Jourml of Food Engineering 26 (1995) 320-350 Copyright 0 1995 Elsevier Science Limited Printed in Great Britain. All rights resewed n26o-x774/9s!$9.s0 ELSEVIER 0260-8774(94)00061-l A Model for the Prediction of Fermentable Sugar Concentrations During Mashing Tatu Koljonen,a Jari J. H$m&Cnen,” * Kirsti Pietili’ Katharina Sjiiholm/’ & “Technical Research Centre of Finland (VTT), V’IT Automation, PO Box 1301 & “Technical Research Centre of Finland (V’IT), VTT Biotechnology and Food Research, PO Box 1500, FIN-02044 VTT, Finland (Received 21 February 1994; accepted 3 October 1994) ABSTRACT A model describing the hydrolysis of starch catalysed by x- and P-amylase in mashing was developed. The model was included in a simulation program that helps the planning of the mashing temperature profile. Measurements from laboratory scale mashings with different temperature profiles were used for estimating the model parameters ,for a Finnish malt made from the two-row barley variety Kymppi. An estimate for the proportion of gelatinized starch at different temperatures was also obtained. The model predictions for glucose, maltose and maltotriose concentrations were compared with independent measurements not used in the parameter estimation. The prediction errors for the final total concentration of fermentable sugars in wort (glucose, maltose and maltotriose) were +@6 to -56% (3 mashings) when Kymppi malt was mashed. For the other two malts tested on the laboratory scale the prediction errors were -1.1 to - 9.9% (4 mashings) and in the industrial scale mashings f4.6 to -2.6% (7 mashings). The model predicted the concentrations of active x- and fI-amylase to a sufficient accuracy in all experiments. Estimating the model parameters for the mashing conditions and the malt used would make the model predictions for fermentable sugar concentrations more accurate. *To whom correspondence should be addressed. 329
Transcript
Jourml of Food Engineering 26 (1995) 320-350 Copyright 0 1995 Elsevier Science Limited Printed in Great Britain. All rights resewed
n26o-x774/9s!$9.s0
ELSEVIER 0260-8774(94)00061-l
A Model for the Prediction of Fermentable Sugar Concentrations During Mashing
Tatu Koljonen,a Jari J. H$m&Cnen,” * Kirsti Pietili’
Katharina Sjiiholm/’ &
“Technical Research Centre of Finland (VTT), V’IT Automation, PO Box 1301 & “Technical Research Centre of Finland (V’IT), VTT Biotechnology and Food
Research, PO Box 1500, FIN-02044 VTT, Finland
(Received 21 February 1994; accepted 3 October 1994)
ABSTRACT
A model describing the hydrolysis of starch catalysed by x- and P-amylase in mashing was developed. The model was included in a simulation program that helps the planning of the mashing temperature profile. Measurements from laboratory scale mashings with different temperature profiles were used for estimating the model parameters ,for a Finnish malt made from the two-row barley variety Kymppi. An estimate for the proportion of gelatinized starch at different temperatures was also obtained. The model predictions for glucose, maltose and maltotriose concentrations were compared with independent measurements not used in the parameter estimation. The prediction errors for the final total concentration of fermentable sugars in wort (glucose, maltose and maltotriose) were +@6 to -56% (3 mashings) when Kymppi malt was mashed. For the other two malts tested on the laboratory scale the prediction errors were -1.1 to - 9.9% (4 mashings) and in the industrial scale mashings f4.6 to -2.6% (7 mashings). The model predicted the concentrations of active x- and fI-amylase to a sufficient accuracy in all experiments. Estimating the model parameters for the mashing conditions and the malt used would make the model predictions for fermentable sugar concentrations more accurate.
*To whom correspondence should be addressed.
