Use of the inlet gas composition to control the respiratory quotient in microaerobic bioprocesses

Chemical

Engineering Science, Vol.

51, No. 13, pp. 3391-3402, 1996 Copyright cs 1996 Elsevier Snence Ltd Printed in Great Britain. All rights reserved 0009%2509/96 $15.00 + 0.00

0009-2509(95)00416-5

USE OF THE INLET GAS COMPOSITION TO CONTROL RESPIRATORY QUOTIENT IN MICROAEROBIC BIOPROCESSES

THE

CARL JOHAN FRANZfiN, EVA ALBERS and CLAES NIKLASSON* Department of Chemical Reaction Engineering, Chalmers University of Technology, S-41296 GGteborg, Sweden (First received 8 September 1995; accepted in revised form 12 December 1995) Abstract-Different aspects of the estimation and control of the respiratory quotient (RQ) have been investigated for the purpose of providing well characterized microaerobic, or oxygen limited, conditions in chemostat cultures. The RQ was controlled by changing the oxygen concentration in the inlet gas. The standard, steady-state equation for calculating the RQ in this case could not be used for dynamic RQ control. However, the dynamic characteristics of the equation could be considerably improved, by applying a first-order exponential filter to the inlet gas composition. Substituting the momentaneous inlet oxygen concentration for the filtered concentration in the standard gas balance equations resulted in favourable dynamic characteristics and high steady-state accuracy. Computer simulations showed that the sensitivity of the RQ to noise and bias in the oxygen analyses was acceptable for precision values typically achieved with mass spectrometry. A PID controller, and an adaptive pole placement controller, have been tried for the control of the RQ, calculated by the filtering procedure, during microaerobic ethanol production with Saccharomyces cerevisiae CBS 8066. The PID controller could not be used with constant control parameters, because the sensitivity of the RQ to the inlet oxygen concentration differed between different RQ setpoints. When the controller gain was adjusted for each RQ setpoint, the PID controller worked very well. The adaptive pole placement controller also worked well at all interesting operating conditions. In situ NAD(P)H fluorescence measurements indicated that the intracellular redox state is correlated to the RQ for RQ values in the range 10-30. Copyright 0 1996 Elsevier Science Ltd

INTRODUCTION The increasing interest in ethanol as a renewable energy source has inspired new interest for optimizing the production process in terms of yield and production rate. The yeast Saccharomyces cerevisiae is the most commonly used microorganism for ethanol production. During anaerobic ethanol fermentation by S. cerevisiae, the ethanol yield is significantly reduced because of formation of byproducts, e.g. glycerol. On the other hand, under aerobic conditions the carbon substrate is, to a large extent, converted into biomass and carbon dioxide due to the increased respiration rate. However, ethanol yield and production rate, as well as cell viability, have been enhanced by low oxygen transfer rates (OTR), or “microaerobic”conditions (Cysewski and Wilke, 1976; Nishizawa et a[., 1978; Hoppe and Hansford, 1984; Ryu et al., 1984; Tyagi, 1984; Grosz and Stephanopoulos, 1990; Kuriyama and Kobayashi, 1993; FranzCn et al., 1994). The optimum oxygen-limited conditions have not yet been completely identified, and are likely to vary with other process variables, due to the metabolic flexibility of S. cerevisiae. The large environmental and economic incentive for an efficient biotechnical

*Corresponding author. Tel: + 46-(0)31-772 30 27. Fax: + 46-(0)31-772 3035.

ethanol fuel production process calls for careful optimization studies, where the possibility of process scale-up also is taken into consideration. Microaerobic conditions have been shown to be advantageous also for other bioprocesses, e.g. xylose fermentation (du Preez et al., 1984; Ligthelm et al., 1988; Dellweg et al., 1989; Skoog and Hahn-HBgerdal, 1990; Guebel et al., 1991; Roseiro et al., 1991), and production of 2,3-butanediol by Enterobacter uerogenes (Zeng et al., 1990) and by Klebsiella oxytoca (Beronio and Tsao, 1993). With few exceptions, studies on low oxygenation rates have only shown qualitative results, and when quantitative results have been determined, they have still been specified for certain reactor configurations and experimental conditions. For example, the “optimum” OTR have often been reported in mmol I- ’h- ‘, or as an optimum air flow rate. This makes the actual figures dependent on the process scale and on the biomass concentration, and therefore also on substrate concentration and other environmental factors. The optimum transfer rates have been determined by keeping either the dilution rate or the oxygen concentration in the inlet gas constant, making the transition to other reactor configurations difficult. The scale-up from laboratory scale to pilot plant or production scale instead requires a parameter which is, as far as possible, independent on the

