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Method for on-line prediction of kinetics of alcoholic fermentation in wine making
JOURNAL OF FERMENTATION AND BIOENGINEERING VOI. 68, No. 2, 131-135. 1989
Method for On-Line Prediction of Kinetics of Alcoholic Fermentation in Wine Making N O U R E D D I N E EL H A L O U I , 1 G E O R G E S C O R R I E U , l* YVON C L E R A N , I AND A R L E T T E C H E R U Y 2 Laboratoire de G~nie des Proc~dds Biotechnologiques Agro-Alimentaires, I.N.R.A., 78850 Thiverval-Grignon, ~ and Laboratoire d'A utomatique de Grenoble, E.N.S.I.E.G., 38402 Saint Martin d'Hbresf France
Received 6 January 1989/Accepted 9 June 1989 The rate of alcoholic fermentation in wine making has been determined in real time from the measurement of the volume of CO2 released. It includes three successive phases characterized by four kinetic parameters: the time of onset of gas release (Td), the acceleration of CO2 production (kl), the maximal rate of CO2 production (Vm,x), and the slope of the logarithm of the rate of CO2 release during the deceleration phase (k2). A model of these four parameters considering only the process temperature and the initial sugar concentration was insufficient, since mean errors were between -+ 20 and -4-50%. Satisfying results were obtained in real time application, modeling Vmax and k2 on the basis of accelerated CO2 production (kl) calculated 5 h after the onset of gas production (Td+5). The precision of the polynomial models obtained were -+5.8% for Vmaxand -+ 10.4% for k2. Their application led to an early prediction of the course of the alcoholic fermentation process in isothermal conditions.
Wine making is a complex process involving several operations, often conducted empirically and traditionally. Alcoholic fermentation is an i m p o r t a n t step, especially because o f its effects on organoleptic characters. A large number of biochemical and microbiological studies, recently reviewed by R i b e r e a u - G a y o n (1), have led to a better understanding of the mechanisms involved. The quality of finished wines has been affected by recent technological progress, e.g. improved treatments of the starting material, such as carbonic maceration (2), and ventage heating (Benard, P. et al., Rep. I . N . R . A . , p. 1-38, 1980). In addition, the use of commercial p r e p a r a t i o n s o f active dry yeast for wine making and the progressive installation of fermentation temperature control have led to better control o f the fermentation process in the wine industry (3). On the other hand, there is practically no industrial use o f automatic techniques using modeling and process optimization (4, 5, Bull, D. N., A n n u . Rep. Ferment. Process, 6, 359-375, 1983). In spite of a large number of modeling studies of the progression of alcoholic fermentation, in the field o f wine making (6), or others (7-9), no predictive model o f fermentation kinetics applicable in real time has yet been published. This a p p r o a c h would be o f considerable value in the wine industry. By predicting the release o f heat, it would lead to better process control and thus to an optimization o f heat removal (10, 11). We recently developed a method for following and controlling the alcoholic fermentation process in wine making, based on the on line measurement of medium density and on the volume of CO2 released (12). These two physical parameters are tightly correlated with the concentrations o f sugars consumed and alcohol produced (13). As a result of this, it is now possible to follow fermentation kinetics in real time reflected by the rate o f CO2 production (14). We followed this work by industrial scale experiments (5000-I wine making tanks) involving specific
algorithms for each type of wine (white or red), including fermentation kinetics and temperature (15). The choice o f the most suitable c o m m a n d algorithm and o f certain setpoints would nevertheless be more relevant if fermentation rates could be predicted several hours beforehand, based on initial data and ongoing processes. This report describes the changes in the rate of alcoholic fermentation in wine making as a function of time, observed in isothermal conditions. It defines the characteristic parameters o f the observed kinetics and proposes an on line predictive method for its course. MATERIALS AND METHODS Strain used, measurement of biomass formed Active dry Saccharomyces cerevisiae was used. The yeast was reactivated before each test in a 5% (w/v) solution of glucose. Musts were inoculated after 30 rain o f incubation at 30°C and each inoculum was equivalent to 0.2 g (5 × 109 cells) per liter o f must. Total biomass formed during fermentation was measured microscopically in T h o m a s counting cells after diluting the sample 1/10. Experimental conditions Two types of musts were used in these experiments. Concentrated must and natural must were used in 11 tests in 700-• tanks (pilot scale) and 10 tests in 5000-/ tanks (industrial scale), respectively. The tests were done in isothermal conditions, in anaerobiosis, and without agitation. The initial conditions o f each test are summarized in Table 1. Instrumentation and automation of tanks The 700and 5000-I tanks had two types of sensors. A volume counter (Magnol G4 or G6) delivered one electrical pulse when 10 1 o f CO2 were produced. Three temperature sensors were composed of standardized platinum thermocouples (100 Ohms at 0°C). Two were used to measure the mean temperature of the fermentation medium and the third, installed at the level o f the gas counter, was used to convert the volume of CO2 released to 20°C. A n electronic
* Corresponding author. 131
132
HALOUI ET AL.
