- Email: [email protected]
Online monitoring of fermentation processes
115
Applications
Online Monitoring of Fermentation Processes J a n A. S p r i e t Belgian National Science Foundation, University of Gent, Coupure Links 533, 9000 Gent, Belgium In biotechnology, few online measurements of biological variables are available. This fact hampers effective monitoring and control in the fermentation field. A novel approach to this is the use of a computer to combine outputs of online sensors for physical and chemical parameters to estimate directly otherwise unaccessible biological quantities like biomass. Here, a sensor configuration is presented for the online computation of the oxygen uptake rate. The equations that have to be implemented on the digital machine are derived and a case study on the fermentation of the antibiotic Gramicidine-S is performed and discussed. The experiments indicate that for a major part of the growth and fermentation period, the computer is suitable for the evaluation of the biomass based on oxygen uptake estimates. Consequently, the process can be monitored online.
Keywords. Biotechnology, net-effect sensor, measurement, fermentation process, online monitoring, oxygen uptake rate, biomass estimate, sensor configuration.
Jan A. Spriet received in 1973 an engineering degree in electrical engineering from the University of Ghent. He obtained an Union Carbide grant and became an ITT-fellow during the academic year 1973-74. In 1974 he received an MS in Electrical Engineering from the Massachusetts Institute of Technology, Cambridge U.S.A. Since 1975, he has been engaged in research towards the application of mathematical and engineering tools in biology at the Belgium National Science Foundation. In 1978, he received a NATO. grant for research as a Visiting Scholar at the University of California Los Anzeles. His current research interests are in pattern recognition, system structure characterization, modeling, identification and control of biochemical and fermentation processes. North-Holland Publishing Company Computers in Industry 2 (1981) 115-121
0166-36 ! 5 / 8 1 / 0 0 0 0 - 0 0 0 0 / $ 0 2 . 5 0 © 1981 North-Holland
1. Introduction Micro-organisms have been used for the benefit of men for a long time. Since early history, microbial phenomena have played their role in the context of certain food and beverage preparations. A much more recent development, but one of greater importance, has been the production of many enzymes and antibiotics along fermentative process patterns. Due to several new factors in our society, such as increased shortage and often difficult supply of fossile fuel and the presence of large amounts of waste, the relevance of many fermentations is growing steadily; and it is to be expected in the near future that cost-benefit analyses will start to indicate the economic feasibility of the microbial production for certain chemicals. Based on these more general considerations the future of the field looks certainly bright. It has to be recognized, however, that the engineering capability to control the processes is still limited: the fermentations are performed in an extremely traditional way; they require a considerable amount of skill and manual intervention; and many operation guidelines are based on past experience or small experiments. A typical example of this unsatisfactory state of the engineering art is the lack of techniques and sensors to monitor the process online. It is well known that the biomass is an important process variable. For an online estimate of that variable, out of the classic techniques, only the evaluation of the optical density can be taken into consideration. For many fermentations, there are factors, like color, particles in the broth, etc., that may interfere so that the estimate is poor or simply has no quantitative value. Faced with the pecularities of the situation, one can easily imagine that the digital machine, as a powerful tool in process engineering, could play an important role in biotechnology. It is another proof of the traditional approach, that the computer has only gradually been accepted in the last decade [1]. It has been recognized only very recently that one of the most promising areas is concerned with the use of
116
Applications
the machine as a net-effect sensor [2,3,4]. As many biological variables cannot be measured directly, it may perhaps be possible to correlate these variables with quantities obtained after computation out of measurements taken by on-line sensors for physical variables. In the paper the computation of the oxygen uptake rate as a net-effect sensor is considered. The concept has been mentioned before [5,6,7], but few details about the engineering aspects are available and few experimental results have been presented. A typical sensor configuration is presented in Section 2, and a digital machine turns out to be an important part of it. In Section 3, the net-effect sensor formula for the computer is derived. All assumptions are clearly stated. The derivation indicates under which conditions the sensor configuration is sufficiently elaborate and for which processes the approach is likely to give acceptable results. Finally in Section 4, the results are given.
2. Sensor Configuration The metabolic activity of a large number of microorganisms is influenced and often controlled by the oxygen conditions within the fermentor. The Oxygen Uptake Rate, OUR ( t ) - consequently, is a key variable linked to the biological activity of the process. As will be seen in the sequel, the quantity can be computed online with a digital machine. The phenomena, related to the oxygen transport, are quite complicated. Usually, an air stream is sent through the fermentor vessel, which is heavily stirred to break up large gas bubbles. Oxygen diffuses across the gasliquid interface to the broth. The intense mixing activity of the stirrer renders the concentration within the fluid homogeneous. The oxygen molecules cross the walls of the micro-organisms and are consumed mainly for energy regeneration in the ADPATP pool. The exit gas, leaving the vessel, will be poor in oxygen but may have been enriched or polluted with gases resulting from the metabolic activity of the cells. In most of the cases, carbon dioxide will be the only waste product of nutrient breakdown. The oxygen uptake rate can be obtained in a sensor configuration shown in Fig. 1. As many of the measurement devices are quite expensive, the number of sensors is kept minimal, It will be shown in Section 3, that a number of assumptions have to be made to obtain a valid estimate.
Computers in Industry sensors
;;r~cess
L-
i
t
C
i 4oo
t.....
Fig. 1. Sensor Configuration.
The most important measurement units are: • A mass flowmeter on the inlet, with a temperature and pressure independent flowrate reading in Standard Liters Per Second, SLPS Fir(t). • An oxygen analyzer, often of the paramagnetic type. It indicates a partial pressure, although it is calibrated in volumetric percentage o f oxygen, tm %02(t) = av (t). • A carbondioxide analyzer, mostly based on an infrared adsorption measurement. The output relates to a gas concentration but the sensor is calibrated in volumetric percentage o f carbondioxide, %CO2 = rm
b v (t).