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biomass concentration and other environmental parameters. The respiratory quotient (RQ) is a variable that is independent of both the biomass concentration and of the process scale. It is rather easily determined from exhaust gas analysis, and has long been used as control variable in fed-batch and continuous cultivation of baker’s yeast (Aiba et al., 1976; Wang et al., 1977, 1979; Spruytenburg et al., 1978). The various control schemes for baker’s yeast production, suggested in these papers, have all been aimed at keeping the mediumfeed rate as high as possible, but low enough to avoid ethanol formation. However, for the optimization of the microaerobic production of other metabolites than biomass, it must instead be possible to control the RQ independently of the feed rate, and at high values. Therefore, the RQ must be controlled by manipulating the oxygen transfer rate across the gas-liquid interphase in the reactor. Recently, the RQ has been successfully used as a control and scale-up parameter for optimum production of 2,3-butanediol by Enterobacter aerogenes under oxygen limited conditions (Zeng et al., 1994). The RQ was controlled between 4.0 and 4.5 by varying the air flow rate, in order to maximize the yield of 2,3-butanediol and acetoin. The optimum RQ that was found experimentally in both batch, fed-batch, and continuous culture agreed well with optimum values determined from stoichiometric considerations. Furthermore, the optimum RQ was not dependent on the scale of the process. It was shown that under conditions of inhomogeneous oxygen supply in large-scale reactors, there exists an optimum circulation time, at which the optimum RQ was achieved (Byun et al., 1994). Successful attempts have been made to control microaerobic xylose fermentation by Pi&a stipitis at constant specific oxygen uptake rates (OUR) (Dellweg et al., 1989; Zhong and Bellgardt, 1990). However, even though the specific OUR is both scale independent and of central importance for the cellular metabolism, its determination requires the measurement or estimation of two variables, the oxygen transfer rate and the biomass concentration. Although several methods have been proposed [see e.g. Randolph et al. (1990), Dantigny et al. (1991), Zeng et al. (1991), Dubach and MHrkl (1992), Pomerleau and Perrier (1992), Sonnleitner et al. (1992) and Yamane (1993)], the on-line determination of the biomass concentration is still a very complicated task, especially in industrial media. Variables, or control schemes, based on the specific OUR are therefore still likely to be plagued by errors. The common idea when controlling the oxygen transfer rate or the RQ by means of the air flow rate or the agitation rate, is to manipulate the overall mass transfer coefficient. However, the mixing conditions in the bioreactor are also affected by these control actions. The gas hold-up, bubble dispersion and size distribution, and the extent of backmixing (deviation from ideality), also depend on the hydrodynamic con-

ditions, and are therefore influenced by changes in the stirring rate and/or air flow rate. It is sometimes difficult to separate effects from changes in these variables from “true” metabolic effects. This can, under unfortunate circumstances, seriously affect the conclusions drawn regarding the microbial response the increasing use (Lecher et al., 1993). Furthermore, of fast on-line optical measurements demands cultivation conditions where the mixing conditions are kept as constant as possible. Measurement of the culture fluorescence has become established as one of the few on-line techniques for direct monitoring of the biomass [for a review, see e.g. Lid&n (1993) or Li and Humphrey (1992b)]. Fluorescence is ideal for monitoring fast changes in the intracellular redox state, because only the reduced forms of NADH and NADPH can fluoresce. This means, that it would be suitable to use the NAD(P)H fluorescence as an indicator of the metabolic state in the microaerobic region, where changes in the intracellular redox level are likely to occur. However, the signal is also dependent on other factors, like pH and temperature. Furthermore, it is highly affected by changes in the size, number and distribution of bubbles in the broth (Li and Humphrey, 1992a). Undesired variations in the aeration and agitation rates must therefore be minimized. One way of controlling either the RQ, the OTR, or the specific OUR, and yet provide constant mixing conditions, would be to manipulate the concentration of oxygen in the inlet gas while keeping the stirring rate and the total gas flow rate constant. In such a scheme, the idea is to vary the driving force for the mass transfer across the gas-liquid interphase, instead of varying the mass transfer coefficient. However, two problems arise when trying to control microaerobic bioprocesses in this way. Firstly, standard gas balancing methods for calculating the OTR or the RQ from gas analysis results are based on the assumption of steady state in the gas phase concentrations. These methods cannot be used when the inlet gas composition undergoes rapid changes. Therefore, methods must be developed to calculate the OTR or the RQ under such transient conditions. Secondly, when controlling the RQ, the controller must cope with nonlinear process dynamics. Stability problems may arise, since small changes in the OTR will have larger effects on the RQ at higher RQ values, than at lower. Furthermore, since living cells are involved, the dynamics of the process may change because of adaptation of the cells. Possible control algorithms in this situation could be some kind of adaptive, or self-tuning, controller, or a standtrd PID regulator coupled with a gain schedule (AstrGm and Wittenmark, 1989). In very large-scale reactors, the situation may be further complicated by local variations in the mass transport. In this study, work aimed at controlling the respiratory quotient under microaerobic conditions, by changing the composition of the inlet gas, has been performed. The momentaneous oxygen concentration

Use of inlet gas composition in the inlet gas, used for calculating the RQ by gas balancing procedures, has been substituted for a dynamically filtered concentration. The effects of noise and bias in the oxygen analyses on the measured RQ at low oxygen concentrations, have been investigated by computer simulations. A PID controller with gain scheduling, and an adaptive pole placement controller, have been tried for on-line RQ control during continuous, microaerobic ethanol fermentation by Saccharomyces cerevisiae CBS 8066, using the exponential filter method for calculating the RQ value. NAD(P)H fluorescence measurements have been performed during these experiments, to investigate the possibility of using this measurement for monitoring RQ controlled, microaerobic fermentations.

THEORY

Calculation of the respiratory quotient The respiratory quotient is defined by (1) RQ=? where rco2 is the carbon dioxide evolution rate (CER, molm-3h-1), and ro2 is the oxygen uptake rate (OUR, mol me3 h-’ ). The RQ is easily calculated during steady-state conditions in a continuous culture, provided that the concentrations of carbon dioxide and oxygen can be analysed with sufficient accuracy in the gas entering and leaving the bioreactor. Thus, mass balances of oxygen, carbon dioxide, and inert gas (nitrogen) over the reactor yields (Heinzle et al., 1984) RQ =

~2.~02 2

. 2

-

yo,co,

yo>02 -

y2 o

.