J. FERMENT.BIOEN(;.,
TABLE 1. Initial conditions for fermentation and experimental values of Td, kt, 1/,..... and k: Installation Pilot scale: 700-1tank Concentrated musts
Industrial scale: 5000-I tank Natural musts
Test no. 1 2 3 4 5 6 7 8 9 10 11 12
So (g//) 240 230 230 215 200 200 200 200 200 170 170 160
0 (°C) 25 18 32 25 35 25 25 20 15 18 32 25
Td (h) 24 26 3 9 4 12 11 20 24 34 4 8
k~ (l. C02/I.h") 0.0787 0.0141 0.0695 0.0752 0.1146 0.0424 0.0914 0.0117 0.0038 0.0134 0.1155 0.0537
V,...... (I.C02/I.h) 0.953 0.264 0.725 0.866 0.784 0.617 1.035 0.327 0.194 0.327 0.911 0.660
k. (tl i) 0.0176 (I.0048 0.0193 0.0153 0.0208 0.0101 0.0202 0.0068 0.0050 0.0063 0.0227 0.0130
13 14 15 16 17 18 19 20 21
176 189 194 194 172 176 190 190 230
25 18 18 17 18 18 18 19 17
16 30 25 25 17 22 27 22 14
0.1369 0.0194 0.0114 0.0073 0.0170 0.0160 0.0131 0.0152 0.0210
1.570 0.306 0.272 0.262 0.486 0.399 0.412 0.448 0.470
0.0773 0.0066 0.0073 0.0065 ND 0.0078 0.0120 0.0013 0.0064
ND, not determined. interface board (Analog-Devices, Mumac 5000) was used for acquisition, filtering, and A / D conversion of the data supplied by the sensors. Software written in Pascal and installed on an IBM P S / 2 computer was used for real time data processing. The parameters calculated were mean temperature of the fermentation medium, the volume of CO2 released, the concentrations of ethanol produced, and residual sugars (by applying models established in prior studies, using the volume of CO2 released) (12, 13), and the instantaneous rate of fermentation (rate of CO2 release, of sugar consumption, and of the ethanol production). Establishing and validating proposed models The fermentation kinetics is represented by the rate of CO2 release, since it is proportional to the rates of sugar consumption and ethanol production: - d S c / d t = 3.92 dCO2/ dt and d E / d t = 1.85 d C O 2 / d t (12). Since the rate of CO2 production includes several distinct phases, our model building procedure was done phase by phase. Thus, each kinetic parameter characteristic of one phase is reflected by a linear correlation with several variables, including fermentation conditions (initial sugar concentration and process temperature) and if necessary the previously acquired kinetic parameters. The fit of linear correlations with the experimental values was characterized by the correlation coefficient, the residual standard deviation, and the mean error. The latter is defined of the mean as the absolute value of differences between the experimental points and those supplied by the correlation equation.
RESULTS AND DISCUSSION Description of fermentation kinetics in isothermal conditions. Definition of characteristic kinetic parameters The on line measurement of the volume of CO2 released led to the real time calculation of the rate of CO2 production. The changes in these values with time are shown in Fig. 1, representative of the results obtained. Changes in the yeast concentration during fermentation are also shown. The changes in the rate of CO2 production with time are divided into three characteristic phases:
Phase 1 The first is devoid of any effective release of CO2 and is characterized by a rate of fermentation considered as null. This phase corresponds to the onset of fermentation (lag phase of cell growth) and to the progressive saturation of the medium with CO2. The end of this phase, characterized by the time of onset of gas release (Td), is equivalent to the first pulse delivered by the volume counter. Phase 2 The second phase is characterized by a rapid and practically linear increase of the rate of CO2 production. The slope of the corresponding line (k0 is used to characterize this phase, which coincides well with cell growth. The constant k~ corresponds to the acceleration of the rate of CO2 release and is proportional to temperature, e.g.O. 115 I. C O i l . h 2 at 35 °C but only 0.004 l. C O i l . h 2 at 15°C. Phase 3 The third phase is characterized by an exponential decrease in the rate of CO: release. This p h e n o m e n o n results from the continually decreasing fermentation by the yeast, due to inhibition of the process, primarily by the ethanol produced (16, 17). We observed that the logarithm of the rate of CO: release varied linearly with time: the slope of the corresponding line (k2) is characteristic of this phase. At the j u n c t i o n of phases 2 and 3, the rate of CO2 production is maximal, denoted Vmax.This rate corresponds to maximal fermentation activity and lasts for a very short time (about 1 h). Table 1 lists values of Td, kl, Vmax and k2 for all the pilot and industrial scale tests done.
