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On-Line Estimation of the State of Biochemical Reactors G R E G O R Y STEPHANOPOULOS and KA-YIU
SAN
California Institute of Technology, Department of Chemical Engineering, Pasadena, CA 91125
E s t i m a t i o n algorithms a r e presented f o r the estima t i o n of the s t a t e of biochemical r e a c t o r s from the o n - l i n e measurement of O2 and CO2 c o n c e n t r a t i o n . The proposed approach combines macroscopic and e l e mental balances on the r e a c t o r w i t h s t a t e - o f - t h e - a r t adaptive e s t i m a t i o n t h e o r i e s . Experiments and simu l a t i o n s show that estimates in e x c e l l e n t agreement w i t h the t r u e values can be obtained without using any growth models and both under t r a n s i e n t and steady state operating conditions. Most m i c r o b i a l c u l t u r e s are very s e n s i t i v e to s m a l l changes of the environment i n which they grow and t h i s r e s u l t s i n r a t h e r s t r i c t o p e r a t i n g c o n d i t i o n s f o r the m a j o r i t y o f the fermentation processes. Despite t h i s f a c t and the almost complete l a c k o f proper sensors f o r the o n - l i n e measurement of the s t a t e v a r i a b l e s and c u l t u r e parameters o f a fermentor, i t i s only r e c e n t l y that a number of s t u d i e s have been c a r r i e d out on the subject of s t a t e e s t i m a t i o n and c o n t r o l of biochemical r e a c t o r s . There are v a r i o u s reasons f o r t h i s delay, the prime one p o s s i b l y being the absolute domination of the batch r e a c t o r i n the fermentation i n d u s t r y and the subsequent l a c k of any need o r p o s s i b i l i t y o f c o n t r o l . Recent advances, however, on s e v e r a l f r o n t s o f biochemical technology suggest that t h i s p i c t u r e i s very l i k e l y to change i n the f u t u r e w i t h the i n t r o d u c t i o n of more advanced r e a c t o r c o n f i g u r a t i o n s and the requirement of c o n t r o l l e r s more s o p h i s t i c a t e d than the conven t i o n a l r e g u l a t o r s p r e s e n t l y i n use, such as, temperature, pH and d i s s o l v e d oxygen c o n t r o l l e r s . The e f f e c t i v e n e s s o f these c o n t r o l schemes w i l l depend to a great extent on how a c c u r a t e l y the v a r i o u s s t a t e v a r i a b l e s and c u l t u r e parameters can be estimated o n - l i n e and under a v a r i e t y of o p e r a t i n g c o n d i t i o n s . Several aspects of the general estima t i o n problem have been s t u d i e d i n s i t u a t i o n s r e l a t e d to chemical r e a c t o r s Ο , 2 ) . With biochemical r e a c t o r s , however, the estima t i o n problem i s c o n s i d e r a b l y more i n v o l v e d because o f the growth 0097-6156/82/0196-0155$06.00/0 © 1982 American Chemical Society Wei and Georgakis; Chemical Reaction Engineering—Boston ACS Symposium Series; American Chemical Society: Washington, DC, 1982.