!f!%

* =Y2,N2 >

(7.) Equation (2) is based on the assumption of perfect backmixing of the liquid phase, of the gas phase held up in the liquid, and of the head space gas phase. Furthermore, steady-state, constant liquid and gas flow rates, constant pressure and volumes of the three phases, and negligible gas transport via the flow of liquid through the system are assumed (Aiba and Furuse, 1990; Royce, 1992). Changing the inlet gas composition would seriously invalidate the assumption of steady state. This forecloses the use of eq. (2) under transient conditions, and if the RQ is to be controlled by the inlet oxygen concentration, other ways of calculating the RQ must. be devised. In a perfectly stirred tank reactor, the exhaust gas composition reflects the conditions in the reactor. Therefore, it must be possible to model the transport processes from the fundamental mass balances, based on the measurement of the exhaust gas composition. However, this would also require reliable measurements of the dissolved gases. A much more simple approach would be to transform eq. (2) so that the dynamic response becomes

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more favourable. This can be done by applying an exponential filter to the inlet gas composition. The exponential filter used here is described by Yo*,i(k)= ayo,i(k) + (1 - ~)yo*,i(k - 1)

(3)

where i is C02, 02, or N2, and yg,i(k) is the filtered inlet concentration of gas i at sample number k. Inserting this in eq. (2) gives

The delay 1is introduced in eq. (4) to account for the lag time, i.e. the number of samples, before a change in the inlet gas composition starts to affect the composition in the outlet gas. The weighting factor CI,and the delay 1,can be chosen, so that the dynamic response of eq. (4) acquires the desired characteristics. Control algorithms A PID controller with a constant proportional gain does not perform satisfactorily for our purposes, since the effect of a small change in the inlet oxygen concentration is much greater at higher RQ values than at lower ones. Therefore, two different control algorithms have been tested. To avoid problems with the stability of the closed-loop system, and excessively slow control, it is possible to make the gain of the controller dependent on the setpoint. This is an example of so-called gain scheduling. Another way of coping with the non-linear and changing process dynamics, that are not unusual in microbial systems, is the use of a self-tuning regulator. A self-tuning, or adaptive, controller automatically adapts the parameters of the controller to the changing process dynamics. The stability of the closed-loop system can thus be maintained over a wide range of operating conditions. Whereas gain scheduling can be used if the changes of the process dynamics are known a priori, the adaptive controller can better handle unforeseen changes. The PID controller An overview of the closed-loop system controlled with a PID regulator, with gain scheduling, is shown in Fig. 1. Expressed in real-time variables, the control law is written u(k)=u(k-l)+&{e(k)[l+~+~]

+e(k-2)?

(5)

where k is the sample number, u is the input to the system, e is the error between the setpoint and the actual output, h is the sample interval, and Kp, T,, and TD are the control parameters related with the proportional, the integral, and the derivative action of the regulator, respectively.

C. J. FRAN&N et al.

3394 I

I ysp

4

Gain Tdule

1

Fig. 1. Block diagram of a closed-loop PID control system with gain scheduling. ysp = setpoint ( - ), y = output (here RQ, - ), u = input (here setpoint voltage to air MFC, V), e = error ( - ), KP = controller gain (V), GplD= transfer function of controller, GProeess= transfer function of bioproccss.

equation error, E, is assumed to be white noise with mean zero. We have used a, “constant trace”, recursive least square algorithm (Astr6m and Wittenmark, 1989) to identify the parameters in the A- and B-polynomials. This algorithm prevents estimator wind-up when the system is not excited, which could happen, e.g. when the control is working well. Possible “bursts” in the control variable are thus prevented. Once the process parameters are estimated, the parameters of the pole placement controller [i.e. the coefficients in C’(q) and D(q)] can be determined. This is done by solving the polynomial identity P(q) = C’(q)A’(q) + B(q)%)

parameters &, TI, and TD can “rule of thumb” values according to method of self-oscillation. Here, the Kp was calculated for each RQ setto

(6)

& = ~o(RQsPP

where K~ and K~ are empirically determined parameters. There was no need to adjust TI and TD to different RQ setpoints. The adaptive pole placement controller An overview of the adaptive pole placement regulator used here is shown in Fig. 2. The bioreactor is modelled by the autoregressive (equation error) model A(&@)

= %)u(k)

(7)

+ E(k)

where A and B are polynomials of order n, and nb, respectively, in the backward shift operator q- I. The input to the system, u, is in our case given by the setpoint voltage for the air mass flow controller. The output, y, is given by the calculated RQ. The

(9)

- 4-l).

The factor (1 - q-‘) introduces an integral action in the controller. By choosing the poles p in eq. (8), it is possible to design the regulator so that the desired dynamic characteristics of the closed-loop system in Fig. 2 are obtained. Furthermore, KSP is determined by K

w

_

” B(q)

q=l

(10)

’

When all parameters are determined, can be calculated by

the input

AU

C’(q)

(11)

where (see Fig. 2) Au(k) = @Ml - 4-l)

= CYSP&P -

Expressed in real-time input becomes

variables,

Au(k) = YSP&P - (day(k) + -(c;A.u(k-1)

1 l-q-’

: U I I I I

I

I I

Wy(k)llC’(d. (12) the change

+

&,y(k

-

J%¶)

I---_-_-_--_-___-----_____(

controller

in the

nd))

+ 1.. +cb,.Au(k-n,,)).(13)

.Y

A(q) Bioreactor

I

Pole placement

u(k)

u(k) = u(k - 1) + Au(k)

I

1

(8)

where A’(q) = AM1

The control easily be set to Ziegler-Nichols controller gain point according

= (1 - pC1)“+l

I

Fig. 2. Block diagram of a closed-loop adaptive pole placement control system. q- 1 = delay operator, A, B, C’, and D = polynom% in q-l, KSP = setpoint gain (V), P = P-matrix in recursive least square algorithm (Astram and Wittenmark, 1989). Other symbols see Fig. 1.