Attempts at off line modeling of kinetics of alcoholic fermentation Our first aim was to establish polynomial models which could be used to reflect the four characteristic parameters of process kinetics (Td, kl, Vmax, and k2) as function of the individual conditions of each test (So and 0). Table 2 lists the models thus obtained. It also shows the mean error, correlation coefficient, and residual standard deviation of each test. Relationship 1 can be used to predict the time of onset of gas release with a mean error of _+3.6h, i.e. _+20%0. Relationship 2 can be used to predict the acceleration of CO: production with a mean er-
VOL. 68, 1989
ON-LINE PREDICTION OF ALCOHOLIC FERMENTATION 1.2
AiB I
C
CYl
8O
0
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120
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FIG. 1. Example of two experimental curves obtained in real time:volume of CO, released ( [] ) and its production rate ( ~ ). Total cell concentration (e). A: Phase 1; B: Phase 2; C: Phase 3. log dVCOz dt
k2t+c
ror of _+0.0127 I . C 0 2 / l . h 2, i.e. +28%o. Relationship 3 can be used to predict the maximal fermentation rate with a mean error of _+0.133 l . C 0 2 / l . h , i.e. +_ 19.8°/oo. Finally, relationship 4 can be used to predict the slope k2 of the deceleration phase with a mean error of _+0.0071 h ], i.e. +_49.5%o. Percentages are mean error calculated with regard to the mean of experimental values. It should be noted in the case of kt, Vmaxand k2 that when only fermentation temperature is taken into account in the polynomial models, practically the same results are obtained (respective mean errors of -+29o//0, +_22%, and +49.5O/oo). In all four cases, the models are unsatisfactory. Thus, the initial sugar concentration and fermentation temperature cannot be used to correctly reflect the kinetics of alcoholic fermentation in the wine industry. It is probable that other factors not measured in this study affect process kinetics. As reported by other authors the quantity of assimilable nitrogen (18), and the initial concentration of dissolved oxygen in the fermentation medium (19), would be two of these factors. On line modeling of kinetics of alcoholic fermentation This procedure is based on the hypothesis that
the acceleration of C O 2 production (k0 is indirectly the reflection of the factors not measured previouly. Method The first step involved detecting the onset of production (Td). Next, after five hours of CO2 production, we proceeded to the on line calculation of acceleration kl (noted kit). This calculation was done with linear regression ( d C O 2 / d t = k l c . t + b ) of the values of rates of CO2 production included between the m i n i m u m detectable (0.03 I. CO2/l.h, precision of measurement method) and the rate recorded at time T d + 5 . We believe that the calculation of k] was satisfying 5 h after the onset of gas release (Table 4). The mean difference with the experimentally observed mean of k~ was less that _+1~ ( + 9 ~ at time T d + 3). On the average, 50 experimental points were used in the regression for a 5-min acquisition period. It should be noted that the mean duration of the linear phase of CO2 production characterized by k~ was 10 h. Finally, k~c and the fermentation temperature (0) were used in the polynomial models to reflect Vmax and k2. Modeling Vmax and k2 at time T d + 5 The second order polynomial models calculated in real time at time T d + 5 are the object of relationships 5 and 6 (Table 3). Us-
TABLE 2. Polynomial models for off-line predictions of Td, k~, Vmax,and k2 as a function of the initial fermentation conditions (0, So) Relation no. 1 2 3 4
Td /q = V,,~a, /,'2
Correlations
Mean error
Correlation coefficient
Residual standard deviation
24.22 13.95 0 2.2010So 0.037002+0.0021 So2+0.0570 O.So 0.544+0.031 0+0.0018 So 0.000302 0.0001 So2-0.0001 O.So 4.078+0.335 0+0.0048 So-0.0050 0z 0.0001 So 2 0.0002O.So 0.156+0.011 0+0.0005 So 0.0001 02 0.0001 So2+0.0001 O.So
3.6 0.0127 0.133 0.0071
0.767 0.799 0.663 0.317
5.238 0.022 0.229 0.015
TABLE 3. Polynomial models for on-line predictions of Vma~and k2 as a function of the fermentation temperature (0) and the acceleration of CO2 production calculated at time Td+ 5 (ktc) Relation no. 5 6
Correlations V..... -0.365 0.0340+26.219 k~c+0.0014 0z+31.902 (k~c)z-0.874 O.k~ kz,. =0.0748-0.009 0+ 1.525 k~,+0.0001 02+9.162 (klc)2 0.099O.ktc
Mean error
Correlation coefficient
Residualstandard deviation
0.039 0.0014
0.973 0.960
0.057 0.003
134
H A L O U I ET AL.
TABLE 4.
J. FERMENT. B1OENO.,
Comparison between measurements and on-line calculated values for k~, Vm,~(relation 5), and k2 (relation 6) at time l-d. 5
k t~
Test no.
(l. CO2/l. h ~)
l 2 3 4 5 6 7 8 9 l0 11 12 13 14 15 16 17 18 19 20 21
0.0782 0.0140 0.0697 0.0752 0.1143 0.0420 0.0913 0.0115 0.0035 0.0138 0.1155 0.0533 0.1367 0.0193 0.0114 0.0070 0.0169 0.0160 0.0128 0.0151 0.0210
k l-ka
V...... (1. C021l" h)
(l. CO2/l. h 2) 0.0005 0.0001 0.0002 0 0.0003 0.0004 0.0001 0.0002 0.0003 0.0004 0 0.0004 0.0002 0.0001 0 0.0003 0.0001 0 0.0003 0.0001 0
Vmax- V......