The first gas analyzer is only pressure dependent, as the housing is kept at constant temperature. The second one is dependent on pressure and temperature. Consequently, for a precise evaluation, one needs also: • A sensor for ambient temperature: T(t), K. • A sensor for atmospheric pressure: p(t), Pa. Finally the oxygen content of the fermentor liquid may vary. An estimate of the dissolved oxygen level in the broth can be obtained from an electrode. A Dissolved Oxygen unit coupled to a silver-lead electrolytic probe system yields %DO(t). All devices give an instantaneous output or an output with a small lag. As will be seen in the sequel, the evaluation of the Oxygen Uptake Rate is quite involved and a computer is required for fast online computation. The output signals can be sampled and fed into a digital machine for further processing.
Computers in Industry
J.A. Spriet / Fermentation Processes
117
over the fermentor volume. One can define the Total
3. The Net-Effect Sensor Formula
Oxygen Uptake Rate TOUR(t), kgO2/sec:
A more rigorous derivation of a useful formula for the Oxygen Uptake Rate (OUR) requires different steps. First, the important quantities have to be defined in a more careful way. 3.1. The Fermentor Model
In order to obtain a useful equation, a lumped macroscopic point of view has to be taken. In fact, the local oxygen uptake r a t e - our(r, t), kgO2/sec. m 3 and also other gas exchanges like the carbondioxide release rate, c02rr(r, t), kgCO2/sec, m 3, at the gas-liquid interface are very erratic functions of space and time due to turbulent phenomena in the liquid. These functions can be smoothed by considering the macroscopic quantities: b-fiT(r, t), and c~22rr(r, t), defined as follows: our(r, t) = ~1 " S1 f J o u r ( r , t ) d V " dt
(3,1)
c o T ( r , t) = 1 " 4
(3.2)
V
(fco2rr(r, t ) d V ' d t
/--~oa
r: point vector of location.
t: time. V: small neighbourhood for r of the order of the gas bubble size. A: small time interval of the order of the transition time in the liquid. f: integration. In the same manner macroscopic quantities b-gg*(r, t) and ~ * ( r , t) can be defined for gas exchanges at the cell walls. Then, the contents of the fermentor is thought to be composed of three phases: a biomass phase, liquid phase, and gas phase - see Fig. 2. Since only a lumped model for the fermentor is used, all macroscopic variables can be integrated
TOUR(O = f ~ ( r , t) d V vf
Vr: fermentor liquid volume. Equations of the same type can be used to define the Total (Carbon dioxide Release Rate at the gasliquid interface TCO2RR(t), the gas exchange quantities at the cell walls: TOUR*(t) and TCO2RR*(t), the total amount of a certain gas A in the liquid phase Q(A) and in the gas phase P(A), and the mass input and output flow rates for a gas A: F~(A) and F~g(A) kgA/sec., respectively (Fig. 2). 3.2. Mass Balances
As all variables have hitherto been defined as masses or mass flow rates, it is easy to write down a number of mass balances concerning the lumped fermentor model (Fig. 2). For further use, the following equations are important: • A mass balance )'or the inlet mass f l o w rate; the air itself is made up of oxygen, carbon dioxide, water vapour and inert gases, with nitrogen as the major component: F~ = F~(O2) + F~(CO2) + F~(H20) + F~tN2)
t 0 UR
(3.4)
• A mass balance ]br the mass f l o w rate at the outlet:
F~ = Fff(O2) + Fff(CO2) + F~(H20)+ F~(N=)
(3.5)
• A mass balance f o r the gas contents in the fermentor:
P = P(O2) + P(CO2) + P(H20) + P(N2)
(3.6)
• A mass balance ]'or the inert gases, mostly nitrogen
in the gas phase. It is to be noted that these gases are not consumed and not produced by the microorganisms. dP(N2) - F~(N2) - F°(N2) dt
GAS-PtIASE
(3.3)
(3.7)
[ T CO2 R R
• A mass balance f o r the oxygen in the gas phase: LIQUID-PHASE I 1 T 0 C R* T
CO2 R P~
dP(O:) _ F~(O2) - F~(O2) - TOUR dt
Fo g
T Fig. 2. Lumped Model for Fermentor and Gas Exchanges.
(3.8)
• A mass balance f o r the oxygen in the liquid phase:
dQ(O2) -- TOUR - TOUR* dt
(3.9)
Applications
118
Computers in Industry
Another equation is required if the carbon dioxide release rate is to be computed. The variable is also a net-effect sensor, but is not considered here.
liquid. I f the hold-up effects in the broth are small, the gas above the liquid is the major part o f the gas phase of the femtentor model (Fig. 2).
3.3. The Oxygen Uptake Rate." An Intermediate Formula
Thanks to Assumption 2, it is possible to obtain from Eqs. 3.6 and 3.11 the following equations:
An intermediate formula for the Oxygen Uptake Rate is expressed in terms of the weight percentage composition of the inlet gas stream: a, b, c, and the weight percentage composition of the outlet gas stream: a',b' ~ C ' .
P(N2) =
100-a'-b'100
de(O2) dt
_
a'
P
[dP
(3.14) o\
+ F~(O2)- 1 - ~ ~-~- + F~ J
(3.15)
Substitution of Eqs. 3.13 and 3.14 in Eq. 3.15 gives:
a lOO
-
Fig(O )/Fig
a' a'100 b ' 100 100 . . . . .
de(O ) dt
b _ i i 1O0 - F)(CO2)/F~ c
It is now possible to make use of mass balance Eq. 3.7 to relate Eq. 3.16 to the input flow Fig(N2). With Eq. 3.12, the unknown nitrogen flow rate can be eliminated. Finally a formula for the Oxygen Uptake Rate at the gas-liquid interface can be obtained with Eqs. 3.8 and 3.10:
(3. I i)
TOUR:
-
bt 100 = F°(CO~)IF° C P
100
-
F~(H20)IF°
(3.16)
(3.10)
!
lOO
c'
× \(alP(N2) +dt F:(N2))
F~(H~OIFig
100 a
c'
l O0(a- a') + (a'b - ab') + (a'c - ac') . ] ~-(]-0-0 -~- a-'-~ b ' - - c-;) F~ (3.17)
As there will be only one flowmeter, usually on the inlet, two assumptions are required to obtain the final result.