Use of inlet gas composition It should be noted, that it is possible to cancel all zeros in the B-polynomial, to introduce extra zeros by adding terms to the KSP factor so that it also becomes a polynomial in 4, and to include measurable and non-measurable disturbances in the algorithms (istram and Wittenmark, 1989). No efforts have been made here to optimize the basic control algorithm in these directions. MATERIALS

AND METHODS

Strain and media The study was performed with the yeast Saccharomyces cereuisiae CBS 8066 obtained from Centraalbureau voor Schimmelcultures (Delft, The Netherlands). All experiments were made with the medium described in Table 1, except that the glucose concentration was only 10 gl-’ in the inoculum and batch cultures, and that no ergosterol or unsaturated fatty acids (Tween 80TM) were added to the inoculum cultures. Note that ergosterol and Tween 80TM were added to batch and continuous cultures even during microaerobic conditions (Andreasen and Stier, 1953, 1954). Cultivation procedures Inoculum cultures were grown for 24 h in a shake flask with a cotton stopper. A 2 ml aliquot of the inoculum was transferred to make a total of 2 1batch medium in the bioreactor. During the batch cultivation, the bioreactor was sparged with a mixture of air and nitrogen containing a total of 0.4% oxygen. When the glucose was almost depleted and before the culture entered the transition phase, continuous pumping of glucose medium into the bioreactor was started. After two to three residence times at a dilution rate of 0.07 h-‘, the biomass concentration was sufficiently high and steady for the RQ control experiments. Table 1. Medium composition Carbon and energy sourcet D-Glucose 4og1-’ Minerals’ WL),SOS KHZP04 MgSO,’ 7H20 Antifoam 289 (Sigma) EDTA CaC1,.2Hz0 ZnS04.7H20 FeSO, 7Hz0 H3B03 MnCI, 2H20 Na,MoO,‘2H,O CoCI, 2HZ0 CuSO,.SH,O KI

7sg1-’ 3.51 0.74 0.1 30.0 mgl-’ 9.0 9.0 6.0 2.0 1.56 0.8 0.6 0.6 0.2

Others Vitamins act. to Bruinenberg et al. (1983) Tween 80TMand ergosterol act. to Verduyn et al. (1990) ‘Autoclaved separately for 20 min at 121°C.

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Experimental equipment and analytical methods All experiments were carried out in a Chemap SG 3.5 bioreactor (Chemap AG, Volketswil, Switzerland), equipped with controllers for total weight, agitation (500 rpm), temperature (3O”C), pH (5.0), and total pressure (1.2 atm). The bioreactor was continuously sparged with a mixture of air and nitrogen. The air flow rate was controlled between 0 and 0.25 mol h-’ (0 and 100 mlmin-‘) with a mass flow controller (MFC) (Bronkhorst HI-TEC, The Netherlands). The air was added to a stream of nitrogen gas, and the total gas flow rate was subsequently held constant at 1.35 mol h-’ (540 mlmin-‘) by a second MFC. Gas analysis was made with a QMS 420 quadrupole mass spectrometer (Balzers AG, Liechtenstein), equipped with a heated stainless steel capillary inlet, an open axial electron impact ion source, and a Faraday cup detector. The QMS was calibrated at the beginning of each experiment, with two gases of known composition. After estimating the partial pressures, the mole fractions were determined by normalizing to 100%. During all calibration procedures, measurements were made on each gas until no more drift in the results was noticed. With this calibration procedure, the relative errors in the gas analysis results were smaller than 5% (including bias) at the lowest concentrations in question (at 0.1% oxygen), and typically smaller than 0.2%. The absolute standard deviations for O2 at 0.1%, CO* at 5%, Ar at l%, and N2 at 99.8% were 0.0003. 0.003, 0.0006, and 0.0005%, respectively. At the beginning of each experiment, a calibration curve of the inlet gas composition, as a function of the air MFC setpoint voltage, was calculated by a linear least squares fit based on analyses of the inlet gas with the QMS. During the actual experiments, the QMS was constantly measuring the exhaust gas, while the inlet gas composition was calculated from the setpoint voltage for the air MFC. The composition of the inlet and the exhaust gas were determined every 30 s. The sampling time for the RQ control was 90 s, so that only every third pair of analyses were used in the control algorithms. Two optical sensors were fitted in the side ports of the bioreactor. NAD(P)H fluorescence was measured with the FluoroMeasure System (BioChem Technology, Malvern, PA, U.S.A.). Total biomass concentration was monitored by a MEX-3 four-channel, alternating beam, near-IR absorbance probe model OD IO/5 (EUR-Control, BTG Kglle Inventing AB, Slffle, Sweden). Error simulation procedures Simulations of the error sensitivity were made for three different cases: (1) normally distributed noise in the oxygen concentrations at various oxygen concentrations and constant outlet CO1 concentration; (2) normally distributed noise in the oxygen concentrations at various oxygen concentrations and constant

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RQ = 30; and (3) bias in the oxygen concentrations at an inlet oxygen concentration of 0.5% at various

