than f o r the l a r g e r ones. Since measurement and c o n t r o l o f degree o f s e g r e g a t i o n i s a d i f f i c u l t t a s k , scale-up o f s t i r r e d b i o r e a c t o r s having CTD c o r responding t o l a r g e Ν can be c a r r i e d out with higher confidence ( i n as much as o n l y the e f f e c t o f changed τ i s t o be accounted f o r , not t h a t o f the unknown changes i n degree o f s e g r e g a t i o n i n regions away from i m p e l l e r ) than those with small N. T h i s s i t u a t i o n i s t r u e r e g a r d l e s s o f the v i s c i o u s nature o f b r o t h s . A l s o the e s t i m a t i o n o f mean c i r c u l a t i o n time, τ, i s c a r r i e d out r e l a t i v e l y more e a s i l y and p r e c i s e l y than those o f N. For the purpose o f d e s i g n o f new b i o r e a c t o r s , i t , t h e r e f o r e , appears t h a t r e a c t o r s with narrow CTD l i k e the pressure r e c y c l e r e a c t o r o f ICI (15) o f f e r advantages with regards t o r e l i a b i l i t y o f s c a l e - u p , and a l s o i n c u r o p e r a t i o n a l b e n e f i t s f o r some systems (e.g. h i g h l y v i s c o u s non-Newtonian b r o t h s ) .
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Figure 4. Predicted observed kinetics for a zero order reaction in continuous stirred tank ( ) and plug flow configurations ( ; for two different mean residence times.
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Legend o f Symbols
C
average c o n c e n t r a t i o n i n the macromixer
a w
αν
C
n u
d i s s o l v e d oxygen c o n c e n t r a t i o n i n the bulk o f broth 2
k IC. Ν q Q Q
n u
n u
r e a c t i o n r a t e constant f o r a zero order k i n e t i c s Michael i s Menten constant f o r uptake of d i s s o l v e d oxygen number o f CSTRs i n s e r i e s f o r a given CTD average v o l u m e t r i c oxygen uptake r a t e
2 s p e c i f i c oxygen uptake r a t e 2 max maximum s p e c i f i c oxygen uptake r a t e
n u
2 (-r) ( "
r
)
a
X η Ψ Φ τ CSTR CTD PFR
w av
reaction rate average r e a c t i o n r a t e i n the macromixer biomass c o n c e n t r a t i o n effectiveness factor general modulus T h i e l e modulus average c i r c u l a t i o n time continuous s t i r r e d tank r e a c t o r c i r c u l a t i o n time d i s t r i b u t i o n plug flow r e a c t o r
Acknowledgments
T h i s work was supported by a grant o f the German M i n i s t r y o f Research and Technology, which i s g r a t e f u l l y acknowledged. Literature Cited 1. 2. 3. 4. 5.
6.
Chen, M. S. K.; AIChE Journal, 1972, 18, 849. Dohan, L. Α.; Weinstein, Η.; I & EC Fundamentals, 1973, 12, 64. Chen, G. K. C . ; Fan, L. T.; Erickson, L. E . ; Can. J . Chem. Eng., 1972, 50, 157. Tsai, B. T.; Fan, L. T . ; Erickson, L. E . ; Chen, M. S. K.; J. Appl. Chem. Biotechnol., 1971, 21, 307. Bryant, J.; Sadeghzadeh, S.; "Circulation Rates in Stirred and Aerated Tanks", paper F3, presented at the Third European Conference on Mixing, held at the University of York, England, between April 4-6, 1979. Mukataka, S.; Kataoka, H.; Takahashi, J.; J . Ferment. Technol., 1980, 58, 155.
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7.
8.
9.
10. 11. 12. 13. 14. 15.
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Bajpai, R. K.; Reuss, M.; "Coupling of Mixing and Microbial Kinetics for Evaluating the Performance of Bioreactors", poster paper at the 2nd European Conference on Biotech nology, held at Eastborne, England between April 6-10, 1981; Can. J . Chem. Eng. (in press). Reuss, M.; Bajpai, R. K.; "Oxygen Consumption in Filamentous Broths - An Approach Based Upon Mass and Energy Distri butions", paper presented at the 1981 Annual Meeting of American Chemical Society held in New York. Reuss, M.; Bajpai, R. K.; Berke, W.; "Effective Oxygen Con sumption Rates in Fermentation Broths with Filamentous Organisms", paper presented at the 2nd European Conference on Biotechnology, held at Eastborne, England between April 6-10, 1981; J . Chem. Technol. Biotechnol. (in press). Cutter, L. Α.; AIChE Journal, 1966, 12, 35. Möckel, H. O.; Chemische Technik, 1980, 32, 127. Manning, F. S.; Wolf, D.; Keairns, D. L . ; AIChE Journal, 1965, 11, 723. Khang, S. J.; Levenspiel, O.; Chem. Eng. S c i . , 1976, 31, 579. Atkinson, B.; Rahman, F . ; Biotechnol. Bioeng., 1979, 16, 221. Hines, D. Α.; "Proceedings of the 1st European Congress on Biotechnology", DECHEMA Monographien Nr. 1693 - 1703, Band 82 - Biotechnologie, Verlag Chemie, 1978, page 55.
Received April 27, 1982.