329
330 T. Koljonen et al.
NOTATION
&;,,(~),B~a,
E;,E$
E”,E”
Hx,H,,
J(P)
K,,
km,k,dU
k:,k):
M n,
nJ
N
P
F-Ill
Activity of r- and fl-arnylase, respectively, in the liquid phase (wort) (U/l) a- and b-amylase activities in the wet malt (U/l) Initial values of c(- and /?-amylase, respectively, in the wet malt (U/I) Maximum concentration of x- and b-amylase in the liquid phase, respectively, obtained from laboratory scale mashing at 50°C (U/l) Kinetic constants of the production of dextrins from ungelatinized and gelatinized starch and maltotriose from gelatinized starch Frequency factors for the conversion of gelatinized and ungelatinized starch into dextrins and gelatinized starch into maltotriose by x-amyIase (Vminlg) Kinetic constants of glucose, maltose, maltotriose, and limit-dextrins production, respectively, by /I-amylase (liminlg) Frequency factors for the conversion of dextrins into glucose, maltose, maltotriose and limit- dextrins by p-amylase (liminlg) Kinetic constant and frequency factor for conversion of dextrins into maltose (min-‘) Activation energies for the denaturation of a- and fl-amylase (J/mol) Activation energies for the activation of x- and fi-amylase (J/mol) Dissolution coefficients corresponding to Y- and p-amylase (l/g/min) Objective function in the parameter estimation problem Michaelis constant for production of maltose from dextrins (g/l) Kinetic constant of the denaturation of a- and fi-amylase (min-‘) Frequency factors for the denaturation of X- and b-amylase (min-‘) Initial amount of malt (g) Number of state variables in the parameter estimation problem Number of samples from the mashing experiment j used in the parameter estimation problem Number of mashing experiments in the parameter estimation problem Parameter vector to be estimated in the parameter estimation problem Proportionality factor for volume displaced by malt in mash
A model for the prediction qf fermentable sugar concentrations during mashing 331
R
t I/
T(t) TU
T, V
v, W,,k
XI X2 X.3 X4
X5
a:, (tii;P)
xkj (6, >
Gas constant (8.3143 J/mol/K) Time (min) Time of ith sample in mashing experiment j in the parameter estimation problem (min) Temperature (K) Highest temperature at which all the starch is ungelatinized (K) Lowest temperature at which all the starch is gelatinized (K) Volume of the liquid phase of the mash (1) Volume of the wet mash (1) (i.e. the volume that malt displaces in mash) Weight for deviations of predicted and measured values of the kth state variable in the mashing experiment j at the ith sampling instant in the parameter estimation problem Concentration of starch in mash (g/l) Concentration of dextrins in mash (g/l) Concentration of glucose in mash (g/l) Concentration of maltose in mash (g/l) Concentration of maltotriose in mash (g/l) Concentration of limit-dextrins in mash (g/l) Predicted value of kth state variable in the mashing experiment j in the parameter estimation problem (g/l or U/l) Measured value of kth state variable in the mashing experiment j at the sampling instant t,, in the parameter estimation problem (g/l or U/l)
INTRODUCTION
Malt mashing is an important process in the production of beverages such as beer and whiskey. The aim of mashing is to produce a wort containing suitable amounts of fermentable sugars, yeast nutrients and flavor compounds. The time course of the mashing temperature (the temperature profile) consisting of periods of constant and linearly increasing temperature is planned beforehand. The goal in choosing a suitable temperature profile is to produce a wort with the desired properties. A model describing the biochemical phenomena taking place during mashing would help the planning of the mashing program.
In this paper, the enzymatic hydrolysis of starch during mashing is considered. Starch is an insoluble glucose polymer that cannot be digested by brewer’s yeast and it has to be converted into shorter saccharides (glucose, maltose and maltotriose) in order to produce fermentable wort. The conversion is mainly a result of the action of the enzymes. At 53-65°C starch begins to gelatinize (Marc et al., 1983; Palmer, 1989) and becomes more susceptible to the hydrolytic enzymes. Large starch granules constitute 90% of the total mass of starch and they are gelatinized at lower temperatures (61-62°C) than the small ones (75-80°C) (Palmer, 1989).
332 1: Koljonen et al.
x-Amylase converts starch into dextrins that are further converted into sugars mainly by P-amylase. As the temperature rises, the reaction rates increase steeply but the enzymes are denaturated faster. A minor part of starch hydrolysis is catalysed by other enzymes such as limit-dextrinase, r-glucosidase and phosphorylase (Manners, 1974).
Marc (1981) and Marc et al. (1983) presented a model for starch hydrolysis. The model presented in this paper has a different structure and fewer parameters to be estimated by model fitting. The parameter estimation problem and model performance are also analysed in more detail.
MATERIALS AND METHODS
Malts
Commercial malts from the Finnish barley varieties Kymppi, Ingrid and Kustaa were used in laboratory scale mashings. The malts were ground in a Biihler-Miag DLFU disc mill with the gap set at 1-O mm. Furthermore malt mixtures produced from different malting barley varieties were used in industrial scale mashing experiments.
All malts were well modified and they differed mainly in enzyme activities. The model parameters were estimated from the measurements of mashing experiments with Kymppi malt.
Mashings
In the laboratory scale mashings, 50 g of ground malt were suspended in 200 ml of prewarmed deionized water containing 75 mg CaCl,.2H,O and O-3 ml O-5 M H,SO,. The experiments on laboratory scale consisted of five isothermal mashings lasting 120 min at 50, 60, 65, 70 and 75°C and five mashings with different temperature profiles: 45”C/20 min, 63”C/35 min, 72”C/35 min, 8OW12 min (profile 1); 5O”C/20 min, 63”C/35 min, 72W35 min, 8O”C/15 min (profile 2); 5O”C/30 min, 66W45 min, 76WlO min (profile 3); 4O”C/50 min, 75W53 min (profile 10); 55YJ57.5 min, 65W57.5 min (profile 11). In all laboratory mashings the rate of temperature increase between the rests was 2Wmin.