RQ. For cases (1) and (2), the inlet oxygen concentration was varied between 0.1 and 1.0%. The outlet oxygen concentration was always assumed to be half the inlet concentration. The concentrations of carbon dioxide in the inlet, and of argon in the inlet and outlet, were set to zero. In case (l), the outlet carbon dioxide concentration was held constant at 6.2%, allowing the RQ to change with the inlet oxygen concentration. In case (2), the outlet carbon dioxide concentration was adjusted to maintain a RQ of 30 at all different inlet oxygen concentrations. The nitrogen concentration was set by addition to 100%. Normally distributed noise of variable absolute standard deviation was then added to the molar fractions of oxygen in the inlet and outlet gas. Normally distributed noise of constant standard deviation was added to the concentrations of nitrogen and carbon dioxide. After the addition of noise, the molar fractions were again normalized to 100% in the inlet and the outlet gas and the resulting RQ was calculated. Data sets of 10,000 points were used in the calculations. For case (3), the effect of bias in the oxygen analysis was investigated. The unbiased inlet oxygen concentration was kept constant at 0.5%, and the CO2 concentration was adjusted to give different “true” RQ values. After addition of a bias term to the inlet and outlet oxygen concentrations, the molar fractions were again normalized to 100%. The resulting RQ was determined and compared to the true value. No addition of noise was made in case (3).

Tuning of controllers The integration and derivative time constants for the PID controller were determined to T, = 135 s and TD = 34 s by Ziegler-Nichols method of self-oscillation. The gain KP was calculated for each RQsp acK,,= - 300 V cording to eq. (6), using parameters and ICY= - 3.3, with a limit at - 0.015 V. In this way, the gain was varied from - 0.015 V at RQ 10 and 20, to - 0.0007 at RQ 50. The pole placement controller was allowed to adapt to the process for approximately 30 h using a pseudo-random binary signal (PRBS) in the setpoint voltage to the air MFC. The PRBS signal had a mean of 0.2 V, an amplitude of 0.03 V, and a probability for sign change of 0.4. This resulted in RQ values varying between 35 and 45. The adapted model had the orders n,=2,nb=3,andthelag1=1.

EXPERIMENTAL RESULTS AND DISCUSSION

Calculation of the respiratory quotient The results of using eq. (2) and eqs (3) and (4) for calculating the RQ, during step changes in the concentration of oxygen in the inlet gas, are shown in Fig. 3. If eq. (2) is used, a step change to a lower concentration of oxygen in the inlet gas resulted in an immediate drop to negative RQ values, followed by a dramatic rise to very large values. This was followed by a decreasing transient, in the calculated RQ value [see Fig. 3(a)]. A step change to a higher oxygen concentration resulted in an immediate decrease, followed by an increasing transient [Fig. 3(b)]. After 15-20 min after the step changes, the RQ levelled off at new, stable values.

70

b

60

2 -

0.6

2

0.4

Time

(min)

Fig. 3. The dynamic response of the respiratory quotient calculated with an exponential filter on the inlet gas composition by eq. (4) (+), and under steady-state assumptions by eq. (2) (solid line), during step changes in the inlet oxygen concentration from (a) 0.8-0.4% and (b) 0.4-0.8% (top panels). Bottom panels show the actual concentration (y,,o,, solid line) and the filtered concentration (Y:,~,, + ) of oxygen in the inlet gas. The dilution rate was 0.12 h-l, and a = 0.16.

Use of inlet gas composition This does not correspond to what we think would actually happen after a change in the inlet gas composition, and illustrates that eq. (2) cannot be used for calculating the RQ under transient conditions. If independent, perfect backmixing of the three phases is assumed, it is instead reasonable to believe that (1) the change in the actual RQ should be rather “smooth” and without discontinuities; and (2) following a step from a lower to a higher inlet oxygen concentration, the actual RQ should change with a more or less monotonous transient from a higher to a lower value, and vice versa. By applying the filtering procedure in eqs (3) and (4) it was possible to obtain RQ values that correspond to the conceptual model outlined above. The dynamic response during the step changes was quite favourable, and the estimated RQ changed smoothly from the original values to the new steady-state values (Fig. 3). Furthermore, the estimated RQ approached the “true” steady-state values [eq. (2)] asymptotically. An additional advantage was that a small noise reduction was obtained when filtering the inlet gas composition in this way. The procedure worked well during step changes from high to lower inlet oxygen concentrations [Fig. 3(a)], as well as during steps from low to higher concentrations [Fig. 3(b)]. A weighting factor c( = 0.16 was used here, but by adjusting the weighting factor, it should be possible.to optimize the step response for different reactor configurations. The lag time can also be adjusted to correspond to the delay in the outlet gas composition. Sensitivity to measurement errors Due to the very low concentrations of oxygen used in microaerobic fermentations, small errors in the oxygen concentrations may be amplified and cause unacceptable errors in the calculated RQ. The situation is further complicated by the fact that errors in the mole fractions of the different gases are correlated, since they are normalized to 100%. It is therefore important to investigate the sensitivity of the estimated RQ to errors in the oxygen concentrations. The propagation of errors in the gas analyses to calculated reaction rates has been investigated previously (Heinzle et al., 1984, 1990) and a method to reduce the noise in the OUR by dynamic filters has been proposed (Royce and Thornhill, 1992). Here, we have investigated the effect of bias and normally distributed noise in the raw data on the calculated RQ by means of simulations, to decide what specifications must be met on the accuracy and precision of the gas analysis in microaerobic experiments. Results from simulations in which the outlet carbon dioxide concentration was fixed at 6.2%, and the inlet oxygen concentration was varied, are shown in Fig. 4. This approximately corresponds to the case of changing the RQ setpoint at a fixed dilution rate. The noise in the RQ increased with increasing RQ (decreasing inlet oxygen content). However, noise of smaller standard deviation than 0.002 mol% resulted in less than 6% relative standard deviation in the RQ, even at the

