Jourml of Food Engineering
26 (1995) 320-350
Copyright
0 1995 Elsevier Science Limited
Printed in Great Britain. All rights resewed
n26o-x774/9s!$9.s0
0260-8774(94)00061-l
ELSEVIER
A Model for the Prediction of Fermentable Sugar
Concentrations During Mashing
Tatu Koljonen,a
Jari J. H$m&Cnen,” * Katharina
Kirsti Pietili’
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
for
the
conversion
of
Frequency
factors
gelatinized and ungelatinized starch into dextrins
starch
into maltotriose
by
and gelatinized
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
maltotriose
and limitinto glucose, maltose,
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
R
t I/
T(t)
TU
T,
V
v,
W,,k
XI
X2
X.3
X4
X5
a:,
(tii;P)
xkj
(6,>
331
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
temperature
first
profile
was
5oW55
67W45
min,
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
offermentable
sugar concentrations during mashing
min, 7O”C/6 min, 78”C/15 min (profile 9). The rate of temperature
between the rests was 1”Cimin.
333
increase
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
centrifuged
at 4”C, and filtered before
further enzymatic conversions,
analysis. r-Amylase
and /j-amylase activities, concentrations
of glucose,
maltose and maltrotriose, and total extract were measured.
activities
determined
x-Amylase
and
P-amylase
were
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
Mean
Maltrotriose (g/l)
Maltose (gil)
Glucose (g/l)
Total FS (g/l)
Total extract (m-%)
Starch (% d.m.)
x -Amylase (U/g)
fl -Amylase (U/g)
CV%=standard
16.4
70.5
14.0
108.X
15.66
54.8
204.0
246.0
deviation/mean;
CV%
CV%
9.5%
Repeatability
Reproducibility
Confidence
(A%,)
1.7
1.8
1.3
1.4
0.04
1.2
3.2
3.7
0.92
1.2
1.1
0.73
N/A
N/A
N/A
N/A
3.9
4.3
3.4
3.2
0.08
2.4
6.4
7.4
FS=fermentable
sugars; N/A=not
available.
334
T Koljonen et al.
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 limitdextrins 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,
~*=sl[x,-u(T)]A~,,(T)-lag,
-u(T)][0.964A~,,(T)+A~,,(T)]
0*9B,,(T)+0.947
(5)
BmaU)
K +x
I,,
2
+B,,,x(T)
(6)
I
336
7: Koljonen et al.
i5=Aidt(T)x[x, -u(T)]
&=Bldex(T)PX2
(9)
(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
(and thus
lower temperatures
than T,, all the starch is ungelatinized
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.
dependence
of functions
k,(T),
Ic,~(T), A,?(T)
The temperature
(j={dex, mlt}), and B,(T) (j={gl, mal, ldex}) are represented by Arrhenius
type relationships (Laldler & Meiser, 1982) in eqns (12)-(U):
A,9(T)=AFge(E’IRT)
(12)
Bj( T) =B:)e(E”IRT)
(13)
k,(T)=k~e’E”lRT’
k,j(T)=kje(EQRT)
(14)
(15)
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 $R, Bi,, BLal, and B&)
in
(12)-(15). The estimated parameter values are shown in Table 2.
There are several differences between the model (l)-(15) and the model
described by Marc et al. (1983). The dissolution coefficients (H, and HP)
are different for s(- and /7-amylase. The hydrolysis of ungelatinized starch
and the production rate of maltotriose from dextrins were found negligible
and are not described in (l)-(15). The activation energies (E’ and E”) are
the same for all the reactions catalysed by the same enzyme, whereas Marc
et al. (1983) allowed different values for different reactions. Moreover, Marc
et al. (1983) described the dissolution of sugars and dextrins from grist to
the liquid phase to be proportional to the concentration
in the grist phase.