0.916 0.351 0.720 0.884 0.782 0.617 1.041 0.340 0.213 0.343 0.912 0.701 1.571 0.412 0.321 0.267 0.384 0.373 0.340 0.367 0.433
k:-k2,
k2c (h I)
(l. CO2~/. h) 0.037 0.087 0.005 0.018 0.002 0 0.006 0.013 0.019 0.016 0.001 0.041 0.001 0.106 0.049 0.005 0.102 0.026 0.072 0.081 0.037
(h I)
0.0165 0.0062 0.0198 0.0148 0.0207 0.0198 0.0243 0.0084 0.0060 0.0062 0.0225 0.0097 0.0765 0.0064 0.0063 0.0060 ND 0.0063 0.0062 0.0067 0.0070
0.0011 0.0014 0.0005 0.0005 0.0001 0.0005 0.0041 0.0016 0.0010 0.0001 0.0002 0.0033 0.0008 (I.0002 0.0010 0.0005 ND 0.0015 0.0058 0.0054 0.0006
ND, not determined.
ing the method described above, the models obtained for predicting Vmax and k2 lead to a satisfactory fit of the values observed experimentally and calculated with the models (Table 4). The mean error of Vmax in comparison with the experimentally observed mean Vmax was _+0.039 l. C02/l.h, i.e. _+5.8O/oo. The mean error of k2 in comparison to the mean experimentally observed k 2 w a s _+0.0014h ~,i.e. _+10.4%0. In three tests in the 700-/tank, the changes in the rate of CO2 release, both experimentally observed and calculated with relationships 5 and 6, beginning at time Td+5, are
shown in Fig. 2. It is seen that the models correctly portray the kinetics of alcoholic fermentation in wine making. The gains calculated from the residual standard deviations due to the use of kit are substantial in comparison with relationships 3 and 4. This confirms the hypothesis that the acceleration of CO2 p r o d u c t i o n (kl) includes inform a t i o n on variables not measured, pertaining to the nature o f the musts used, which can affect fermentation kinetics. In conclusion, the modeling done here offers the advantage o f being easy to use and applicable in real time. It constitutes a mean to detect premature stopping of fermenta-
1,1
Q.
flu
o.4
ii
u L1 o 0
M
M
M
M
1M
IM
140
IM
IM
IO0
FIG. 2. Evolution of the rate of CO2 production, for three trials in the 700-I tank. On-line measurements: ( + ) , So 200g/l;O 25°C; (•), S o = 200 g/l;O 35°C; (II,), So=240g/l;0 On-line predictions: ( ).
25°C.
VOL. 68, 1989
ON-LINE PREDICTION OF ALCOHOLIC FERMENTATION
t i o n a n d t h e e n d o f f e r m e n t a t i o n , to e s t i m a t e t o t a l f e r m e n t a t i o n t i m e , to m a n a g e a c c i d e n t a l or p r e - s e t o p e n i n g o f t a n k s (e.g. g o i n g up), a n d m a i n l y t o i m p r o v e a p p l i c a t i o n of the c o m m a n d algorithm. NOMENCLATURE
So
: initial s u g a r c o n c e n t r a t i o n , g/I 0 : fermentation temperature, °C d C O z / d t : r a t e o f CO2 release, l - C O 2 / / , h dSc/dt : rate o f sugar c o n s u m p t i o n , g/l.h : rate o f e t h a n o l p r o d u c t i o n , g/l. h dE/dt Td : t i m e o f o n s e t o f CO2 release, h kt : a c c e l e r a t i o n o f CO2 p r o d u c t i o n , -CO2/1. h 2 : m a x i m a l r a t e o f CO2 p r o d u c t i o n , I. C O 2 / / - h Vmax : s l o p e o f l o g a r i t h m o f t h e CO2 p r o d u c t i o n rate k2 a g a i n s t t i m e at p h a s e 3, h -~ I n d e x c : values o f kinetic p a r a m e t e r s c a l c u l a t e d at t i m e
Td+ 5 ACKNOWLEDGMENT The research was done in the framework of contract No. BAP0031-F from the Biotechnology Action Programme of the Commission of the European Communities.
REFERENCES 1. Rib6reau-Gayon, P.: New developments in wine microbiology. Am. J. Enol. Vitic., 36, 1-10 (1985). 2. Tesni6re, C., Nicol, M., Sarris, J., Verries, C., Bourseix, M., and Flanzy, C.: Relations entre le degr6 d'int6grit~ des baies de raisin et leur m6tabolisme ana6robie. Sci. Aliments, 6, 31-46 (1986). 3. Blouin, J.: L'automatisme en vinification: r6alit6s d'aujourd'hui et perspectives de demain. Ind. Agri. A|im., 12, 1243-1246 (1986). 4. Mor, J . R . : A review of instrumental analysis in fermentation technology. Computer application in fermentation technology. Soc. Chem. Ind., 2th ed., 109-118 (1982). 5. Fox, R. I.: Computers and micro-processors in industrial fermentation. Topics in enzyme and fermentation biotechnology, 125-
135
175 (1984). 6. Boulton, R.: The prediction of fermentation behavior by a kinetic model. Am. J. Enol. Vitic., 31, 40-45 (1980). 7. Bovee, J.P., Strehaiano, P., Goma, G., and Sevely, Y.: Alcoholic fermentation: modelling based on sole substrate and product measurement. Biotechnol. Bioeng., 26, 328-334 (1984). 8. Converti, A., Perego, P., Lodi, A., Parisi, F., and Borghio M.: A kinetic study of Saccharomyces strains: performance at high sugar concentrations. Biotechnol. Bioeng., 27, 1108-1114 (1985). 9. Dourado, A., Goma, G., Albuquerque, U., and Sevely, Y.: Modeling and static optimization of the ethanol production in a cascade reactor. Biotechnol. Bioeng., 29, 187-194 (1987). 10. du Plessis, C. S.: Influence de la temperature d'61aboration et de conservation sur les caract6ristiques physico-chimiques et organoleptiques des vins. Bull. O.I.V., 56, 104-115 (1983). 11. Barre, P.: Le vin et les biotechnologies. Biofutur, 28, 43-47 (1984). 12. El Haloui, N., Picque, D., and Corrieu, G.: Alcoholic fermentation in wine making: on-line measurement of density and carbon dioxide evolution. J. Food. Eng., 8, 17-30 (1988). 13. El Haloui, N., Picque, D., and Corrieu, G.: Mesures physiques permettant le suivi biologique de la fermentation alcoolique en oenologie. Sci. Aliments, 7, 241-265 (1987). 14. Corrieu, G., Picque, D., and El Haloui, N.: Nouveau proced~ de contr61e automatique de la fermentation alcoolique bas6 sur la mesure en ligne de la production de CO 2. Ed. Lavoisier, Technique et Documentation, Paris, 1, 29-34 (1987). 15. El Haloui, N., Cleran, Y., Sablayrolles, J.M., Grenier, P., Barre, P., and Corrieu, G.: Suivi et contr61e de la fermentation alcoolique en oenologie. Essais /~ 6chelle industrielle. Rev. Ft. Oenol., 115, 12-17 (1988). 16. Leao, C. and van Uden, N.: Effects of ethanol and others alkanols on the temperature relations of glucose transport and fermentaion in Saccharomyces cerevisiae. Appl. Microbiol. Biotechnol., 22, 359-363 (1985}. 17. Richter, K.: Inhibitory effects of ethanol in alcoholic fermentation. Acta Biotechnol., 6, 239-243 (1986). 18. Bezenger, M. C. and Navarro, J. M.: Influence de l'azote sur la fermentation alcoolique en milieu mod61e simulant les conditions de l'oenotogie. Sci. Aliments, 7, 41-60 (1987). 19. Sablayrolles, J. M. and Barre, P.: Evaluation des besoins en oxyg6ne de fermentations alcooliques en conditions oenologiques simul6es. Rev. Fr. Oenol., 107, 34-38 (1987).