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18 16 14

2 0 0

0.2

0.4

0.6

0.8

1.0

Yo.0, (%) Fig. 4. Simulation of the relative standard deviation in the RQ as a consequence of noise in the gas analyses. Constant inlet COz concentration (6.2%), variable RQ. RSD = relative standard deviation in RQ (%), s = absolute standard deviation in inlet and outlet oxygen (%). Standard deviations for CO* and N2 were 0.005 and O.Ol%, respectively.

lowest oxygen concentrations of 0.1%. For oxygen, the precision of our MS system is typically better than this value. Worse precision resulted in unacceptable errors in the RQ (Fig. 4). Varying the carbon dioxide concentration to keep the RQ constant at 30 for all the different inlet oxygen concentrations gave essentially the same effects (not shown). This corresponds to varying the dilution rate under RQ control. The noise level was again acceptable under the conditions in the present investigation. It is clear, that the main source of error is the oxygen analyses, i.e. the levels of the noise and the concentrations of carbon dioxide and nitrogen has little effect on the quality of the calculated RQ. To avoid error propagation, it is therefore necessary to further reduce the noise level in the oxygen analyses. This can be done, for example, by additional filtering of the concentrations (Royce and Thornhill, 1992). The effect of bias in the oxygen analyses was investigated at different RQ values (Fig. 5). It is evident that even a relatively large bias does not give any extreme errors in the RQ determination. A bias of k 0.1 abs% (relative bias of 20% in the inlet and of 40% in the outlet) gave less than 5% relative bias in the resulting RQ. Therefore, bias should not present a problem under normal conditions. If the bias is different in the analyses of the inlet and the outlet gases, the error will obviously increase. Comparison of control algorithms The possibility of using the filter method for controlling the RQ under microaerobic conditions, with either of the two control algorithms, was investigated by subjecting continuous cultures of Saccharomyces cerevisiae CBS 8066 to step changes in the RQ setpoint and in the dilution rate (Figs 6-9). Figure 6 shows the results of a series of setpoint changes in the range of 10 to 50 at the dilution rate of

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4 S v % ._

2-

;

’ .RQ=lO

72 . -2 !x

20

E

30 40 50

-4 -

-0.08

-0.12

-0.04 0,

0

0.08

0.04

bias (%)

60

Fig. 5. Simulation of the relative bias in the RQ, as a consequence of absolute bias in the inlet and outlet oxygen analyses, at different RQ values. The concentrations of O2 in the inlet was OS%, and in the outlet 0.25%. The CO2 concentration was varied to reach the indicated RQ.

S ‘;, 8 k

3.8 3.6 3.4 3.2 3.0

:: 7 30 5 PS 20 10 0

0.5

0.4 0.3 vg 0.2 $ 0.1 x 0

1.0 ,s 0.8 23 0.6 B 0.4 ,J 0.2 0

0

5

10

15 20 Time (h)

25

30

Fig. 7. Microaerobic RQ control by a PID controller with gain scheduling at RQ setpoint 40, during step changes in the dilution rate between 0.07 and 0.26 h- I. (a) The concentration of carbon dioxide (yz, co2),and of oxygen (yz, 02),in the outlet gas (X), (b) the setpoint voltage to the air mass flow controller (V), (c) the RQ value, calculated by eq. (4) ( - ), of and the dilution rate (D, h-l), (d) on-line measurements NAD(P)H fluorescence (Fluor., V) and near-IR absorbance (NIR, V).

60 50 ‘;‘ 40 5 30 g 20 10 0 2.4 S z ;; 2.0 a^8 $8 I.6 2 2 1.2 E 0.8 1 0

23 Z .:: d

1.0 0.8 0.6 0.4 0.2

5

10

15 20 Time (h)

25

1 30

Fig. 6. Microaerobic RQ control by a PID controller with gain scheduling, during a series of setpoint changes at a dilution rate of 0.07 h _ ’ (a) The concentration of carbon dioxide (y2,cq2), and of oxygen (y2, o,), in the outlet gas (%), (b) the setpomt voltage to the air mass flow controller(V), (c) the RQ value, calculated by eq. (4) ( - ), (d) on-line measurements of NAD(P)H fluorescence (Fluor., V) and near-IR absorbance (NIR, V).