Having computed the Oxygen Uptake Rate by the fluid using Eq. 3.17, the uptake by the biomass follows from Eq. 3.9.
Assumption 1: There are no leaks in the gas system, Therefore all inert gases that enter the fermentor, will leave it through the analyzers.
3.4. The Oxygen Uptake Rate from Sensor Output Values
For the inert gas flow at the inlet, Eqs. 3.4 and 3.10 yield: Fig(N=) = 100 - a - b - c 100 Fig
(3.12)
The composition of the inlet stream will be constant in time or otherwise known; the composition of the outlet stream is measured. Eqs. 3.5 and 3.11 give:
Fig(t) : Fvi(t) MWA
t
Fg(N,/=
100
--
a' - b' 100
--
Equations 3.17 and 3.9 are the basic equations. They need however to be expressed in the variables that can be measured directly by the sensors. A number of considerations will result in the final equations. A thermal mass flow meter gives temperature and pressure independent readings in Standard Liters Per Second. The relationship in Eq. 3.18 is useful:
C
F°
(3.13t
(3.18)
VM
Eq. 3.13 will only be useful, under a new assumption.
MWA: molecular weight of the air VM: volume of 1 mole gas in Standard Liters.
The gas composition in the outlet is the same as the gas composition above the fermentor
The sensor outputs for gas analysis are related to volumetric percentages. Based on the law that 1 mole
Assumption
2:
J . A . S p r i e t / F e r m e n t a t i o n Processes
C o m p u t e r s in I n d u s t r y
of any gas has the same volume under standard environmental conditions, the following relationships can be obtained:
a =100"F~'O2"i() Fi g
= 100.
VM' F~(O2)/MG02 . MG02 _ MGo2
VM' F~/MGA
MGA
MGo2 MGcc~ a v ' - - - b v ' - MG A MGA
100
=(100
av-bv-Cv)'--
, MG02 av • MG A
100
= ( 1 0 0 - a v -t b v
MG A : MG02 : MGc02 : MGmo: t
av, av:
by, b'v: !
Cv, Cv :
(3.19)
MGmo MGA (3.20)
MGA
t Cv)" MGI MG A
av
C v ' - -
MGI
, MGco2 bv • MGA t
MGA
, MGH20 Cv" MG a
tm
Pi
p(t)
100(avp i - av,m ( t ), p ( t ,))' r(t') + f ( t ' ) lO0.g(t')
X MGo2 Fi(t) VM
(3.22)
:actual volumetric percentage reading of oxygen at time t. : atmospheric pressure at calibration time. : atmospheric pressure at time t.
The carbon dioxide analyzer is pressure and temperature dependent. The real volumetric percentage relates to the indicated one in the following way: t ,m p ( t ) . Ti by(t) =by (t)" Pi T(t)
In general, the air is dried before use and so c = 0. At the exit a condensor reduces the water content of the gas stream and drying occurs also before gas analysis, so c' = 0. The approach weakens Assumption 2. For small fermentors, well-filled fermentors or high flow rates, the approximation is not very critical. Finally, it has to be noted, that there is a time lag between flow measurement and exit gas analysis. The lag r is flow rate dependent. Taking into consideration all the equations and approximations of this subsection, substitution in Eq. 3.17 yields the final equation 3.24:
(3.21)
The oxygen analyzer is calibrated at the beginning of the fermentation under a current atmospheric pressure. The device is pressure dependent, as it measures partial pressures. The true volumetric percentage of oxygen can be obtained from Eq. 3.22.
~v (t)
TF T(t):
actual volumetric percentage reading of carbon dioxide at time t. ambient temperature at calibration time. ambient temperature at time t.
TOUR(t) =
molecular weight of air. molecular weight of oxygen. molecular weight of carbon dioxide. molecular weight of water. volumetric percentage of oxygen in the inlet and outlet gas. volumetric percentage of carbon dioxide in inlet and outlet. volumetric percentage of water in the inlet and outlet stream.
a,v(t) -- av,m ( t ) . p(t) Pi
tm
bv (t):
119
(3.23)
(3.24)
f(t') =bvp(t') r(t') a v' m ( t ') - a v T i p ( t ) bv,m ( t ), t
,m
i
g(t') = 100" P i T ( f ) - p(t') T(t ) av (t ) -
, ,m , T,.p(t)bv (t)
t ' = t +r av, by: constant oxygen and carbon dioxide volumetric percentages in the inlet stream. At last, from Eq. 3.9 one can deduce: TOUR*(t) = TOUR(t)
-
+ T') d(%DO(t dt\ ~0R ( O 2 ) " Vf)
(3.25) %DO: R(Q): Vf: r":
percentage oxygen dissolved in the liquid as measured by a dissolved oxygen probe. maximum amount of oxygen that can be dissolved at calibration time. volume of the broth. lag of the dissolved oxygen probe.
The correction factor in Eq. 3.25 is often small so that environmental influences on its elements can be neglected. Eqs. 3.24 and 3.25 can now be implemented on a computer and as long as the assumptions mentioned are acceptable, the net-effect sensor of Fig. 1 is achieved.
120
Applications
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4. Application
•
Although the importance of the Oxygen Uptake Rate as a measure for metabolic activity may be obvious and the derivation of the neteffect sensor equations 3.24 and 3.25 quite precise, case-studies on specific microbial processes have to further validate the approach so that better assessments of the procedure can be made. As an example the fermentation of an antibiotic is considered. It is well known that Bacillus Brevis ATCC 9999 produces an antibiotic Gramicidine-S under suitable environmental conditions. The organism was cultivated in a complex medium made up of 3% peptone and 3% yeast extract. The Oxygen Uptake Rate is an important parameter for the process. It has been found [8,9] that the oxygen supply to the fermentation is indeed a crucial control parameter in the sense that limited oxygen will inhibit growth, while full supply inactivates the biosynthesis mechanism of the product, Grarnicidine-S. Due to the unavoidable inherent random effects of any fermentation process, an online estimate for the biomass is necessary for proper oxygen control. Unfortunately, experiments have shown [9], that optical density measurements are inappropriate. The net~effect sensor developed above could be useful in the context of the problem described in this section. In Fig. 3 and Fig. 4, the rough data as collected at the sensor outputs is shown for a fermentation experiment, where the major objective was to keep the dissolved oxygen above 10% without excessive foaming of the broth. For the case, discussed here,
+.22E+OP
i-
i
q
t
÷--4
i
--~-~-
6.