Method for On-Line Prediction of Kinetics of Alcoholic Fermentation in Wine Making N O U R E D D I N E EL H A L O U I , 1 G E O R G E S C O R R I E U , l* YVON C L E R A N , I AND A R L E T T E C H E R U Y 2 Laboratoire de G~nie des Proc~dds Biotechnologiques Agro-Alimentaires, I.N.R.A., 78850 Thiverval-Grignon, ~ and Laboratoire d'A utomatique de Grenoble, E.N.S.I.E.G., 38402 Saint Martin d'Hbresf France
Received 6 January 1989/Accepted 9 June 1989 The rate of alcoholic fermentation in wine making has been determined in real time from the measurement of the volume of CO2 released. It includes three successive phases characterized by four kinetic parameters: the time of onset of gas release (Td), the acceleration of CO2 production (kl), the maximal rate of CO2 production (Vm,x), and the slope of the logarithm of the rate of CO2 release during the deceleration phase (k2). A model of these four parameters considering only the process temperature and the initial sugar concentration was insufficient, since mean errors were between -+ 20 and -4-50%. Satisfying results were obtained in real time application, modeling Vmax and k2 on the basis of accelerated CO2 production (kl) calculated 5 h after the onset of gas production (Td+5). The precision of the polynomial models obtained were -+5.8% for Vmaxand -+ 10.4% for k2. Their application led to an early prediction of the course of the alcoholic fermentation process in isothermal conditions.
Wine making is a complex process involving several operations, often conducted empirically and traditionally. Alcoholic fermentation is an i m p o r t a n t step, especially because o f its effects on organoleptic characters. A large number of biochemical and microbiological studies, recently reviewed by R i b e r e a u - G a y o n (1), have led to a better understanding of the mechanisms involved. The quality of finished wines has been affected by recent technological progress, e.g. improved treatments of the starting material, such as carbonic maceration (2), and ventage heating (Benard, P. et al., Rep. I . N . R . A . , p. 1-38, 1980). In addition, the use of commercial p r e p a r a t i o n s o f active dry yeast for wine making and the progressive installation of fermentation temperature control have led to better control o f the fermentation process in the wine industry (3). On the other hand, there is practically no industrial use o f automatic techniques using modeling and process optimization (4, 5, Bull, D. N., A n n u . Rep. Ferment. Process, 6, 359-375, 1983). In spite of a large number of modeling studies of the progression of alcoholic fermentation, in the field o f wine making (6), or others (7-9), no predictive model o f fermentation kinetics applicable in real time has yet been published. This a p p r o a c h would be o f considerable value in the wine industry. By predicting the release o f heat, it would lead to better process control and thus to an optimization o f heat removal (10, 11). We recently developed a method for following and controlling the alcoholic fermentation process in wine making, based on the on line measurement of medium density and on the volume of CO2 released (12). These two physical parameters are tightly correlated with the concentrations o f sugars consumed and alcohol produced (13). As a result of this, it is now possible to follow fermentation kinetics in real time reflected by the rate o f CO2 production (14). We followed this work by industrial scale experiments (5000-I wine making tanks) involving specific
algorithms for each type of wine (white or red), including fermentation kinetics and temperature (15). The choice o f the most suitable c o m m a n d algorithm and o f certain setpoints would nevertheless be more relevant if fermentation rates could be predicted several hours beforehand, based on initial data and ongoing processes. This report describes the changes in the rate of alcoholic fermentation in wine making as a function of time, observed in isothermal conditions. It defines the characteristic parameters o f the observed kinetics and proposes an on line predictive method for its course. MATERIALS AND METHODS Strain used, measurement of biomass formed Active dry Saccharomyces cerevisiae was used. The yeast was reactivated before each test in a 5% (w/v) solution of glucose. Musts were inoculated after 30 rain o f incubation at 30°C and each inoculum was equivalent to 0.2 g (5 × 109 cells) per liter o f must. Total biomass formed during fermentation was measured microscopically in T h o m a s counting cells after diluting the sample 1/10. Experimental conditions Two types of musts were used in these experiments. Concentrated must and natural must were used in 11 tests in 700-• tanks (pilot scale) and 10 tests in 5000-/ tanks (industrial scale), respectively. The tests were done in isothermal conditions, in anaerobiosis, and without agitation. The initial conditions o f each test are summarized in Table 1. Instrumentation and automation of tanks The 700and 5000-I tanks had two types of sensors. A volume counter (Magnol G4 or G6) delivered one electrical pulse when 10 1 o f CO2 were produced. Three temperature sensors were composed of standardized platinum thermocouples (100 Ohms at 0°C). Two were used to measure the mean temperature of the fermentation medium and the third, installed at the level o f the gas counter, was used to convert the volume of CO2 released to 20°C. A n electronic
* Corresponding author. 131
132
HALOUI ET AL.