0.07 h- I, using the PID controller with variable gain. The control worked very well during step changes both from higher to lower, as well as for lower to higher RQ setpoints. Each new setpoint was reached

within 10 to 50 min (90% response time typically smaller than 25 min), and the noise was typically less than _+ 1% of the setpoint (RSD < 0.6%) after the initial transients. Changes in the RQ set-points also had a small effect on the concentration of carbon dioxide in the exhaust gas, which varied between approximately 3.4 and 3.7% (Fig. 6). This indicates that changes in the oxygen transfer rate affect the metabolism in this domain. The PID control worked well also during step changes in the dilution rate (Fig. 7). As a consequence of the increase in dilution rate after a step change from 0.07 and 0.26 h- ‘, there was an increase in the overall carbon flux through the bioreactor. Since the metabolic rates were far from maximum at the dilution rates in question, there was also a large increase in the concentration of carbon dioxide in the exhaust gas. The changes in y2,co, followed a biphasic pattern, with an initial, rapid increase from 4 to 11% immediately after the step change, followed by a slower increase from 11 to 13% (see Fig. 7). After a short overshoot, the CO1 concentration then stabilized at approximately 12%. The controller could not quite

3399

Use of inlet gas composition

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12 8

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4

0.2 0.1

1.0 2

0.8

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0.8

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0.6

iz .L Q

0.2

0.4 0.2

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0 0

5

10

15

20

Time (h)

0

5

10

15

20

25

z

4 3

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30

Time (h)

Fig. 8. Microaerobic RQ control by an adaptive pole placement controller, during a series of setpoint changes at a dilution rate of 0.07 hK’. See Fig. 6 for notation.

Fig. 9. Microaerobic RQ control by an adaptive pole placement controller at RQ setpoint 40, during step changes in the dilution rate (D). See Fig. 7 for notation.

compensate for the changes immediately after the increase in dilution rate, and the RQ was about 10% too high until 5 h after the step change, corresponding to less than 1.5 residence times. However, the time constants for changes in the concentrations of metabolites in the liquid phase, as well as for metabolic adaptation, are usually larger than this. Therefore, no problems should appear in reaching new steady states using this controller. The controller handled the step change from 0.26 to 0.07 h-’ very well, and the RQ was within _+ 1% of the setpoint after only about 2 h from the step (Fig. 7). The steps in dilution rate illustrated, that after the initial transients, the most difficult situation to control would be the combination of low dilution rate and high RQ setpoint, since this situation would require the lowest oxygen concentrations. In spite of the same controller gain at the two dilution rates, the noise was reduced by almost 50% when the dilution rate was increased to 0.26 h-’ (RSD = 0.33% at D = 0.26 h-‘, compared to 0.59% at D = 0.07 h-l). The adaptive pole placement controller also worked well during step changes both in the RQ setpoint (Fig. S), and in the dilution rate (Fig. 9). The noise was somewhat larger than during the PID experiments (RSD < 0.7%). However, the adaptation had to be made at high RQ values, in order to adapt

a model that worked in the entire range of RQ setpoints. Therefore, the control was slower at the lower setpoints, with 90% response times ranging from 26 min for the steps between high RQ setpoints, to 100 min for the step to RQsp 10 (see Fig. 8). This should still not be a problem, as long as the time constant for the closed control loop is smaller than the dominating time constant of the process. It should also be possible to speed up the control without loss of stability by adapting the model around the setpoint of specific interest. The characteristic changes in the CO, concentration during the step change in dilution rate from 0.07 to 0.26 h-‘, was observed also in this experiment (Fig. 9). By dividing the large step change into two smaller steps, it was possible to shorten the time for the transient. When interpreting the responses of the NIR absorbance probe and the fluorescence probe, it should be borne in mind that many factors affect the signals. For example, the NIR absorbance is affected not only by the total biomass concentration, but also by the cell size distribution and changes in the cell membrane properties, plus other factors. The fluorescence reflects the total amount of reduced NAD(P)H in the bioreactor, and is therefore dependent on both the biomass concentration and the intracellular redox state.

3400

C. J. FRANZBNet al.

Changing the RQ in the range lo-30 had direct, fast effects on the NAD(P)H fluorescence (Figs 6 and 8). Adding more oxygen to the culture (lowering the RQ setpoint), should make it possible for the cells to reoxidize a larger proportion of the reducing equivalents, and it is therefore reasonable that the fluorescence decreased with decreasing RQsp. Changes in the range 40-50 did not affect the fluorescence to the same extent. It is possible that respiration does not contribute to the overall metabolism of the culture at these RQ values, and that changing the OTR in this low range may therefore have no or little immediate effect on the redox state of the cells. Increasing the RQ further may thus have minor effects on metabolism, unless other factors than the redox state are affected. However, it is clear that the range chosen here is relevant for the study of microaerobic metabolism in S. cereuisiae. Furthermore, the results indicate that it should be possible to control microaerobic metabolism indirectly by controlling the respiratory quotient. The NIR absorbance measurements showed that under these short-term experiments, changes in the RQ setpoint did not have any clear effect on the biomass concentration (Figs 6 and 8). It is well known that S. cerevisiae requires trace amounts of oxygen for the biosynthesis of sterols and unsaturated fatty acids (Andreasen and Stier, 1953, 1954; Tyagi, 1984; Zitomer and Lowry, 1992). In this study, ergosterol and polyoleic acid were added to the media also under microaerobic conditions, so the large effects of traces of oxygen on the biomass formation associated with the synthesis of these compounds should not be observed. However, apart from the redox balance and synthesis of sterols and fatty acids, oxygen may affect other growth related functions (Zitomer and Lowry, 1992), and the effects may be more substantial when looking over a longer time period. The investigation of these matters should be made in well-controlled chemostat experiments, but is beyond the scope of the present work. The results of the optical measurements were much more complex for the step changes in dilution rate (Figs 7 and 9). The concentrations of biomass and residual glucose, as well as of other metabolites, vary with changes in the dilution rate. The culture fluorescence is affected by these concentrations, too, which complicates the interpretation of the fluorescence response. After the step-up in dilution rate, the fluorescence immediately dropped, followed by a slower decrease and then a slow increase. It has been shown, that the fluorescence decreases after a glucose pulse or a step-up in dilution rate in an aerobic chemostat operated in the oxido-reductive domain at relatively high dilution rates (Scheper and Schtigerl, 1986). Therefore, the rapid drop observed here may be due to the increased oxygen concentration, but may also be a direct consequence of the increased glucose flux and/or growth rate. The slow decrease probably reflects the decrease in the total biomass concentration, as indicated by the NIR absorbance probe, but the OTR and the CER also change in this period, so the

