State Observation of Phenol Degradation by Ralstonia Eutropha Based on Dissolved Oxygen Measurement

Copyright ® IF AC Advanced Control of Chemical Processes, Pisa, Italy, 2000

STATE OBSERVATION OF PHENOL DEGRADATION BY RALSTONIA EUTROPHA BASED ON DISSOLVED OXYGEN MEASUREMENT I. Queinnec' D. Leonard ",1 G. Denou'

* LAAS-CNRS, 7 av. du CoLonel Roche, 31077, Toulouse cedex

4,

France •• Centre de Bioingenierie Gilbert Durand, UMR CNRS/INSA and Lab. Ass. INRA, INSA, Complexe scientifique de Rangueil, 31077 Toulouse cedex 4, France

Abstract: This paper concerns the design and experimental evaluation of a state observer, implemented in a control system for fed batch phenol degradation by Ralstonia eutropha, expressed in terms of phenol regulation. The state observer, based on extended Kalman filtering, allows to recover the unmeasured phenol concentration, by using dissolved oxygen measurement. Particular emphasis is made on the determination of the [{La, mainly function of the stirrer speed. The extended Kalman filter is implemented on the non-linear continuous-time system with discretetime observation. Copyright © 2000 IFAC Keywords: State observer, Kalman filter,

[{La,

Fedbatch.

possible disturbances occuring on the process, and then ensure process reliability (Charbonnier and Cheruy, 1996).

1. INTRODUCTION The concern of phenol consumption from industrial wastewater has been generating considerable research interest in technologies for biological treatment of industrial wastes (Hill and Robinson, 1975). Most of the currently used technologies are based on aerobic process and activated sludge systems which are known to be sensitive to fluctuation in the pollutant load, especially in the case of inhibitory even toxic substrate as phenol. Fedbatch operation to treat effluents avoids a direct release in the environment of the treated stuff, i.e. of a residual phenol load. This strategy then appears to be adapted in the case of a toxic pollutant such as phenol (Queinnec et al. , 1999) . In this operation mode, regulation of the substrate concentration does not provide exact optimal solution, but its advantage is to maintain the process under efficient operating conditions in spite of

Off-line phenol detection can be performed by chromatographic or spectrophotometric methods or by analytical systems based on immobilized enzymes. However, on-line biological state variables measurements suffer from the lack of reliable sensors suited to real-time advanced control. This is why indirect measurement and estimation techniques have been developed and applied to provide on-line evaluation of biological variables. Because of the strongly nonlinear dynamic behaviour of bioprocesses, estimators are designed by nonlinear estimation techniques, generally extended from classical linear ones. However, it must be kept in mind that these methods may be difficult to tune and can suffer from convergence problems. The main contribution of this paper is to illustrate that the oxygen measurement may be used to estimate the time evolution of the phenol and R. eutropha concentrations by extended Kalman

1 Present adress : SOREDAB, La Tremblaye, 78125 La Boissiere Ecole, France

467

filtering (San and Stephanopoulos, 1984), then to control the feeding of a fedbtach process. This is possible since phenol is degradated in presence of oxygen, which is used both by the catabolic pathway of phenol degradation and by the respirometric pathway (Leonard, 1997). Section 1 presents the experimental process. A model of the process is decribed in section 2 based on mass-balanced considerations. Section 3 is devoted to the KLa determination while section 4 focuses on the extended Kalman filter. Finally the application of the observer to control the fed batch culture is presented in section 5.

3. PROCESS MODELLING In biotechnological processes, bacterial growth behavior is usually described by a set of non-linear equations derived from mass-balance considerations. Phenol degradation by R . eutropha in fedbatch cultures may then be described by the following equations :

dX dt

= \.La (0'2 dV Tt = Qin 2

2. PROCESS DESCRIPTION A schematic diagram of the experimental fed batch plant is shown in Figure 1.

Feeding

}"

0) 2

-

S) q0 2 X

(2) -

QinO 2 V

(3)

(4)

where X is the biomass concentration (g/I), S is the phenol concentration (g/I), Sin is the influent phenol concentration (g/I), O 2 is the oxygen concentration (mmol/I), V is the working volume (I) and Qin is the feed flow rate (I/h). J.l , q. and q0 2 are the specific growth rate , the specific rate of phenol consumption and the specific rate of oxygen consumption, respectively. The evaluation of the volumetric oxygen transfer coefficient KLa and the air-saturated oxygen concentration 0; (mmol/l) is presented in the next section.