J. FERMENT.BIOEN(;.,
TABLE 1. Initial conditions for fermentation and experimental values of Td, kt, 1/,..... and k: Installation Pilot scale: 700-1tank Concentrated musts
Industrial scale: 5000-I tank Natural musts
Test no. 1 2 3 4 5 6 7 8 9 10 11 12
So (g//) 240 230 230 215 200 200 200 200 200 170 170 160
0 (°C) 25 18 32 25 35 25 25 20 15 18 32 25
Td (h) 24 26 3 9 4 12 11 20 24 34 4 8
k~ (l. C02/I.h") 0.0787 0.0141 0.0695 0.0752 0.1146 0.0424 0.0914 0.0117 0.0038 0.0134 0.1155 0.0537
V,...... (I.C02/I.h) 0.953 0.264 0.725 0.866 0.784 0.617 1.035 0.327 0.194 0.327 0.911 0.660
k. (tl i) 0.0176 (I.0048 0.0193 0.0153 0.0208 0.0101 0.0202 0.0068 0.0050 0.0063 0.0227 0.0130
13 14 15 16 17 18 19 20 21
176 189 194 194 172 176 190 190 230
25 18 18 17 18 18 18 19 17
16 30 25 25 17 22 27 22 14
0.1369 0.0194 0.0114 0.0073 0.0170 0.0160 0.0131 0.0152 0.0210
1.570 0.306 0.272 0.262 0.486 0.399 0.412 0.448 0.470
0.0773 0.0066 0.0073 0.0065 ND 0.0078 0.0120 0.0013 0.0064
ND, not determined. interface board (Analog-Devices, Mumac 5000) was used for acquisition, filtering, and A / D conversion of the data supplied by the sensors. Software written in Pascal and installed on an IBM P S / 2 computer was used for real time data processing. The parameters calculated were mean temperature of the fermentation medium, the volume of CO2 released, the concentrations of ethanol produced, and residual sugars (by applying models established in prior studies, using the volume of CO2 released) (12, 13), and the instantaneous rate of fermentation (rate of CO2 release, of sugar consumption, and of the ethanol production). Establishing and validating proposed models The fermentation kinetics is represented by the rate of CO2 release, since it is proportional to the rates of sugar consumption and ethanol production: - d S c / d t = 3.92 dCO2/ dt and d E / d t = 1.85 d C O 2 / d t (12). Since the rate of CO2 production includes several distinct phases, our model building procedure was done phase by phase. Thus, each kinetic parameter characteristic of one phase is reflected by a linear correlation with several variables, including fermentation conditions (initial sugar concentration and process temperature) and if necessary the previously acquired kinetic parameters. The fit of linear correlations with the experimental values was characterized by the correlation coefficient, the residual standard deviation, and the mean error. The latter is defined of the mean as the absolute value of differences between the experimental points and those supplied by the correlation equation.
RESULTS AND DISCUSSION Description of fermentation kinetics in isothermal conditions. Definition of characteristic kinetic parameters The on line measurement of the volume of CO2 released led to the real time calculation of the rate of CO2 production. The changes in these values with time are shown in Fig. 1, representative of the results obtained. Changes in the yeast concentration during fermentation are also shown. The changes in the rate of CO2 production with time are divided into three characteristic phases:
Phase 1 The first is devoid of any effective release of CO2 and is characterized by a rate of fermentation considered as null. This phase corresponds to the onset of fermentation (lag phase of cell growth) and to the progressive saturation of the medium with CO2. The end of this phase, characterized by the time of onset of gas release (Td), is equivalent to the first pulse delivered by the volume counter. Phase 2 The second phase is characterized by a rapid and practically linear increase of the rate of CO2 production. The slope of the corresponding line (k0 is used to characterize this phase, which coincides well with cell growth. The constant k~ corresponds to the acceleration of the rate of CO2 release and is proportional to temperature, e.g.O. 115 I. C O i l . h 2 at 35 °C but only 0.004 l. C O i l . h 2 at 15°C. Phase 3 The third phase is characterized by an exponential decrease in the rate of CO: release. This p h e n o m e n o n results from the continually decreasing fermentation by the yeast, due to inhibition of the process, primarily by the ethanol produced (16, 17). We observed that the logarithm of the rate of CO: release varied linearly with time: the slope of the corresponding line (k2) is characteristic of this phase. At the j u n c t i o n of phases 2 and 3, the rate of CO2 production is maximal, denoted Vmax.This rate corresponds to maximal fermentation activity and lasts for a very short time (about 1 h). Table 1 lists values of Td, kl, Vmax and k2 for all the pilot and industrial scale tests done.