transition itself may affect the response as well. The increase in fluorescence that followed may indicate a further adaptation of metabolism to the new conditions of higher growth rate and carbon flux. The step down in dilution rate (Figs 7 and 9) was also accompanied by changes in the OTR, CER, and the glucose flux. A step-down in the dilution rate under constant aeration would result in an increased fluorescence (cf. Scheper and Schiigerl, 1986). However, following the step change, the OTR remained too high for a short period (reflected in the drop in the RQ), which temporarily enabled the cells to reoxidize the excess NADH (Fig. 7). Therefore, the fluorescence first increases due to the lowered glucose concentration, then decreases due to the oxygen effect, followed by further transient behaviour as the cells adapt to the new conditions. The RQ controllers handled the step changes in dilution rate well, in spite of the large changes in both biomass concentration (NIR measurements) and the NAD(P)H fluorescence during these steps. However, to investigate the cellular response to step changes in the dilution rate at constant RQ fully, even tighter control is required. This can probably be achieved by optimizing the control algorithms around the RQ setpoint and dilution rates of interest. For the investigation of the steady-state behaviour and step changes in the RQ setpoints at constant dilution rate, the present control algorithms seem quite sufficient.

CONCLUSIONS

Accurate investigations of the steady-state metabolic response of microaerobic continuous cultures at different RQ setpoints and different dilution rates require reliable control schemes, so that the RQ can be kept constant while the culture approaches stationary state. To minimize the disturbance of the control actions on the mixing pattern of the bioreactor, it is advantageous to control the RQ by means of the composition of the inlet gas. Both favourable dynamic characteristics and accurate steady-state estimations of the RQ can be achieved by applying an exponential filter to the inlet gas composition. The filter contains two parameters, a weighting factor and a delay, and is used together with standard gas balancing procedures. With this method, the dynamic response of the calculated RQ corresponds to a conceptual model of the response of the actual RQ to changing inlet oxygen concentrations. An analysis of the sensitivity of the calculated RQ to errors in the oxygen analysis showed that using standard mass spectrometry for gas analysis provides sufficient precision and accuracy for acceptable estimation of the RQ under microaerobic conditions. A standard PID control algorithm works very well for controlling the RQ during microaerobic continuous cultures, if the controller gain is adjusted to the RQ setpoint. To maintain stability over the entire

3401

Use of inlet gas composition

range of RQ setpoints investigated, Kp must be adjusted by more than a factor 20. A more complex control algorithm, an adaptive pole placement controller, also works satisfactorily, but needs time for adaptation for proper function. In some cases, it is somewhat slower than the PID controller, but this can probably be overcome with further optimization. It has the advantage of adapting to minor changes in the process dynamics, and is therefore preferentially used when “new” situations arise, e.g. during fed-batch cultivations. Measurements of the culture NAD(P)H fluorescence during chains of RQ setpoint changes indicate that it is relevant to study the responses of S. cereuisiae in the range of RQ values of 10-50. In spite of large changes in the intracellular redox state and the biomass concentration, it was possible to control the RQ within close limits. Therefore, it should be possible to control microaerobic metabolism indirectly by controlling the respiratory quotient. Acknowledgements-The authors would like to thank Mr BjGrn Westerberg and Mr Staffan Asplund for inspiring discussions on controller design and signal filtering techniques, and Dr Gunnar Lid&n for helpful comments on the manuscript. This work was financially supported by biotechnology research funds from Chalmers University of Technology, and by the Nordic Industrial Fund.

Y

Y(q) Greek variables u

A

0 2

inlet gas outlet gas

PID Process SP true

gas (COZ, 02, Nz, or Ad PID controller bioreactor process setpoint unbiased value

Superscripts *

filtered concentration

Abbreviations

CER

A(q),

MFC OTR

A’(q)* B(q),

C’(q), D(q) D G h k KP KSP

n P P(q) 4 4

-1

S

TLJ

u

polynoms in pole placement controller dilution rate, h- ’ transfer function sample time, h sample number, dimensionless control parameter, proportional, V setpoint gain in pole placement controller, V delay, number of samples, dimensionless dimension of polynom, dimensionless. Note: dimension is in q - ‘. pole in P(q), dimensionless characteristic polynom forward shift operator, dimensionless Backward shift (delay) operator, dimensionless volumetric reaction rate, mol me3 h-’ standard deviation, dimensionless control parameter, derivation time, h integration control parameter, time, h input to bioreactor process (volt signal to air mass flow meter), V

exponential weighting factor, dimensionless difference equation error, dimensionless factors for gain schedule, V, dimensionless

Subscripts

NOTATION Variables

molar fraction in gas phase, dimensionless output from bioreactor process (RQ), dimensionless transformed output, dimensionless

OUR

QMS RQ RSD

carbon dioxide evolution rate, mm01 I-’ h-’ mass flow controller oxygen transfer rate, mmol I-’ h-’ oxygen uptake rate, mmoll-’ h-‘, and uptake rate, specific oxygen mmolg-‘h-l quadrupole mass spectrometer respiratory quotient, dimensionless relative standard deviation, dimensionless

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