~

.HH >w.

(1)

Qin X V

~~ = -q.X + Q~n (Sin d0 Tt

-

= J.lX _

""""'O .. ':'

-:;

Preliminary batch and chemostat cultures have allowed to establish the kinetic parameters modelling. Even if the growth of micro-organisms depends on many environmental conditions (temperature, pH , inhibitor co-metabolites, mineral salts , dissolved oxygen, phenol concentration ... ), the kinetic parameters generally only express the dependance on the main process variables. The growth behavior of R. eutropha on phenol has been studied in previous work (Leonard and Lindley, 1998) and the double effect of inhibition and limitation of phenol concentration has been modelled by an Haldane equation :

Fig. 1. Experimental fed batch plant Cultures of Ralstollia eutropha 355 (ATCC 17697) on a mineral salts medium previously described (Leonard and Lindley, 1998) , have been carried out in a 1.5 liter bioreactor from Setric, Toulouse. Stirrer speed, temperature and pH were maintained under local analogue control at 200 - 700 rev .min- i , 30°C and 7 (with automatic addition of KOH 3M) respectively. Oxygen partial pressure was maintained above 25% of air saturation by gradually modifying the stirrer speed . The bioreactor was inoculated with 10% (vol/vol) lateexponential-phase shaked flask culture grown on phenol (0 .59/1) which was first aseptically centrifuged (50009 for 10 min at ambiant temperature) and resuspended in fresh medium to remove any accumulated metabolites . Phenol solution sterilized through membrane and containing growth medium was supplied by a peristaltic minipulse pump (Gibson) monitored by the control procedure.

S

J.l

= J.lmax }_\..' + S + K,52

(5)

where the influence of other experimental conditions is implicitely put in J.lmax . Although the influence of the oxygen concentration should be also expressed in (5) through a multiplicative Monod relation, this term is neglected in the expression of J.l since K02 is generally evaluated to 5-10 % of the oxygen solubility, and then much smaller than the oxygen concentration maintained in the vessel during the process operation. It has also been shown that J.l and q. are correlated by a linear relationship:

The plant was linked to a PC/AT-compatible micro-computer through a RTI 815 board from Analog Devices family. This micro-computer assumed functions of data acquisition and storage, graphic display, numerical application of observer and control algorithms and control of the phenol feed pump.

q.

468

J.l =--

Yxj •

(6)

=

and that the specific rate of oxygen consumption involves both a term of proportionnality with the growth rate and a maintenance term :

qo, =

J1. +mo, xlo

y

(Po, 100%) and the measured partial pressure of oxygen: 1

(7)

= OA1 h- 1

= 0.557 mmol/g/h Yxl o = 0.018 g/mmol mo,

1 s K La

with s the Laplace operator. The electrode time constant TR is determined by measuring the probe response after switching from nitrogen-saturated liquid to oxygen-saturated liquid. The [{La is then identified by examinating the step response of the second-order system . The main advantage of such an approach is that it can be used to determine high oxygen transfer coefficients (i .e. time constant of the transfer of the order of the probe time constant), contrary to some classical methods where the second-order system is approximated to a first-order system which time constant of is the sum of the two previous time constants (Rainer , 1990).

The parameters involved in equations (5) , (6), (7) have been previously identified by using a simplex method as follows (Leonard et al., 1999) : J1.max

1

G(s)=1+TRS1+

f{. = 2 mg/l K = 350 mg/l Yxl' = 0.68 gig

4. OXYGEN TRANSFER DETERMINATION

In constrast to the apparent simplicity of the well known equation for oxygen transfer (3) , the physical oxygen transfer parameters f{La and 0; involved are widely related to the environmental and culture conditions, such as temperature , pressure, stirred speed (Van 't Riet , 1979), mineral salts (Lee and Meyrick , 1970) , (Popovic et al., 1979), (Schumpe, 1985) , viscosity, organic compounds and sugars (Popovic et al. , 1979), microorganisms (Merchuk, 1977) ...

The f{La is determined for different stirrer speeds, on the material used for biological experiments with the same physical conditions (temperature, pH). The electrode time constant is first evaluated to TR = 16 seconds . The f{La are identified for several stirrer speeds, either by using the firstorder approximation (Rainer, 1990), or by using the second-order representation (Table 4) .

The theoretical determination of those parameters even in some particular culture conditions being very complex, they are determined by preliminar experimental methods, whose many of them have been reviewed in the literature (Van 't Riet , 1979), (Rainer, 1990) . The dynamic method , without biological system, is one common technique of determining f{La in bioreactors , which can be performed easily, provided that the microorganisms do not affect too much the oxygen gas-liquid transfer .