Attempts at off line modeling of kinetics of alcoholic fermentation Our first aim was to establish polynomial models which could be used to reflect the four characteristic parameters of process kinetics (Td, kl, Vmax, and k2) as function of the individual conditions of each test (So and 0). Table 2 lists the models thus obtained. It also shows the mean error, correlation coefficient, and residual standard deviation of each test. Relationship 1 can be used to predict the time of onset of gas release with a mean error of _+3.6h, i.e. _+20%0. Relationship 2 can be used to predict the acceleration of CO: production with a mean er-
VOL. 68, 1989
ON-LINE PREDICTION OF ALCOHOLIC FERMENTATION 1.2
AiB I
C
CYl
8O
0
" ~ 0.8
133
~4o6O C~
~ 0.6
o
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L
,0
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+
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20 0.2
[] 10
•
-
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i
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40
i
i
IO
,
1 IO Time
i
I
[
100
i
120
,
I
o
,
1~
1110
(h)
FIG. 1. Example of two experimental curves obtained in real time:volume of CO, released ( [] ) and its production rate ( ~ ). Total cell concentration (e). A: Phase 1; B: Phase 2; C: Phase 3. log dVCOz dt
k2t+c
ror of _+0.0127 I . C 0 2 / l . h 2, i.e. +28%o. Relationship 3 can be used to predict the maximal fermentation rate with a mean error of _+0.133 l . C 0 2 / l . h , i.e. +_ 19.8°/oo. Finally, relationship 4 can be used to predict the slope k2 of the deceleration phase with a mean error of _+0.0071 h ], i.e. +_49.5%o. Percentages are mean error calculated with regard to the mean of experimental values. It should be noted in the case of kt, Vmaxand k2 that when only fermentation temperature is taken into account in the polynomial models, practically the same results are obtained (respective mean errors of -+29o//0, +_22%, and +49.5O/oo). In all four cases, the models are unsatisfactory. Thus, the initial sugar concentration and fermentation temperature cannot be used to correctly reflect the kinetics of alcoholic fermentation in the wine industry. It is probable that other factors not measured in this study affect process kinetics. As reported by other authors the quantity of assimilable nitrogen (18), and the initial concentration of dissolved oxygen in the fermentation medium (19), would be two of these factors. On line modeling of kinetics of alcoholic fermentation This procedure is based on the hypothesis that
the acceleration of C O 2 production (k0 is indirectly the reflection of the factors not measured previouly. Method The first step involved detecting the onset of production (Td). Next, after five hours of CO2 production, we proceeded to the on line calculation of acceleration kl (noted kit). This calculation was done with linear regression ( d C O 2 / d t = k l c . t + b ) of the values of rates of CO2 production included between the m i n i m u m detectable (0.03 I. CO2/l.h, precision of measurement method) and the rate recorded at time T d + 5 . We believe that the calculation of k] was satisfying 5 h after the onset of gas release (Table 4). The mean difference with the experimentally observed mean of k~ was less that _+1~ ( + 9 ~ at time T d + 3). On the average, 50 experimental points were used in the regression for a 5-min acquisition period. It should be noted that the mean duration of the linear phase of CO2 production characterized by k~ was 10 h. Finally, k~c and the fermentation temperature (0) were used in the polynomial models to reflect Vmax and k2. Modeling Vmax and k2 at time T d + 5 The second order polynomial models calculated in real time at time T d + 5 are the object of relationships 5 and 6 (Table 3). Us-
TABLE 2. Polynomial models for off-line predictions of Td, k~, Vmax,and k2 as a function of the initial fermentation conditions (0, So) Relation no. 1 2 3 4
Td /q = V,,~a, /,'2
Correlations
Mean error
Correlation coefficient
Residual standard deviation
24.22 13.95 0 2.2010So 0.037002+0.0021 So2+0.0570 O.So 0.544+0.031 0+0.0018 So 0.000302 0.0001 So2-0.0001 O.So 4.078+0.335 0+0.0048 So-0.0050 0z 0.0001 So 2 0.0002O.So 0.156+0.011 0+0.0005 So 0.0001 02 0.0001 So2+0.0001 O.So
3.6 0.0127 0.133 0.0071
0.767 0.799 0.663 0.317
5.238 0.022 0.229 0.015
TABLE 3. Polynomial models for on-line predictions of Vma~and k2 as a function of the fermentation temperature (0) and the acceleration of CO2 production calculated at time Td+ 5 (ktc) Relation no. 5 6
Correlations V..... -0.365 0.0340+26.219 k~c+0.0014 0z+31.902 (k~c)z-0.874 O.k~ kz,. =0.0748-0.009 0+ 1.525 k~,+0.0001 02+9.162 (klc)2 0.099O.ktc
Mean error
Correlation coefficient
Residualstandard deviation
0.039 0.0014
0.973 0.960
0.057 0.003
134
H A L O U I ET AL.