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CHEMICAL REACTION ENGINEERING
r a t e model Inadequacy and l a c k of proper sensors. More d e t a i l e d s t r u c t u r e d models f o r growth and product formation can be cons t r u c t e d , but t h e i r complexity and the u n c e r t a i n t y introduced by the l a r g e number of model parameters precludes t h e i r use f o r the e s t i m a t i o n of the s t a t e v a r i a b l e s or any c o n t r o l purposes. Also, there are no commercially a v a i l a b l e sensors f o r the d i r e c t measurement o f the s t a t e v a r i a b l e s o n - l i n e . T h i s i s a c o n s i d e r a b l e departure from the s i t u a t i o n i n chemical r e a c t o r s where accurate temperature measurements can be obtained and are, i n most cases, s u f f i c i e n t f o r the e s t i m a t i o n of the r e a c t o r s t a t e . Finally, s i n c e the majority o f the b i o r e a c t o r s p r e s e n t l y i n use i n the fermentation i n d u s t r y are unsteady-state r e a c t o r s , an e s t i m a t i o n theory should be a p p l i c a b l e both under t r a n s i e n t and steady-state o p e r a t i n g c o n d i t i o n s to p r o v i d e estimates of the s t a t e v a r i a b l e s and c u l t u r e parameters without making use o f growth models and from a l i m i t e d number of measurements. The p r e s e n t a t i o n o f a gene r a l framework which achieves t h i s o b j e c t i v e by u t i l i z i n g a v a i l able macroscopic and elemental balances and a p p r o p r i a t e , s t a t e - o f t h e - a r t e s t i m a t i o n techniques i s the s u b j e c t of t h i s paper. The
Estimation
Problem
Measurements. U n t i l r e c e n t l y , s t a t e e s t i m a t i o n r e l i e d on a r a t h e r i n v o l v e d chemical a n a l y s i s and the d i r e c t o f f - l i n e measurement of the biomass c o n c e n t r a t i o n (dry weight, c e l l counts and t u r b i d i t y ) . The r e c o g n i t i o n o f the need f o r o n - l i n e measurements spurred a n o t i c e a b l e a c t i v i t y on the development o f a p p r o p r i a t e sensors. Most of these sensors, however, are not steam s t e r i l i z able and seem to s u f f e r from convergence and slow response problems, and they are not as y e t f u l l y t e s t e d and commercially a v a i l able. Consequently, the e s t i m a t i o n s t u d i e s proposed h e r e i n w i l l be based on the o n - l i n e measurement o f the O2 and CO2 concentrat i o n s i n the a i r stream f l o w i n g through the b i o r e a c t o r , because the corresponding sensors are commercially a v a i l a b l e and are a l s o c h a r a c t e r i z e d by f a s t response and high r e l i a b i l i t y . Other sens o r s , such as f o r d i s s o l v e d oxygen, pH and temperature, are a l s o a v a i l a b l e and t h e i r use, i n connection w i t h the e s t i m a t i o n o f add i t i o n a l s t a t e v a r i a b l e s and c u l t u r e parameters, w i l l be discussed i n a later section. Balances. The measurements of the O2 and CO2 concentrations i n the gas stream a t the entrance and e x i t o f the b i o r e a c t o r can be u t i l i z e d by making a macroscopic balance over the b i o r e a c t o r . Thus, i f R i s the t o t a l r a t e o f growth ( i n gr biomas/cm »s), V the r e a c t o r volume and Q » ^ Q Q ^ biomass y i e l d s w i t h respect to O2 3
Y
2
2
T
IE
and CO2, r e s p e c t i v e l y , i n gr biomass formed/gr o f 0 2 ( C 0 2 ) consumed (produced), and Q. , Q are the volumetric flow r a t e s at the in out entrance and e x i t of the b i o r e a c t o r , the macroscopic balance yields : fc
Wei and Georgakis; Chemical Reaction Engineering—Boston ACS Symposium Series; American Chemical Society: Washington, DC, 1982.
14.
STEPHANOPOULOS AND SAN
Biochemical Reactors
157
E i t h e r o f the above equations can be used f o r t h e e s t i m a t i o n o f R provided that the y i e l d s and Q Q a r e constant, an assumption Y
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2
which i s questionable f o r a l a r g e number o f fermentations and very l i k e l y not v a l i d a t the v a r i o u s phases o f growth o r under t r a n s i e n t c o n d i t i o n s . This problem, however, can be bypassed by coup l i n g w i t h the above equations the f o u r elemental balances f o r C, Η, 0 and Ν which allows f o r the continuous e s t i m a t i o n o f the y i e l d s and, t h e r e f o r e , R. The b a s i c f e a t u r e o f t h i s approach, a l ready employed i n v a r i o u s i n v e s t i g a t i o n s (5-9), i s to represent the process o f growth by a chemical r e a c t i o n i n which s u b s t r a t e i s converted, i n the presence o f oxygen and ammonia, t o biomass, carbon d i o x i d e and water, according to the r e a c t i o n (assume i n i t i a l l y that no product i s formed):
a G
H
+
x y°z
b
carbonenergy source
°2
+
C N H
oxygen
3
*
Η
Ν
°α Β°γ