£ o2
2E+0~ I
. . . . . . . . . . .
{DO t
i i <....... }/-
~
ii !
'\'
+. 8 0 E + 0 2 t
\\
f4
f
]/ ~
C-
*. 40E+O2 I
~.
[30. i t/min.
/
i 4
l
i'
!8.
?
00E+001 . . .50E+03 ............ ~-.90E+03 . .+.
f i 4.
'Oh*:~ ~12. rain.
Fig. 4. The Percentage of Dissolved Oxygen in the Broth and Air Flow Rate During Fermentation.
1
..........!tuw '!!
f
il
~. 3 8 E + 0 3
+. 5 8 t
{0 ?
+. 7 0 E + 0 3
mln,
Fig. 5. The Correction Factor to be Applied to the Oxygen Uptake Rate at the Gas-Liquid Interface in order to Obtain the Uptake Rate by the Biomass.
• .90E+0£
L
i
~
-.-+-
--4-
i
% co 2
gr.O/2/L
|
//J
10.
f i
÷.20E~0~
L.
f
•-60E+01
t t ÷.
i8E÷0~
2.
~.
30E÷0~ !J I
//
,, , , ~
/
j
,
,
/
'x
/ +.16E+02 t. 3@E÷03
~-. ~ e E
*03
+. 7 0 E ~ 0 . 3
mln.
Fig. 3. The volumetric Percentage of Oxygen and Carbon dioxide in the Outlet Gas Stream during Fermentation.
•
00E+0~I +. 3 8 E + 0 3
+. 5 0 E ~ 0 3
~.
8E,03
rain
Fig. 6. The Oxygen Uptake Rate and TOtal Oxygen Uptake by Bacillus Brevis.
Computers in Industry +.
1 2E÷02~_-+_
J.A. Spriet / Fermentation Processes i
i
i
i
t
F
¢
gq t
i
[Z°
°4 . -,-_ gr. dry w,~[,
121
take Rate can be computed directly. As the sensors are quite expensive a manufacturor will provide a minimal set-up. It has been shown here that, under such a configuration, the fermentation experiment has to fulfill certain conditions so that a number of assumptions can be made to guarantee proper evaluation of the uptake rate. The final equations are involved and consequently a computing device is required. It is illustrated for the production of Gramicidine-S by Bacillus Brevis how the biomass could be monitored online using the net-effect sensor presented. Further research towards other net-effect sensors bears a promise for improved process control of microbial phenomena.
Fig. 7. The Correlation between Oxygen Uptake and Dry Weight. Acknowledgements ambient temperature and atmospheric pressure remained as good as constant. The correction factor (Eq. 3.25), that has to be applied to the Oxygen Uptake Rate, is displayed in Fig. 5 per liter fermentation content. The final results are shown in Fig. 6. They were obtained with Eqs. 3.24 and 3.25, but the Oxygen Uptake Rate at the biomass interface was computed per unit volume of the broth. The total oxygen uptake itself was found after integration of the uptake rate. In order to evaluate the usefulness of that value, the total oxygen uptake has been compared with an offline biomass measurement technique. Although cumbersome, dry weight was chosen as it is known as one of the most trustworthy estimators for the biomass. As can be seen in Fig. 7, no statistical analysis is required to be able to conclude that there exists a linear correlation between uptake and dry weight as long as the biomass remains below a certain level. It can thus be concluded that for the example, the total oxygen uptake can directly be used as an indicator for the biomass during a major part of the experiment; in the final stages of the growth, the relationship between uptake and dry weight is nonlinear and therefore more involved.
5. Conclusion Even in the traditional field of fermentation, the computer can play an important role. In this paper its potential as a correlator o f sensor output data for online process monitoring was investigated and experience with a net-effect sensor was reported. With a proper sensor configuration the Oxygen Up-
The author is thankful to Dr. It. E. Vandamme for his introduction to the problems concerning the Gramicidine-S fermentation. Financial support of the Belgian National Science Foundation is also gratefully acknowledged.
References [1] A.E. Humphrey, 'The use of computers in fermentation systems', Process Biochemistry, March pp. 19-25, 1977. [2] L.K. Nyiri, 'Application of computers in biochemical engineering', Advances in Biochemical Engineering 2, Ed. T. Ghose, A. Fiechter, N. Blakebrough, pp. 49-93, Springer Verlag, 1973. [3] A.E. Humphrey, 'Rationale and problems in the use of computer-coupled fermentation systems', US/USSR Seminar on Measurements in Fermentation, Philadelphia, Aug. 12-14, 1975. [4] R.P. Jefferis, 'Computers in the fermentation pilot plant', Process Biochemistry, pp. 15, 1975. [5] L.K. Nyiri, G.M. Toth, M. Charles, 'Measurement of gasexchange conditions in fermentation processes', Bintechnology and Bioengineering, 17 pp. 1664, 1975. [6] C.L. Cooney, H. Wang, D.I.C. Wang, 'Computer-aided material balancing for prediction of fermentation processes', Biotechnology and Bioengineering, 18, 1976. [7] D.W. Zabriskie, W.B. Armiger, A.E. Humphrey, 'Application of computers to the indirect measurement of biomass concentration and growth rate by component balancing', Workshop Computer Applications in Fermentation Technology, Verlag Chemie, Weinheim, 1977. [8] T.P. Udulova, T.M. Guskova, A.B. Silaev, 'Growth of Bacillus Brevis G.B. and production of Gramicidine-S in relation to intensity of aeration', Microbiologeja USSR, 41,280-286, 1972. [9] D. De Buyser, 'Studie van Gramicidine-S fermentatie in bet licht van data-verwerking', Master's Thesis, University of Ghent, Belgium, 1980.