Table 1 Comparison of KLa (h- 1 )

RPM first-order second-order

95 15.5 15 .5

219 22.23 22 .3

340 42.7 42.7

450 115.6 95.0

620 281.7 195.0

This table clearly shows that the first-order arr proximation is valuable for small f{La values, i.e., large time constant, where the probe time constant does not influence the solution. However, when the f{La increases such that the time constant becomes in the order of the probe time constant , the [{La evaluation is no more correct when using the first-order approximation.

The underlying principle of the method is to record the dissolved oxygen concentration evolution after a step of the air inflow, from an initialliquid deoxygenated by passing nitrogen. The main limitations of the method results from :

The influence of the culture medium is shown on Table 4 by comparison of the [{La determined from measurements in water and in the culture medium . Moreover , after deoxygenation by nitrogen, the gas sky if formed with nitrogen . This may alter the system time response when the aeration is started. Then , one can first replace the nitrogen sky by air sky (with stir halted) before to apply the influent air step and simultaneously start again stir. This interference due to surface exchanges is also shown by examinating the [{La identified from experiments done with nitrogen sky then with air sky. Those three types of experiments are summarized in Table 4.

• the inherent dynamic response of the oxygen electrode; • the mixing dynamic response in the reactor when starting the air inflow. It can be neglected with our material geometry and mixmg ; • the presence of nitrogen in the gas sky after deoxygenation . The oxygen gas-liquid transfer is commonly described as a first order system with time constant 1/ [{La . The probe response time may also be described by a first order system with time constant TR, which results in a second-order transfer function between the influent oxygen concentration

Remark 1. : It is also possible to identify the f{La associated to biological reactions modelled by equations (1)-(4) . This has been done from

469

Table 2 K La for different stirrer speeds and different experimental conditions

Consider the general nonlinear dynamical representation of the form :

K L a measured in RPM

water nitrogen sky 11,2 15,5 19,6 22,3 32,3 42,1 95 195

45 95 160 219 216 340 450 620

(8)

medium nitrogen sky 15,2 11,1 21,0 23,3

medium air sky

44,1

53,5

where F is a nonlinear function of state vector x and input vector u. w is a gaussian white noise with zero mean and covariance matrix Qt, ant t is the time variable. The discrete observation equation is given by

255

300

(9)

18,4 29,4

previous experiments in batch and fed batch cultures (Queinnec et al., 1999) . All these values are plotted on figure 2 and compared with values given in Table 4.

where H is the observation function, y is the observation vector of dimension m (measurement vector) and v is a gaussian white noise with zero mean and covariance matrix Rk. k corresponds to the iteration at time tk.

wel.,

The algorithm is based on three steps of prediction , observation , reajustement. It also implies a step of linearization of F and H by Taylor series expansion of first order around the prediction of the state at time k : Xk/k-l. The mathematical algorithm is expressed from the state estimate at time k - 1, Xk-l/k-l , and a new measurement Yk to obtain the new estimate Xk/k.

~h"m

o

o 6

m.dil"m + el, .ky fedbatcM

,..,.tch2

""h

!r

.150 e o

~~--~--~~~~--=-~~~=---~--~~~

..,....

..,...(."..,..)

The essential difficulty of such an approach for on-line opimal state estimation lies in the choice of noise covariance matrices Rk and Qt and in the initialisation of the covariance matrix Pto . They are considered as synthesis parameters.

Fig. 2. f{La for different stirrer speeds, obtained from physical or biological experiments In the same way, the oxygen solubility 0; in the culture medium is strongly influenced by mineral salts (Schumpe, 1985) , which main of is f{2H P0 4 , and by temperature. The french norm NF T 90-032 furnishes a linear relation between the variations of oxygen solubility and temperature. Finally, one obtains:

Remark 2. : Since the determination of the transfer coefficient is not very precise and influenced by many factors (see previous section) , it could be considered as another state variable, whose time evolution would be given by f{~a = O. However, this solution induces problems of matrix conditionning. Moreover, it does not lead to significant improvement of the results. In fact, better results are obtained when the f{/a is directly corrected on the computer from the values determined offline , when the stirrer speed is changed. It is then abandoned .