TABLE 4.
J. FERMENT. B1OENO.,
Comparison between measurements and on-line calculated values for k~, Vm,~(relation 5), and k2 (relation 6) at time l-d. 5
k t~
Test no.
(l. CO2/l. h ~)
l 2 3 4 5 6 7 8 9 l0 11 12 13 14 15 16 17 18 19 20 21
0.0782 0.0140 0.0697 0.0752 0.1143 0.0420 0.0913 0.0115 0.0035 0.0138 0.1155 0.0533 0.1367 0.0193 0.0114 0.0070 0.0169 0.0160 0.0128 0.0151 0.0210
k l-ka
V...... (1. C021l" h)
(l. CO2/l. h 2) 0.0005 0.0001 0.0002 0 0.0003 0.0004 0.0001 0.0002 0.0003 0.0004 0 0.0004 0.0002 0.0001 0 0.0003 0.0001 0 0.0003 0.0001 0
Vmax- V......
0.916 0.351 0.720 0.884 0.782 0.617 1.041 0.340 0.213 0.343 0.912 0.701 1.571 0.412 0.321 0.267 0.384 0.373 0.340 0.367 0.433
k:-k2,
k2c (h I)
(l. CO2~/. h) 0.037 0.087 0.005 0.018 0.002 0 0.006 0.013 0.019 0.016 0.001 0.041 0.001 0.106 0.049 0.005 0.102 0.026 0.072 0.081 0.037
(h I)
0.0165 0.0062 0.0198 0.0148 0.0207 0.0198 0.0243 0.0084 0.0060 0.0062 0.0225 0.0097 0.0765 0.0064 0.0063 0.0060 ND 0.0063 0.0062 0.0067 0.0070
0.0011 0.0014 0.0005 0.0005 0.0001 0.0005 0.0041 0.0016 0.0010 0.0001 0.0002 0.0033 0.0008 (I.0002 0.0010 0.0005 ND 0.0015 0.0058 0.0054 0.0006
ND, not determined.
ing the method described above, the models obtained for predicting Vmax and k2 lead to a satisfactory fit of the values observed experimentally and calculated with the models (Table 4). The mean error of Vmax in comparison with the experimentally observed mean Vmax was _+0.039 l. C02/l.h, i.e. _+5.8O/oo. The mean error of k2 in comparison to the mean experimentally observed k 2 w a s _+0.0014h ~,i.e. _+10.4%0. In three tests in the 700-/tank, the changes in the rate of CO2 release, both experimentally observed and calculated with relationships 5 and 6, beginning at time Td+5, are
shown in Fig. 2. It is seen that the models correctly portray the kinetics of alcoholic fermentation in wine making. The gains calculated from the residual standard deviations due to the use of kit are substantial in comparison with relationships 3 and 4. This confirms the hypothesis that the acceleration of CO2 p r o d u c t i o n (kl) includes inform a t i o n on variables not measured, pertaining to the nature o f the musts used, which can affect fermentation kinetics. In conclusion, the modeling done here offers the advantage o f being easy to use and applicable in real time. It constitutes a mean to detect premature stopping of fermenta-
1,1
Q.
flu
o.4
ii
u L1 o 0
M
M
M
M
1M
IM
140
IM
IM
IO0
FIG. 2. Evolution of the rate of CO2 production, for three trials in the 700-I tank. On-line measurements: ( + ) , So 200g/l;O 25°C; (•), S o = 200 g/l;O 35°C; (II,), So=240g/l;0 On-line predictions: ( ).
25°C.
VOL. 68, 1989
ON-LINE PREDICTION OF ALCOHOLIC FERMENTATION
t i o n a n d t h e e n d o f f e r m e n t a t i o n , to e s t i m a t e t o t a l f e r m e n t a t i o n t i m e , to m a n a g e a c c i d e n t a l or p r e - s e t o p e n i n g o f t a n k s (e.g. g o i n g up), a n d m a i n l y t o i m p r o v e a p p l i c a t i o n of the c o m m a n d algorithm. NOMENCLATURE
So
: initial s u g a r c o n c e n t r a t i o n , g/I 0 : fermentation temperature, °C d C O z / d t : r a t e o f CO2 release, l - C O 2 / / , h dSc/dt : rate o f sugar c o n s u m p t i o n , g/l.h : rate o f e t h a n o l p r o d u c t i o n , g/l. h dE/dt Td : t i m e o f o n s e t o f CO2 release, h kt : a c c e l e r a t i o n o f CO2 p r o d u c t i o n , -CO2/1. h 2 : m a x i m a l r a t e o f CO2 p r o d u c t i o n , I. C O 2 / / - h Vmax : s l o p e o f l o g a r i t h m o f t h e CO2 p r o d u c t i o n rate k2 a g a i n s t t i m e at p h a s e 3, h -~ I n d e x c : values o f kinetic p a r a m e t e r s c a l c u l a t e d at t i m e
Td+ 5 ACKNOWLEDGMENT The research was done in the framework of contract No. BAP0031-F from the Biotechnology Action Programme of the Commission of the European Communities.
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