Applications
Online Monitoring of Fermentation Processes J a n A. S p r i e t Belgian National Science Foundation, University of Gent, Coupure Links 533, 9000 Gent, Belgium In biotechnology, few online measurements of biological variables are available. This fact hampers effective monitoring and control in the fermentation field. A novel approach to this is the use of a computer to combine outputs of online sensors for physical and chemical parameters to estimate directly otherwise unaccessible biological quantities like biomass. Here, a sensor configuration is presented for the online computation of the oxygen uptake rate. The equations that have to be implemented on the digital machine are derived and a case study on the fermentation of the antibiotic Gramicidine-S is performed and discussed. The experiments indicate that for a major part of the growth and fermentation period, the computer is suitable for the evaluation of the biomass based on oxygen uptake estimates. Consequently, the process can be monitored online.
Keywords. Biotechnology, net-effect sensor, measurement, fermentation process, online monitoring, oxygen uptake rate, biomass estimate, sensor configuration.
Jan A. Spriet received in 1973 an engineering degree in electrical engineering from the University of Ghent. He obtained an Union Carbide grant and became an ITT-fellow during the academic year 1973-74. In 1974 he received an MS in Electrical Engineering from the Massachusetts Institute of Technology, Cambridge U.S.A. Since 1975, he has been engaged in research towards the application of mathematical and engineering tools in biology at the Belgium National Science Foundation. In 1978, he received a NATO. grant for research as a Visiting Scholar at the University of California Los Anzeles. His current research interests are in pattern recognition, system structure characterization, modeling, identification and control of biochemical and fermentation processes. North-Holland Publishing Company Computers in Industry 2 (1981) 115-121
0166-36 ! 5 / 8 1 / 0 0 0 0 - 0 0 0 0 / $ 0 2 . 5 0 © 1981 North-Holland
1. Introduction Micro-organisms have been used for the benefit of men for a long time. Since early history, microbial phenomena have played their role in the context of certain food and beverage preparations. A much more recent development, but one of greater importance, has been the production of many enzymes and antibiotics along fermentative process patterns. Due to several new factors in our society, such as increased shortage and often difficult supply of fossile fuel and the presence of large amounts of waste, the relevance of many fermentations is growing steadily; and it is to be expected in the near future that cost-benefit analyses will start to indicate the economic feasibility of the microbial production for certain chemicals. Based on these more general considerations the future of the field looks certainly bright. It has to be recognized, however, that the engineering capability to control the processes is still limited: the fermentations are performed in an extremely traditional way; they require a considerable amount of skill and manual intervention; and many operation guidelines are based on past experience or small experiments. A typical example of this unsatisfactory state of the engineering art is the lack of techniques and sensors to monitor the process online. It is well known that the biomass is an important process variable. For an online estimate of that variable, out of the classic techniques, only the evaluation of the optical density can be taken into consideration. For many fermentations, there are factors, like color, particles in the broth, etc., that may interfere so that the estimate is poor or simply has no quantitative value. Faced with the pecularities of the situation, one can easily imagine that the digital machine, as a powerful tool in process engineering, could play an important role in biotechnology. It is another proof of the traditional approach, that the computer has only gradually been accepted in the last decade [1]. It has been recognized only very recently that one of the most promising areas is concerned with the use of
116
Applications
the machine as a net-effect sensor [2,3,4]. As many biological variables cannot be measured directly, it may perhaps be possible to correlate these variables with quantities obtained after computation out of measurements taken by on-line sensors for physical variables. In the paper the computation of the oxygen uptake rate as a net-effect sensor is considered. The concept has been mentioned before [5,6,7], but few details about the engineering aspects are available and few experimental results have been presented. A typical sensor configuration is presented in Section 2, and a digital machine turns out to be an important part of it. In Section 3, the net-effect sensor formula for the computer is derived. All assumptions are clearly stated. The derivation indicates under which conditions the sensor configuration is sufficiently elaborate and for which processes the approach is likely to give acceptable results. Finally in Section 4, the results are given.
2. Sensor Configuration The metabolic activity of a large number of microorganisms is influenced and often controlled by the oxygen conditions within the fermentor. The Oxygen Uptake Rate, OUR ( t ) - consequently, is a key variable linked to the biological activity of the process. As will be seen in the sequel, the quantity can be computed online with a digital machine. The phenomena, related to the oxygen transport, are quite complicated. Usually, an air stream is sent through the fermentor vessel, which is heavily stirred to break up large gas bubbles. Oxygen diffuses across the gasliquid interface to the broth. The intense mixing activity of the stirrer renders the concentration within the fluid homogeneous. The oxygen molecules cross the walls of the micro-organisms and are consumed mainly for energy regeneration in the ADPATP pool. The exit gas, leaving the vessel, will be poor in oxygen but may have been enriched or polluted with gases resulting from the metabolic activity of the cells. In most of the cases, carbon dioxide will be the only waste product of nutrient breakdown. The oxygen uptake rate can be obtained in a sensor configuration shown in Fig. 1. As many of the measurement devices are quite expensive, the number of sensors is kept minimal, It will be shown in Section 3, that a number of assumptions have to be made to obtain a valid estimate.
Computers in Industry sensors
;;r~cess
L-
i
t
C
i 4oo
t.....
Fig. 1. Sensor Configuration.
The most important measurement units are: • A mass flowmeter on the inlet, with a temperature and pressure independent flowrate reading in Standard Liters Per Second, SLPS Fir(t). • An oxygen analyzer, often of the paramagnetic type. It indicates a partial pressure, although it is calibrated in volumetric percentage o f oxygen, tm %02(t) = av (t). • A carbondioxide analyzer, mostly based on an infrared adsorption measurement. The output relates to a gas concentration but the sensor is calibrated in volumetric percentage o f carbondioxide, %CO2 = rm
b v (t).