The industrial scale mashing experiments were carried out in two Finnish breweries (A and B). The total volumes of the mash tuns were 35 m3 and 40 m3, respectively. In the first experiment in brewery A, the temperature profile consisted of four rests at 5OW54 min, 6O”C/30 min, 67”C/40 min, 76”C/25 min (profile 4). The rate of temperature increase between the rests in brewery A was O.S”C/min. In the second experiment in brewery A, the first temperature profile was 5oW55 min, 67W45 min, 76W25 min (profile 6). The temperature of the saccharification rest (67°C) was then increased and decreased by 2°C ( - 2°C: profile 5; + 2°C: profile 7) and the mashing-in temperature decreased by 2°C (profile 8). In brewery B, two mashings with slightly different malt-to-water ratios (O-26 and 0.25) were carried out. The temperature profile consisted of mashing-in with linearly increasing temperature 35-45”C/52 min and the rests at 62W15
A model for the prediction of fermentable sugar concentrations during mashing 333
min, 7O”C/6 min, 78”C/15 min (profile 9). The rate of temperature increase between the rests was 1”Cimin.
Analytical methods
The model development and parameter estimation required measurements during mashing from the liquid phase of mash. The samples were taken at intervals of lo-25 min, immediately cooled to 4°C in ice-water to prevent further enzymatic conversions, centrifuged at 4”C, and filtered before analysis. r-Amylase and /j-amylase activities, concentrations of glucose, maltose and maltrotriose, and total extract were measured.
x-Amylase and P-amylase activities were determined spectrophotometrically from the color change of dyed substrates at 40°C temperature (McCleary & MacFadden, 1990). The initial enzyme concentrations in malt were determined from the dissolved enzyme concentrations during isothermal mashings at 50°C. The enzymes did not substantially denature during a 120 min mashing.
The sugar concentrations (glucose, maltose, maltotriose) of the samples taken during the mashing were analysed by HPLC and the results were expressed as a percentage of the dry matter of malt. The initial sugar concentrations and extract in malt were determined by extraction at 0°C in order to avoid hydrolysis of polymers. The extraction time was 5 min for sugars and 1 h for the soluble extract. The content of starch in malt was determined polarimetrically (Marc et al., 1983).
The extract content is the concentration of substances dissolved from malt into wort. It was determined from the samples taken during mashing by a specific gravity measurement at 20°C. The results were expressed as a percentage of the dry matter of malt. Extract content was also used to determine an estimate of concentration of dextrins and limit-dextrins.
The repeatabilities and reproducibilities of the analysis methods used are shown in Table 1. The repeatabilities and reproducibilities for the HPLC
TABLE 1 Repeatability and Reproducibility of the Analysis Methods. The Repeatability and Reproducibility Errors were Assumed Independent. Normally Distributed Errors
were Assumed in the Calculation of the Confidence Interval
analysis were determined by two sets of experiments (a and b). The repeatability for sugars (HPLC analysis) and the total extract were deduced from the experiments of set a (8 measurements), in which all samples were analysed with the same calibration. In the experiments of set b (10 measurements), different calibrations were used in order to analyse the reproducibility of the HPLC analysis. The repeatabilities for starch analysis was calculated from two samples and the repeatabilities for cx- and ,!3-amylase were given by Henry and Butler (1992).
MODELING ASPECTS
Model description
Figure 1 shows the processes included in the model. The enzymes dissolve from gList to wort and the enzymatic conversions are assumed to take place only by the action of dissolved enzymes. The dissolution of carbohydrates from grist to wort is not described in detail, because the soluble carbohydrates dissolve very rapidly.
Ungelatinized starch is assumed not to be hydrolysed by the action of amylases. Gelatinized starch is converted into dextrins and maltotriose by the action of dissolved a-amylase. Dextrins are converted into sugars and limit-dextrins by the action of dissolved P-amylase. Dextrins were defined as r-limit-dextrins that cannot be hydrolysed further by rx-amylase, and limit- dextrins as a-P-limit-dextrins that cannot be hydrolysed further by u- or p-amylase. Starch, dextrins and limit-dextrins consist of a vast variety of glucose polymers. The sum of dextrins and limit-dextrins could be estimated by subtracting the amount of sugars (i.e. glucose, maltose and maltotriose) from the total carbohydrates in the extract. The total concentration of carbohydrates was obtained by assuming that there are 91% carbohydrates in wort dry matter, as was concluded by Palmer (1989). Starch is assumed to be insoluble and thus not present in the extract. Saccharose and fructose are not included in the model since their concentration in wort is insignificant
Fig. 1. Schematic representation of the reactions included in the model. Solid lines represent mass flow and dashed lines represent the actions of the enzymes.