0; = 0.23 mmol/l 5. STATE OBSERVATION The observed design problem is solved in this study with an extended Kalman filter. It has been already used with success in biotechnology processes (San and Stephanopoulos, 1984), (MarsiliLibelli, 1989) . However, mere continuous bioprocesses were involved, where the system converged towards a steady state. In the present case, variables of an unstationnary process have to be estimated, for which the time evolution is of exponential type. The design of the extended kalman observer is based on the minimization of mean square observation error, under the constraint of the linearized tangent approximation of the nonlinear dynamical model previously described. It allows to realize the state estimation using a continuous process model and discrete measurements .

Remark 3. : The differential equation relative to the volume evolution (4) is not considered when implementing the extended Kalman filter . In fact, if one considers that the volume is not measured , system (1)-(4) with observation equation y Po, is not observable. On the other hand, one can consider that the volume is measured (since the control variable Qin is known and the volume is corrected on the computer after each sample), but the use of this variable has more negative effects than improvements to observe the phenol concentration . In practice the equation relative to the volume is considered to simulate the model, but is not used by the Kalman filter since the volume does not have a strong influence on the

=

470

estimation but would increase the sIze of the estimated state vector if used .

The results are plotted on figures 3 and 4. Subplots exhibit the feed flow rate, the oxygen concentration, the biomass concentration, the stirrer speed, the yellow color evolution, which is related to 2hydroxymuconate semiladehyde (co-metabolite of the reaction) (Queinnec et al., 1999) and phenol concentration, respectively.

The extended Kalman filter has been applied in this paper to the reduced three states fed batch model (1)-(3) with measurement vector Yk PO,k and input variable Ut = qt. The numerical values of the covariance matrices were given by :

=

In the first experiment, the exponential profile of the feed flow-rate is clearly perceptible (dashed line), although with large variations, and reconstruction of both biomass and substrate concentration is satisfying. The main problem arises from the modification of the stirrer speed, then of the KLa , especially at time t 5 hours. In the second experiment the sampling period T has been reduced from 5 minutes to 2 minutes to overcome this problem. Moreover the influent concentration Sin has been reduced from 50g/1 to 30g/1 to smooth the input profile.

Pto = Qt = diag{O.l, 0.1, 0.1}

6. FEDBATCH CONTROL

=

Fedbatch control problem is first an optimal control problem . However, the global optimization problem corresponding to maximize the final quantity of phenol consumed in a minimal time may be transformed into a mere regulation problem, corresponding to a sub-optimal problem (Queinnec and Dahhou, 1994). Indeed, in the case of phenol degradation by R. eutropha, it has been shown in section 2 that the phenol degradation rate (which has to be maximized all along the reaction) is correlated to the growth rate with a constant conversion yield. According to the dependance of the specific growth rate to the phenol concentration, improving the productivity of phenol degradation corresponds to maintain a constant residual phenol concentration corresponding to a rapid growth rate.

7. CONCLUDING REMARKS The controlled fed batch presented in this work exhibits good productiviy since on-line monitoring of substrate concentration prevents phenol accumulations and avoids cell activity being affected by inhibition phenomena. The contol approach was based on dissolved oxygen measurement related to phenol concentration according to mass-balance modelling, extended Kalman filering to observe the time evolution of the pollutant and PI control of the influent feed flow rate to maintain a high constant specific growth rate. Determination of KLa , which is an essential part of the process modelling, has been discussed.

This standard regulation problem of one state variable of the process, i.e. the phenol concentration derived from the extended Kalman filter, can then be solved by any control stategy. However , note that this constant setpoint regulation problem leads to an exponential evolution of the biomass concentration and of the control input (flow-rate). A closed-loop control strategy has then to be applied to adjust the flow rate Qink from the error ek between the phenol concentration Sk and its set point S*. A PI controller has been used, which discrete version of is given by :

8. REFERENCES Charbonnier, S. and A. Cheruy (1996) . Estimation and control strategies for a lipase production process. Control Eng. Practice 4(11) , 15211534. Hill, A.K. and C.W. Robinson (1975). Substrate inhibition kinetics: phenol degradation by pseudomonas putida. Biotechnol. Bioeng. 17,1599-1615. Lee, J.C. and D.L. Meyrick (1970) . Gas-liquid interfacial areas in salt solutions in an agitated tank. Tans. Instn. Chem. Engrs. 48, T37T45 . Leonard, D . (1997) . Etude du metabolisme du phenol chez alcaligenes eutrophus : mise au point de strategie de depollution performantes. In: PhD Thesis of INSA. Toulouse, France. (in french). Leonard, D . and N.D. Lindley (1998) . Carbon and energic flux constraints in continuous culture

where T is the sampling period, Kp is the gain and Ti is the integration time. The numerical parameters of the controller have been selected as : Ti = 0.3 , Kp = 0.2 . The numerical value of the set point has been chosen as : S* = O.lg/l. This value corresponds to a suboptimal specific growth rate Jl* = 0.31 h- I . Note that the optimal value of Jl is Jlopt 0.36 h- 1 , obtained for S vi K.Ki = 0.026 9 /1. This optimal setpoint would be too difficult to maintain, due to the perturbations on the estimation of the phenol concentration, and the exponential evolution of the system.