The first gas analyzer is only pressure dependent, as the housing is kept at constant temperature. The second one is dependent on pressure and temperature. Consequently, for a precise evaluation, one needs also: • A sensor for ambient temperature: T(t), K. • A sensor for atmospheric pressure: p(t), Pa. Finally the oxygen content of the fermentor liquid may vary. An estimate of the dissolved oxygen level in the broth can be obtained from an electrode. A Dissolved Oxygen unit coupled to a silver-lead electrolytic probe system yields %DO(t). All devices give an instantaneous output or an output with a small lag. As will be seen in the sequel, the evaluation of the Oxygen Uptake Rate is quite involved and a computer is required for fast online computation. The output signals can be sampled and fed into a digital machine for further processing.
Computers in Industry
J.A. Spriet / Fermentation Processes
117
over the fermentor volume. One can define the Total
3. The Net-Effect Sensor Formula
Oxygen Uptake Rate TOUR(t), kgO2/sec:
A more rigorous derivation of a useful formula for the Oxygen Uptake Rate (OUR) requires different steps. First, the important quantities have to be defined in a more careful way. 3.1. The Fermentor Model
In order to obtain a useful equation, a lumped macroscopic point of view has to be taken. In fact, the local oxygen uptake r a t e - our(r, t), kgO2/sec. m 3 and also other gas exchanges like the carbondioxide release rate, c02rr(r, t), kgCO2/sec, m 3, at the gas-liquid interface are very erratic functions of space and time due to turbulent phenomena in the liquid. These functions can be smoothed by considering the macroscopic quantities: b-fiT(r, t), and c~22rr(r, t), defined as follows: our(r, t) = ~1 " S1 f J o u r ( r , t ) d V " dt
(3,1)
c o T ( r , t) = 1 " 4
(3.2)
V
(fco2rr(r, t ) d V ' d t
/--~oa
r: point vector of location.
t: time. V: small neighbourhood for r of the order of the gas bubble size. A: small time interval of the order of the transition time in the liquid. f: integration. In the same manner macroscopic quantities b-gg*(r, t) and ~ * ( r , t) can be defined for gas exchanges at the cell walls. Then, the contents of the fermentor is thought to be composed of three phases: a biomass phase, liquid phase, and gas phase - see Fig. 2. Since only a lumped model for the fermentor is used, all macroscopic variables can be integrated
TOUR(O = f ~ ( r , t) d V vf
Vr: fermentor liquid volume. Equations of the same type can be used to define the Total (Carbon dioxide Release Rate at the gasliquid interface TCO2RR(t), the gas exchange quantities at the cell walls: TOUR*(t) and TCO2RR*(t), the total amount of a certain gas A in the liquid phase Q(A) and in the gas phase P(A), and the mass input and output flow rates for a gas A: F~(A) and F~g(A) kgA/sec., respectively (Fig. 2). 3.2. Mass Balances
As all variables have hitherto been defined as masses or mass flow rates, it is easy to write down a number of mass balances concerning the lumped fermentor model (Fig. 2). For further use, the following equations are important: • A mass balance )'or the inlet mass f l o w rate; the air itself is made up of oxygen, carbon dioxide, water vapour and inert gases, with nitrogen as the major component: F~ = F~(O2) + F~(CO2) + F~(H20) + F~tN2)
t 0 UR
(3.4)
• A mass balance ]br the mass f l o w rate at the outlet:
F~ = Fff(O2) + Fff(CO2) + F~(H20)+ F~(N=)
(3.5)
• A mass balance f o r the gas contents in the fermentor:
P = P(O2) + P(CO2) + P(H20) + P(N2)
(3.6)
• A mass balance ]'or the inert gases, mostly nitrogen
in the gas phase. It is to be noted that these gases are not consumed and not produced by the microorganisms. dP(N2) - F~(N2) - F°(N2) dt
GAS-PtIASE
(3.3)
(3.7)
[ T CO2 R R
• A mass balance f o r the oxygen in the gas phase: LIQUID-PHASE I 1 T 0 C R* T
CO2 R P~
dP(O:) _ F~(O2) - F~(O2) - TOUR dt
Fo g
T Fig. 2. Lumped Model for Fermentor and Gas Exchanges.
(3.8)
• A mass balance f o r the oxygen in the liquid phase:
dQ(O2) -- TOUR - TOUR* dt
(3.9)
Applications
118
Computers in Industry
Another equation is required if the carbon dioxide release rate is to be computed. The variable is also a net-effect sensor, but is not considered here.
liquid. I f the hold-up effects in the broth are small, the gas above the liquid is the major part o f the gas phase of the femtentor model (Fig. 2).
3.3. The Oxygen Uptake Rate." An Intermediate Formula
Thanks to Assumption 2, it is possible to obtain from Eqs. 3.6 and 3.11 the following equations:
An intermediate formula for the Oxygen Uptake Rate is expressed in terms of the weight percentage composition of the inlet gas stream: a, b, c, and the weight percentage composition of the outlet gas stream: a',b' ~ C ' .
P(N2) =
100-a'-b'100
de(O2) dt
_
a'
P
[dP
(3.14) o\
+ F~(O2)- 1 - ~ ~-~- + F~ J
(3.15)
Substitution of Eqs. 3.13 and 3.14 in Eq. 3.15 gives:
a lOO
-
Fig(O )/Fig
a' a'100 b ' 100 100 . . . . .
de(O ) dt
b _ i i 1O0 - F)(CO2)/F~ c
It is now possible to make use of mass balance Eq. 3.7 to relate Eq. 3.16 to the input flow Fig(N2). With Eq. 3.12, the unknown nitrogen flow rate can be eliminated. Finally a formula for the Oxygen Uptake Rate at the gas-liquid interface can be obtained with Eqs. 3.8 and 3.10:
(3. I i)
TOUR:
-
bt 100 = F°(CO~)IF° C P
100
-
F~(H20)IF°
(3.16)
(3.10)
!
lOO
c'
× \(alP(N2) +dt F:(N2))
F~(H~OIFig
100 a
c'
l O0(a- a') + (a'b - ab') + (a'c - ac') . ] ~-(]-0-0 -~- a-'-~ b ' - - c-;) F~ (3.17)
As there will be only one flowmeter, usually on the inlet, two assumptions are required to obtain the final result.