A model for the prediction of,fermentahle sugur concentrations during mushing 335
when pure malt is mashed. The reaction rates of enzyme denaturation and enzymatic conversions depend on the temperature according to Arrhenius type relationships (Laidler & Meiser, 1982).
The model used to describe the carbohydrate and enzyme concentrations during mashing is given in eqns (l)-( 15).
M i=H, - ” (x,-x)-k,(T)r (2)
M ,‘jg= -H,,- (/1,-/j)
“,
The concentrations of active x- and b-amylase are described by eqns (l)-(4). The dot denotes the time derivative. The enzyme concentration (g/l) and activity in constant conditions at 40°C (U/l) are considered to be proportional. During mashing the enzymes gradually dissolve from the grist and the dissolution rate is assumed to depend linearly on the difference between enzyme concentrations in the grist and in the liquid phase. The dissolution coefficient H is divided by the volumes of the wet malt P’, in (1) and (3) and the liquid phase I/ in (2) and (4) in order to satisfy the mass balance condition. The initial weight of malt M takes into account the effect of malt-to-water ratio on enzyme dissolution. Enzymes are denaturated as the temperature increases. In (2) and (4), the thermal denaturation of enzymes is assumed to take place only in the liquid phase. The denaturation rates of x- and P-amylase are proportional to concentrations of active enzyme in wort.
The mass balance equations of the enzymatic hydrolysis of starch are given by eqns (5)-(10). The numerical coefficients in (5) and (6) represent the mass increase due to water in the compounds formed in the hydrolysis:
X,= -r[x, -u(T)][0.964A~,,(T)+A~,,(T)] (5)
~*=sl[x,-u(T)]A~,,(T)-lag, 0*9B,,(T)+0.947 BmaU) K +x +B,,,x(T) (6)
I,, 2 I
336 7: Koljonen et al.
i5=Aidt(T)x[x, -u(T)] (9) &=Bldex(T)PX2 (10)
Second-order rate expressions are used to describe the enzymatic conversions of different carbohydrates. The reaction rate is proportional to the product of concentrations of the enzyme and the substrate. The total enzyme activity results from the interaction of the concentration and the hydrolysing activity of an active enzyme. For the conversion of dextrins into maltose by b-amylase, a Michealis-Menten reaction rate expression is used [in (6) and (S)]. Th e amount of ungelatinized starch is determined by
; T<T,
u(T)= Tg -+-
T,-T, > Xl(O) ; T&TIT,
; T>T, (11)
In the model, starch is assumed to be gelatinized gradually so that at lower temperatures than T,, all the starch is ungelatinized (and thus nonhydrolysable), between temperatures T, and Tg the proportion of gelatinized starch increases linearly until, at temperatures higher than Tg, all the starch is assumed to be gelatinized. The gelatinization reaction is assumed to be irreversible so that gelatinized starch would not become ungelatinized even if the temperature were decreased.
The temperature dependence of functions k,(T), Ic,~(T), A,?(T) (j={dex, mlt}), and B,(T) (j={gl, mal, ldex}) are represented by Arrhenius type relationships (Laldler & Meiser, 1982) in eqns (12)-(U):
The model parameters to be estimated based on the measurements are the enzyme dissolution coefficients (H,, Hp), the activation energies (E”, E”, E$ E z), the Michealis constant Km, the gelatinization temperatures (T,, T,) and the frequency factors (kf, k;, A !& A $R, Bi,, BLal, and B&) in (12)-(15). The estimated parameter values are shown in Table 2.
There are several differences between the model (l)-(15) and the model described by Marc et al. (1983). The dissolution coefficients (H, and HP) are different for s(- and /7-amylase. The hydrolysis of ungelatinized starch and the production rate of maltotriose from dextrins were found negligible and are not described in (l)-(15). The activation energies (E’ and E”) are the same for all the reactions catalysed by the same enzyme, whereas Marc et al. (1983) allowed different values for different reactions. Moreover, Marc et al. (1983) described the dissolution of sugars and dextrins from grist to the liquid phase to be proportional to the concentration in the grist phase. In (l)-(15) the dissolution of sugars and dextrins is assumed to occur
A model for the prediction of fermentable sugar concentrations during mashing 337
TABLE 2 Parameter Values for Kymppi Malt Estimated from Laboratory Scale Mashing
Experiments
a-Amylase /j-Amylase
Hydrolysis Frequency factor (liminig)
Activation energy (J/mol)
Denaturation Frequency factor (min -- ‘)
Activation energy (Jimol)
Dissolution (Vgimin)
Tg = 336.5 K T, = 315.4 K
A’d& = 3.77 x 10”’ A ;fi = 6.42 x lo9
E’ = 1.03 x 10”
k’,’ = 3.86 x 10j4
E ,; = 2.377 x 10’ E$ = 4.439 x 105
H, = 9.72 x 10 5
B;, = 1.62 x 10”” B’A,, = 1.05 x 10”’ min ’ BI:,, = 1.09 x 104’
K, = 2.8 (gil)
E” = 2.93 x 10’
k’,: = 9.46 x 10 67
instantaneously at the beginning of mashing. Thus, no time-dependent dissolution is included and no dissolution coefficients need to be estimated. In the model presented here, the gelatinization of starch is gradual, while Marc et al. (1983) described the gelatinization to take place instantly at 55°C. The gradual gelatinization is a more natural description, since the gelatinization temperature is different for starch granules of different size (Palmer, 1989). The model has 16 parameters that have to be estimated due to experimental data by model fitting. The model of Marc et al. (1983) had 23 such parameters which makes the model identification problem more difficult.