=

=

471

. '.

02~ ~::!"'~~.'~+~~ !:-:~iJijfji

o

.. . . .. . ... ": - . . .. - .. . -.

~o

- -

o

..

o

.

. .. .

:

:

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6

•

2

Oxygen

.

o

Slom • • •

4

2:

6

Stirrer ap._d

: :: II-'_-,I

•..

.. 1

I

°O~-------2---------4~-------6----J

. p:n:' . x. fd~ .· · · · · -:~!~•••~ -o~·:f?±=d~ ~

~

o

4

2:

0.1

. . - , -.

",

0 . 05

. . .. . .

- . . . ; _. .

, .

~

. "

.. . . . .

. . .. . . - .. :. . . . _ . _ . . . . - :- .. . -. . .

°O~------~2~-------4~--~L--6~--~

6

time (h)

time (h)

Fig. 3. Experiment 1 Oxygen

!~t · · · ~ o

,

2:

:3

4

i

~

o.~ ~.:. ..> " -... '.~ ' ... . ---

0.1 5 0 .1

.

8' 0,05

°o

5

.

... .

. . ...

.

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j

2:

.~.•.•.... . . . ..•... .....•. . . .' .~. f~t

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.

:2:3

4

:3

4

I

>
. .. .

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Stlr,..r sp_ed

B l ornaaa

:§ " :

. .. . . . .:. . . . . .. . . .. . . . . . . . . . . • . . . . .. . ...

.• . . . .. .. .. . ..... . , .. . .... .•. . .... ..

··· 1

°0L-----------~2------3~----4~--~5

5

PhenO'l

Coler

0_2~

~o~~·L ~ 0.15

. .. . . . . .: . . . . . . - .:. .

o

1

:2

- .. .. -: . .

:3

~ 4

5

Urn_ (h)

Fig. 4. Experiment 2 tropha. In: Proc. of European Control Conference (ECC). Karlsruhe, Germany. Rainer, B.W. (1990) . Determination methods of the volumetric oxygen transfer coefficient kLa in bioreactors. Chem. Biochem. Eng. 4(4), 185-196. San, K.Y. and G. Stephanopoulos (1984). Studies on online bioreactor identification. 11. Numerical and experimental results. Biotechnol. Bioeng. 26, 1189-1197. Schumpe, A. (1985). Gas solubility in biomedia. In: Biotechnology (H . Brauer, Ed.). Vol. 2. Chap. 10. Van 't Riet , K. (1979) . Review of measuring methods and results in nonviscous gas-liquid mass transfer in stirred vessels. Ind. Eng. Chem. Process Des. Dev. 18(3),357-364.

of alcaligenes eutrophus grown on phenol. Microbiology 144,241-248. Leonard, D., C. Ben Youssef, C . Destruhaut, N.D . Lindley and I. Queinnec (1999). Phenol degradation by alcaligenes eutrophus: colourimetric determination of 2-hydroxymuconic semi aldehyde accumulation to control feed strategy. Biotechnol. & Bioeng. 65(4),407-415. Marsili-Libelli, S. (1989). Modelling, identification and control of the activated sludge process. Adv. Biochem. Eng. Biotech. 38, 90-158. Merchuk, J .C. (1977). Further considerations on the enhancement factor for oxygen absorption into fermentation broth. Biotechnol. Bioeng. 19, 1885-1889. Popovic, M., H. Niebelschutz and M. Reuss (1979). Oxygen solubilities in fermentation fluids. European J. Appl. Microbiol. Biotechnolo 8, 1-15. Queinnec, I. and B. Dahhou (1994). Optimization and control of a fed batch fermentation process. Optimal Control, Appli. and Methods 5, 175-19l. Queinnec, I., D. Leonard and C. Ben Youssef (1999) . State observation for fed batch control of phenol degradation by ralstonia eu-

472