Having computed the Oxygen Uptake Rate by the fluid using Eq. 3.17, the uptake by the biomass follows from Eq. 3.9.
Assumption 1: There are no leaks in the gas system, Therefore all inert gases that enter the fermentor, will leave it through the analyzers.
3.4. The Oxygen Uptake Rate from Sensor Output Values
For the inert gas flow at the inlet, Eqs. 3.4 and 3.10 yield: Fig(N=) = 100 - a - b - c 100 Fig
(3.12)
The composition of the inlet stream will be constant in time or otherwise known; the composition of the outlet stream is measured. Eqs. 3.5 and 3.11 give:
Fig(t) : Fvi(t) MWA
t
Fg(N,/=
100
--
a' - b' 100
--
Equations 3.17 and 3.9 are the basic equations. They need however to be expressed in the variables that can be measured directly by the sensors. A number of considerations will result in the final equations. A thermal mass flow meter gives temperature and pressure independent readings in Standard Liters Per Second. The relationship in Eq. 3.18 is useful:
C
F°
(3.13t
(3.18)
VM
Eq. 3.13 will only be useful, under a new assumption.
MWA: molecular weight of the air VM: volume of 1 mole gas in Standard Liters.
The gas composition in the outlet is the same as the gas composition above the fermentor
The sensor outputs for gas analysis are related to volumetric percentages. Based on the law that 1 mole
Assumption
2:
J . A . S p r i e t / F e r m e n t a t i o n Processes
C o m p u t e r s in I n d u s t r y
of any gas has the same volume under standard environmental conditions, the following relationships can be obtained:
a =100"F~'O2"i() Fi g
= 100.
VM' F~(O2)/MG02 . MG02 _ MGo2
VM' F~/MGA
MGA
MGo2 MGcc~ a v ' - - - b v ' - MG A MGA
100
=(100
av-bv-Cv)'--
, MG02 av • MG A
100
= ( 1 0 0 - a v -t b v
MG A : MG02 : MGc02 : MGmo: t
av, av:
by, b'v: !
Cv, Cv :
(3.19)
MGmo MGA (3.20)
MGA
t Cv)" MGI MG A
av
C v ' - -
MGI
, MGco2 bv • MGA t
MGA
, MGH20 Cv" MG a
tm
Pi
p(t)
100(avp i - av,m ( t ), p ( t ,))' r(t') + f ( t ' ) lO0.g(t')
X MGo2 Fi(t) VM
(3.22)
:actual volumetric percentage reading of oxygen at time t. : atmospheric pressure at calibration time. : atmospheric pressure at time t.
The carbon dioxide analyzer is pressure and temperature dependent. The real volumetric percentage relates to the indicated one in the following way: t ,m p ( t ) . Ti by(t) =by (t)" Pi T(t)
In general, the air is dried before use and so c = 0. At the exit a condensor reduces the water content of the gas stream and drying occurs also before gas analysis, so c' = 0. The approach weakens Assumption 2. For small fermentors, well-filled fermentors or high flow rates, the approximation is not very critical. Finally, it has to be noted, that there is a time lag between flow measurement and exit gas analysis. The lag r is flow rate dependent. Taking into consideration all the equations and approximations of this subsection, substitution in Eq. 3.17 yields the final equation 3.24:
(3.21)
The oxygen analyzer is calibrated at the beginning of the fermentation under a current atmospheric pressure. The device is pressure dependent, as it measures partial pressures. The true volumetric percentage of oxygen can be obtained from Eq. 3.22.
~v (t)
TF T(t):
actual volumetric percentage reading of carbon dioxide at time t. ambient temperature at calibration time. ambient temperature at time t.
TOUR(t) =
molecular weight of air. molecular weight of oxygen. molecular weight of carbon dioxide. molecular weight of water. volumetric percentage of oxygen in the inlet and outlet gas. volumetric percentage of carbon dioxide in inlet and outlet. volumetric percentage of water in the inlet and outlet stream.
a,v(t) -- av,m ( t ) . p(t) Pi
tm
bv (t):
119
(3.23)
(3.24)
f(t') =bvp(t') r(t') a v' m ( t ') - a v T i p ( t ) bv,m ( t ), t
,m
i
g(t') = 100" P i T ( f ) - p(t') T(t ) av (t ) -
, ,m , T,.p(t)bv (t)
t ' = t +r av, by: constant oxygen and carbon dioxide volumetric percentages in the inlet stream. At last, from Eq. 3.9 one can deduce: TOUR*(t) = TOUR(t)
-
+ T') d(%DO(t dt\ ~0R ( O 2 ) " Vf)
(3.25) %DO: R(Q): Vf: r":
percentage oxygen dissolved in the liquid as measured by a dissolved oxygen probe. maximum amount of oxygen that can be dissolved at calibration time. volume of the broth. lag of the dissolved oxygen probe.
The correction factor in Eq. 3.25 is often small so that environmental influences on its elements can be neglected. Eqs. 3.24 and 3.25 can now be implemented on a computer and as long as the assumptions mentioned are acceptable, the net-effect sensor of Fig. 1 is achieved.
120
Applications
Computers in Industry
4. Application
•
Although the importance of the Oxygen Uptake Rate as a measure for metabolic activity may be obvious and the derivation of the neteffect sensor equations 3.24 and 3.25 quite precise, case-studies on specific microbial processes have to further validate the approach so that better assessments of the procedure can be made. As an example the fermentation of an antibiotic is considered. It is well known that Bacillus Brevis ATCC 9999 produces an antibiotic Gramicidine-S under suitable environmental conditions. The organism was cultivated in a complex medium made up of 3% peptone and 3% yeast extract. The Oxygen Uptake Rate is an important parameter for the process. It has been found [8,9] that the oxygen supply to the fermentation is indeed a crucial control parameter in the sense that limited oxygen will inhibit growth, while full supply inactivates the biosynthesis mechanism of the product, Grarnicidine-S. Due to the unavoidable inherent random effects of any fermentation process, an online estimate for the biomass is necessary for proper oxygen control. Unfortunately, experiments have shown [9], that optical density measurements are inappropriate. The net~effect sensor developed above could be useful in the context of the problem described in this section. In Fig. 3 and Fig. 4, the rough data as collected at the sensor outputs is shown for a fermentation experiment, where the major objective was to keep the dissolved oxygen above 10% without excessive foaming of the broth. For the case, discussed here,
+.22E+OP
i-
i
q
t
÷--4
i
--~-~-
6.