Initial values
The initial values for the model state variables for different malts are listed in Table 3 and they were obtained as follows. In the beginning of mashing all the enzymes are in the malt grist
Q)=Q, (16)
B,(O)=&,0 (17)
and there are no enzymes in the liquid, i.e.
cc(O)=0 (18)
P(O)=0 (19)
When the concentration of an active enzyme in wort during mashing at 50°C temperature obtained its maximum value (A, and B. for r- and
338 T. Koljonen et al.
/I-amylase, respectively), the concentrations in the malt grist and liquid phase of mash were assumed to be equal. Then
v+ v, @g,o =p A0
v, (20)
and
(21)
The initial carbohydrate concentrations [Xi(O), i= 1,. . . ,5] were obtained by dividing the amount of each carbohydrate in malt by the total volume of mash (V+ Vg). The initial concentration of limit-dextrins [x6(O)] was assumed to be zero.
The volume displaced by malt when mixed with water, VP, was determined (when no measurement was available) by assuming that the same amount of malt always displaces the same volume in mash, i.e.
Vh=Ym.M (22)
where the proportionality factor rrn= 0.656 I/kg was obtained by observing that the 0.05 kg malt grist used (moisture content 75%) increased the total volume of mash by 0.0328 1 when the malt to water ratio was 1:4. This approximation is valid if the moisture content of malt, malt-to-water ratio, and grist coarseness can be assumed constants.
Model (l)-(15) with the initial conditions listed in Table 3 was solved numerically by the fourth-order Runge-Kutta method with an adaptive step size.
Parameter estimation
The model parameters were estimated by model fitting such that the model predictions were compared with the measured values of the state variables and the parameters were changed in order to minimize the prediction error. The model parameters were estimated in three stages: six parameters related to the dissolution and denaturation of (i) IX- and (ii) fl-amylase, and (iii) 10 parameters related to the breakdown of starch. The enzyme dissolution and denaturation parameters were estimated from the isothermal (50, 60, 65, 70 and 75°C) laboratory scale mashings. Mashings with temperature profiles were used for model verification. For the estimation of the parameters of starch hydrolysis, measurements from two laboratory mashings with increasing temperature profiles (profiles 10 and 11) were also used for the parameter estimation.
The objective of each subproblem (i)-(iii) was to find the parameter vector p that minimized the square root of the sum of the squared errors between the model output and the measurements [=root mean square
A model for the prediction of fermentable sugar concentrations during mashing 339
c v, ,r. 5 a In w, 000 000s
h--i3 33---s
sxxx xxxx
340
(RMS) error], i.e.
RMS@)=
i7 Koljonen et al.
(23)
In (i) and (ii) only enzyme activity in the liquid phase of the mash was measured (number of measured state variables ns=l). In (iii) there were observations of glucose, maltose, maltotriose, and dextrin concentrations (n,=4). Because the reactions that produced the highest carbohydrate concentrations in wort were considered the most important, equal weighting (~;-,~=l, for all j,i,k) was used in eqn (23). The evaluation of RMS(p) required solving of N initial value problems. The fourth-order Runge-Kutta method with an adaptive step size was used (Press et al., 1988).
In the minimization problems (i), (ii) and (iii), the minimum was searched by a two-level estimation method (Koljonen et al., 1992). In problem (iii), the production of maltose was described by Michealis-Menten kinetics:
reaction rater B,,i[dexl
[dex] +K,, (24)
where B,,, and the Michaelis constant K,,, were the parameters to be estimated. The objective function formed long and narrow contours on the
(B maI, &,)-plane (Holmberg, 1982). The Michaelis constant K,,, was estimated on the upper level and other parametersp were estimated on the lower level for fixed Km. Powell’s conjugate direction method was used on the lower level and Brent’s parabolic interpolation method on the upper level.
In all estimation problems, the physically unfeasible parameter values that were encountered during the estimation procedure were dealt with by a suitable penalization term. C-language implementations of Powell’s direction set method, Levenberg-Marquardt method and Brent’s method described by Press et al. (1988) were used in the calculations.
RESULTS
Laboratory scale mashings
The model was verified by predicting the wort carbohydrate and enzyme concentrations in laboratory scale mashings with different temperature profiles and different malts. The parameter values and the initial values for the state variables shown in Tables 2 and 3 were used.
Figures 2-4 show the temperature profiles, the measurements, and the model predictions when different malts (Kymppi, Kustaa and Ingrid) were mashed. The predicted carbohydrate concentrations generally matched well the measured values in all three mashings. However, in the beginning of mashing the predicted maltose concentration was always lower than the measured concentration. The errors in the measured and predicted concentrations of fermentable sugars in final wort were +0.6-9.9%
A model for the prediction of fermentable sugar concentrations during mashing 34 1
20
0
a)
temperature 1 ; : ~~
maltose ,+- 5
- - ‘--i ‘*- -
Ii’ _I
__-
0 50 100
Time [min]
/ /i
t ____ _,’ \esr iLs+Lmit -@it r ins
i
80
80
20
0 50 100
b) Time [min]
Fig. 2. Predicted (lines) and measured (symbols) concentrations of (a) maltose (*) and maltrotriose (A), (b) starch (predicted only), dextrins + limit-dextrins ([II), and glucose (0) in two laboratory scale mashings with Kympppi malt (profile I). (-) represents the 95% confidence limits for glucose and maltotriose and (-) for
maltose and dextrins + limit-dextrins predictions.
(Table 4). The model also predicted accurately the time period of the rapid increase in maltose concentration.
The differences in sugar concentrations of final wort between mashings with different malts were small, since the initial starch concentrations of the malts were close to each other. Ingrid malt had the lowest CL- and fi-amylase activities, but produced higher sugar concentrations than the other malts
342 T Koijonen et al.
0 20
0 50 100
Time [min]
Fig. 3. Predicted (lines) and measured (symbols) concentrations of starch (predicted only), dextrins+limit-dextrins (o), maltotriose (A), maltose (*), and
glucose (0) in a laboratory scale mashing with Kustaa malt (profile 1).
120 T :r starch
temperat”re~‘~
l-l k-61 \ maltotriose 1
80
70
20
0 50 100
Time [min]
Fig. 4. Predicted (lines) and measured (symbols) concentrations of starch (predicted only), dextrins+limit-dextrins (o), maltotriose (A), maltose (+), and
glucose (0) in a laboratory scale mashing with Ingrid malt (profile 1).
with the profile 3 (Table 4). This may be due to the difference in the limit- dextrinase activity. The effect of limit-dextrinase on the hydrolysis of starch is not included in the model.
Figure 2 illustrates the confidence of the predictions induced by the inaccuracy of the measurements. Assuming the model itself is correct, there
A model for the prediction qf fermentable sugar concentrations during mashing 343
TABLE 4 Predicted Final Concentrations of Fermentable Sugars in the Laboratory and Indus- trial Scale Mashings. Parameter Values Correspond to Laboratory Scale Mashings. The Relative Error Between Measurements and Predictions was Calculated from
the Mean of the Measurements for Repeated Measurements
Malt Mashing Final concentration of fermentable sugars
are three possible sources of inaccuracy in the predictions: (i) errors in the independent variables (e.g. initial values, sampling time and temperature), (ii) errors in the estimated parameter values due to the error in measurements used in parameter estimation, and (iii) errors in the independent measurements with which the predictions are compared. The sampling time and temperature profile were assumed to contain no error. The measurement errors for initial values and independent measurements were assumed to be normally distributed with standard deviations in Table 1. The sampling distribution for the parameter estimates was generated by the Monte Carlo method (100 replications) (Bard, 1974). The 95%) confidence intervals were generated by allotting realizations for each type of errors from their respective probability distributions (1000 replications) and dropping the 25 smallest and largest predictions at each sampling point.
At the beginning of mashing, the measured concentrations of maltose and glucose were higher than predicted and not within the error limits (Figs 2(a) and (b)). This may be caused by the action of thermolabile enzymes (a-glucosidase or limit-dextrinase) not included in the model. Also the measured dextrin concentration of the 9.5 min sample was lower than predicted in one of the two mashings with Kymppi malt (Fig. 2(b)). This difference was most likely a measurement error, since the sugar concentrations had evened out after 50 min of mashing.
344 7: Koljonen et al.
Industrial scale mashings
Experiments in two breweries Industrial scale experiments in two Finnish breweries (brewery A and B) were performed in order to verify the validity of the model in brewery conditions. The parameter values estimated from the laboratory mashings (Table 2) and the initial values in Table 3 (brewery A, malt 1; brewery B, malt 3) were used.