£ o2
2E+0~ I
. . . . . . . . . . .
{DO t
i i <....... }/-
~
ii !
'\'
+. 8 0 E + 0 2 t
\\
f4
f
]/ ~
C-
*. 40E+O2 I
~.
[30. i t/min.
/
i 4
l
i'
!8.
?
00E+001 . . .50E+03 ............ ~-.90E+03 . .+.
f i 4.
'Oh*:~ ~12. rain.
Fig. 4. The Percentage of Dissolved Oxygen in the Broth and Air Flow Rate During Fermentation.
1
..........!tuw '!!
f
il
~. 3 8 E + 0 3
+. 5 8 t
{0 ?
+. 7 0 E + 0 3
mln,
Fig. 5. The Correction Factor to be Applied to the Oxygen Uptake Rate at the Gas-Liquid Interface in order to Obtain the Uptake Rate by the Biomass.
• .90E+0£
L
i
~
-.-+-
--4-
i
% co 2
gr.O/2/L
|
//J
10.
f i
÷.20E~0~
L.
f
•-60E+01
t t ÷.
i8E÷0~
2.
~.
30E÷0~ !J I
//
,, , , ~
/
j
,
,
/
'x
/ +.16E+02 t. 3@E÷03
~-. ~ e E
*03
+. 7 0 E ~ 0 . 3
mln.
Fig. 3. The volumetric Percentage of Oxygen and Carbon dioxide in the Outlet Gas Stream during Fermentation.
•
00E+0~I +. 3 8 E + 0 3
+. 5 0 E ~ 0 3
~.
8E,03
rain
Fig. 6. The Oxygen Uptake Rate and TOtal Oxygen Uptake by Bacillus Brevis.
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1 2E÷02~_-+_
J.A. Spriet / Fermentation Processes i
i
i
i
t
F
¢
gq t
i
[Z°
°4 . -,-_ gr. dry w,~[,
121
take Rate can be computed directly. As the sensors are quite expensive a manufacturor will provide a minimal set-up. It has been shown here that, under such a configuration, the fermentation experiment has to fulfill certain conditions so that a number of assumptions can be made to guarantee proper evaluation of the uptake rate. The final equations are involved and consequently a computing device is required. It is illustrated for the production of Gramicidine-S by Bacillus Brevis how the biomass could be monitored online using the net-effect sensor presented. Further research towards other net-effect sensors bears a promise for improved process control of microbial phenomena.
Fig. 7. The Correlation between Oxygen Uptake and Dry Weight. Acknowledgements ambient temperature and atmospheric pressure remained as good as constant. The correction factor (Eq. 3.25), that has to be applied to the Oxygen Uptake Rate, is displayed in Fig. 5 per liter fermentation content. The final results are shown in Fig. 6. They were obtained with Eqs. 3.24 and 3.25, but the Oxygen Uptake Rate at the biomass interface was computed per unit volume of the broth. The total oxygen uptake itself was found after integration of the uptake rate. In order to evaluate the usefulness of that value, the total oxygen uptake has been compared with an offline biomass measurement technique. Although cumbersome, dry weight was chosen as it is known as one of the most trustworthy estimators for the biomass. As can be seen in Fig. 7, no statistical analysis is required to be able to conclude that there exists a linear correlation between uptake and dry weight as long as the biomass remains below a certain level. It can thus be concluded that for the example, the total oxygen uptake can directly be used as an indicator for the biomass during a major part of the experiment; in the final stages of the growth, the relationship between uptake and dry weight is nonlinear and therefore more involved.
5. Conclusion Even in the traditional field of fermentation, the computer can play an important role. In this paper its potential as a correlator o f sensor output data for online process monitoring was investigated and experience with a net-effect sensor was reported. With a proper sensor configuration the Oxygen Up-
The author is thankful to Dr. It. E. Vandamme for his introduction to the problems concerning the Gramicidine-S fermentation. Financial support of the Belgian National Science Foundation is also gratefully acknowledged.
References [1] A.E. Humphrey, 'The use of computers in fermentation systems', Process Biochemistry, March pp. 19-25, 1977. [2] L.K. Nyiri, 'Application of computers in biochemical engineering', Advances in Biochemical Engineering 2, Ed. T. Ghose, A. Fiechter, N. Blakebrough, pp. 49-93, Springer Verlag, 1973. [3] A.E. Humphrey, 'Rationale and problems in the use of computer-coupled fermentation systems', US/USSR Seminar on Measurements in Fermentation, Philadelphia, Aug. 12-14, 1975. [4] R.P. Jefferis, 'Computers in the fermentation pilot plant', Process Biochemistry, pp. 15, 1975. [5] L.K. Nyiri, G.M. Toth, M. Charles, 'Measurement of gasexchange conditions in fermentation processes', Bintechnology and Bioengineering, 17 pp. 1664, 1975. [6] C.L. Cooney, H. Wang, D.I.C. Wang, 'Computer-aided material balancing for prediction of fermentation processes', Biotechnology and Bioengineering, 18, 1976. [7] D.W. Zabriskie, W.B. Armiger, A.E. Humphrey, 'Application of computers to the indirect measurement of biomass concentration and growth rate by component balancing', Workshop Computer Applications in Fermentation Technology, Verlag Chemie, Weinheim, 1977. [8] T.P. Udulova, T.M. Guskova, A.B. Silaev, 'Growth of Bacillus Brevis G.B. and production of Gramicidine-S in relation to intensity of aeration', Microbiologeja USSR, 41,280-286, 1972. [9] D. De Buyser, 'Studie van Gramicidine-S fermentatie in bet licht van data-verwerking', Master's Thesis, University of Ghent, Belgium, 1980.