Figure 5 shows model predictions for X- and P-amylase activities in the experiment in brewery A and Fig. 6 shows one of the experiments in brewery B. The predictions were in close accordance with the measurements. It was observed that an unreliable measurement of initial malt X- or a-amylase activity caused a gap between the predicted and measured maximum enzyme activity. According to the simulations, however, the model predictions for sugar concentrations are not very sensitive to small variations in the initial values of amylases.
Predicted carbohydrate concentrations in the experiment in brewery A (Fig. 7) matched the measured concentrations quite accurately (the error in the final total sugar concentration was less than 1.8%). The predicted glucose concentrations were always lower than the measured concentrations.
The measured and predicted carbohydrate concentrations in mashing with malt-to-water ratio of 0.25 in brewery B are shown in Fig. 8. The prediction errors in the final sugar concentration of wort in both mashings in brewery B were less than 4.7 g/l (~4.6%). As in the other industrial scale experiments, the predicted glucose concentration was lower than the measured one during the whole mashing. The mashing with the slightly thicker mash (malt-to-water ratio of O-26) produced less sugars, although there were higher initial amounts of starch, dextrins, sugars, and enzymes.
2 80
1.8 75
z
1.6
1.4
SJ 0” 1.2
5 1 .$ 0.8
F OX 0.4
0.2
0
0 100 200
Time [min]
Fig. 5. Predicted (lines) and two determinations of x- (0) and P-amylase (0) activities in a mashing in brewery A (profile 4).
A model for the prediction of fermentable sugar concentrations during mashing 345
temperaturer
1.8
1.6
s 1.4
L-Y 1.2 $ L 1
.g 0.8
.?j 0.6 a
0.4
0.2
0
80
70
20
0 50 100
Time [min]
Fig. 6. Predicted (lines) and measured n- (0) and P-amylase (0) activities m a mashing in brewery B (profile 1).
100
90 starch
80 R
F 70
B 5 60
.z 50
2 40
8 s 30
0 20
10 45
40 0
0 100 200
lime [min]
Fig. 7. Predicted (lines) and two determinations of the concentrations (symbols) of starch (predicted only), dextrins + limit-dextrins (predicted only), maltotriose (A),
maltose (+), and glucose (0) in the first experiment-in brewery A (profile 4).
Small changes in the temperature profile
In the second experiment in brewery A (Table 3: brewery A, malt 2), the effects of small changes (&2”C) in the temperature profile on carbohydrate composition of wort were studied. The changes of the order of f2”C are often used in breweries in order to compensate, e.g. small changes in malt properties. The predicted concentrations of total fermentable sugars and
80
75
346
60 G e i?!
50 2 .E 60
H F m 8 40 40 E s 0 F
20 ---a__ 30
80
70
0 50 100
Time [min]
Fig. 8. Predicted (lines) and measured concentrations (symbols) of starch (predicted only), dextrins + limit-dextrins (o), maltotriose (A), maltose (+), and
glucose (0) in a mashing in brewery B (profile 9).
120
20
0
Fig. 9. Predicted and measured concentrations of fermentable sugars and dextrins + limit-dextrins in four mashings in brewery A (profiles 5-8): n corresponds to measurements from mashing with saccharification rest at 65°C o at 67°C and o at 69°C and the corresponding model predictions are represented by solid lines; A corresponds to measurements from mashing with mashing-in at 48°C and the
corresponding model predictions are shown by dashed lines.
+ limit-de&ins
80
75
70 5 e
65 !j
P 60 g
E 55 $
50
45
0 50 100 150 200
Time [min]
A model for the prediction of fermentable sugar concentrations during mashing 341
dextrins (Fig. 9) were in agreement with the measurements in all four mashings (prediction errors for final fermentable sugar concentrations were +0*7 to -2.6%). However, the predicted final maltose concentrations were 4.7 to 7.1% higher than the measured concentrations and as in other industrial scale mashings the predicted glucose concentration was lower than measured. The predicted concentration of fermentable sugars increased slightly faster than the measured concentration.
The mashing conditions in the brewery and the properties of the malt were different from those in the laboratory experiments. The possibly different conversion rates in the industrial environment were analysed by re- estimating the frequency factors for the conversion of starch and dextrins into dextrins and fermentable sugars (A “,.,9x, A zfi, B$, B&i, By,,,) in (12) and (13) by using the measurements from the industrial scale mashings. In the so-called leave-one-out tests, the parameters were estimated based on the measurements from three of the above mashings and the model predictions were compared with observations of the fourth independent mashing.
Figure 10 shows one of the four leave-one-out predictions (profile 6). The model predictions were very close to the measured concentrations. The prediction error in the final fermentable sugar concentration of wort in leave-one-out tests varied between + 1.8 and -3.8%. When the temperature of the saccharification rest was increased and decreased by 2”C, the difference between the measured lowest and highest final maltose concentration was 2 g/l. The corresponding difference in the total concentration of fermentable sugars was 4 g,/l. It should be noted that differences in both maltose and total fermentable sugar concentrations are
80
75
0 50 100 150 200
Time [min]
Fig. 10. Predicted (lines) and measured (symbols) concentrations of starch (predicted only), dextrins +limit-dextrins (o), maltotriose (A), maltose (+), and
glucose (0) in brewery A in a leave-one-out test.
348 i? Koljonen et al.
within the confidence intervals of the analysis methods (Table 1). Thus, it is also possible that there may not have been any real differences in the sugar concentrations of the mashings with different temperature profiles. The difference between the predicted lowest and highest maximum maltose concentrations was 0.2 g/l.
The four sets of parameter values obtained from the leave-one-out tests were close to each other. The frequency factors related to the degradation of starch (4 12, A zi) decreased to one half of the values estimated from the laboratory scale mashings. This suggests that starch degraded more slowly in the brewery than in laboratory mashings. The changes in the values of parameters related to the conversion of dextrins into sugars were very small except that the frequency factor related to the production of glucose (BE,) was doubled and the frequency factor related to the production of maltose (BL,,) decreased by 30%. The increase in the formation rate of glucose is in accordance with the fact that in all industrial scale simulations with parameter values corresponding to the laboratory scale, the predicted glucose concentrations were consistently lower than the measured concentrations (Figs 7 and 8). The duration of the mashing-in in the brewery conditions is much longer than on the laboratory scale, which promotes the action of r-glucosidase. a-Glucosidase converts maltose into glucose and thus the difference in the estimated values of Bi, and BL,, for laboratory and industrial scale may implicitly describe the action of a-glucosidase.
DISCUSSION
The basic structure of the model for predicting the concentrations of carbohydrates and active (x- and fl-amylase is mainly based on second order reaction kinetics with the Arrhenius type temperature dependences. The necessary measurements for the estimation of model parameters included the concentrations of glucose, maltose, and maltotriose and the concentrations of active x- and p-amylase in the malt and liquid phase of the mash. Also malt starch content and total extract of the wort during mashing were analysed.
The model predicted qualitatively correctly the effect of mashing temperature on the wort sugar concentrations both on laboratory and industrial scale. When small changes were made in the temperature profile in a brewery, the predicted changes in carbohydrate concentrations were smaller than the measured changes. However, since the measured changes in the final fermentable sugar concentration were within the 95% confidence limits of the analysis method, the model predictions can be considered accurate enough, also quantitatively.
Differences in the structure of starch in different malts, differences in agitation and heating, and the time spent for mashing-in were not explicitly taken into account when brewery mashings were simulated. However, the effect of mashing temperature on the time period of rapid increase in maltose concentration and the directions of changes in wort sugar concentrations were correctly predicted.
A model for the prediction of fermentable sugar concentrations during mashing W
Marc et al. (1981, 1983) also described a mode1 for starch hydrolysis by r- and P-amylase during mashing. The differences between the predicted and measured final maltose concentrations in a pilot and in an industrial scale mashing were about 10% (Marc et al., 1983, Figs 6 and 7). The corresponding prediction errors of the mode1 (l)-(15) were 3.2-7-l% in the seven industrial scale mashings analysed. Thus, the predictions of the model (l)-( 1.5) seem to be more accurate.
Predicted glucose concentrations at low temperatures (~60°C) were in many cases smaller than the measured concentrations. This may have been caused by the action of a-glucosidase which promotes the conversion of dextrins and sugars into glucose and is very heat labile. Also the action of limit-dextrinase may be significant in certain conditions. The descriptions of the actions of R-glucosidase and limit-dextrinase in the mode1 could improve the glucose concentration predictions.
The normal malt analysis does not provide sufficiently detailed information about the malt properties for predicting the biochemical phenomena during mashing. In order to have reliable and quantitatively accurate mode1 predictions, it is essential to know the concentrations of starch, dextrins, fermentable sugars, and active X- and fl-amylase in the malt. The above analyses are laborious and there certainly is a need for fast and inexpensive new analysis techniques.
The mode1 for starch hydrolysis presented in this paper and a model predicting the hydrolysis and dissolution of P-glucans have recently been programmed on a PC as a simulation tool for the research and development of mashing processes (Koljonen et al., 1993).
ACKNOWLEDGEMENT
This work was supported by the Technology Development Centre, Oy Panimolaboratorio, Alko Ltd, Oy Lahden Polttimo Ab, and Raisio Group Maltings Division.
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