In (l)-(15)
the dissolution of sugars and dextrins is assumed to occur
A model for the prediction of fermentable sugar concentrations during mashing
TABLE 2
Parameter Values for Kymppi Malt Estimated from Laboratory
Experiments
Frequency factor
(liminig)
Tg
T,
A’d&
A ;fi
Scale Mashing
/j-Amylase
a-Amylase
Hydrolysis
= 336.5 K
= 315.4 K
= 3.77 x 10”’
= 6.42 x lo9
B;, = 1.62 x 10””
B’A,, = 1.05 x 10”’ min ’
BI:,, = 1.09 x 104’
K, = 2.8 (gil)
Activation energy
(J/mol)
E’ = 1.03 x 10”
E” = 2.93 x 10’
Frequency factor
(min --‘)
Activation energy
(Jimol)
k’,’ =
k’,: = 9.46 x
Denaturation
Dissolution
3.86 x 10j4
E ,; = 2.377 x
337
10’
1067
E$ = 4.439 x 105
H, = 9.72 x 10 5
(Vgimin)
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,
B,(O)=&,0
and there are no enzymes in the liquid, i.e.
(16)
(17)
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
@g,o=p
v+ v,
A0
(20)
v,
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
c v,
000
h--i3
sxxx
,r.
a
000s
5
33---s
xxxx
In
w,
during mashing
339
i7 Koljonen et al.
340
(RMS) error], i.e.
RMS@)=
(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)
to be
where B,,, and the Michaelis constant K,,, were the parameters
estimated. The objective function formed long and narrow contours on the
1982). The Michaelis constant K,,, was
(Holmberg,
(B maI, &,)-plane
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
80
1; : ‘--i
temperature
~~
maltose
5
,+-
-
‘*-
-
-
__Ii’
_I
20
0
0
50
a)
Time
100
[min]
80
/
t
/i
_____,’\esr
iLs+Lmit -@it r ins
i
20
0
b)
50
100
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
T Koijonen
342
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
80
:r
starch
temperat”re~‘~
70
l-l
k-61
\
maltotriose
1
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 limitdextrinase 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 Industrial 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
Kymppi
Kymppi
Kymppi
Kustaa
Kustaa
Ingrid
Ingrid
Final concentration of
fermentable sugars
(glucose + maltose + maltotriose)
Predicted (g/l)
Measured (gll)
Relative error (5%)
Laboratory
Profile
Profile
Profile
Profile
Profile
Profile
Profile
1
2
3
1
3
1
3
109.9
107.8
107.8
103.5
101.2
103.9
101.2
111.3/116~1
114.2
107.2
104.7
107.8
109.0
112.4
-3.3
-5.6
+0.6
-1.1
-6.1
-4.7
-9.9
94.0
114.2
114.2
114.2
114.8
93.2197.2
117.3
113.4
114.0
117.4
-1.8
-2.6
+0.7
-to.2
-2.2
105.8
103.4
101.1
101.5
+4.6
+0.9
Brewery A
Malt
Malt
Malt
Malt
Malt
1
2
2
2
2
Profile
Profile
Profile
Profile
Profile
4
5
6
7
8
Brewery B
Malt 3
Malt 3
Profile 9
Profile 9
-
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.
7: Koljonen et al.
344
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
1.6
z 1.4
0” 1.2
SJ
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
activities in a mashing in brewery A (profile 4).
(0)
A model for the prediction
of fermentable
sugar concentrations
temperaturer
during mashing
345
80
1.8
70
1.6
s
1.4
L-Y 1.2
$
L
1
.g 0.8
.?j 0.6
a
0.4
0.2
0
20
0
50
100
Time [min]
Fig. 6.
(lines) and measured n- (0) and P-amylase (0) activities m a
mashing in brewery B (profile 1).
Predicted
80
100
90 starch
80 R
F
70
B5
60
.z
50
2
40
s8
30
0
20
75
10
45
0
40
0
100
lime
200
[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
346
80
70
60 G
e
i?!
50 2
m
40 E
.E 60
H
F
8 40
0s
20
F
---a__
0
30
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).
80
120
75
70 5
e
65
!j
P
g
E
55 $
60
+ limit-de&ins
20
50
0
45
0
50
100
150
200
Time [min]
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.
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 reestimating 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
Predicted
(lines) and measured
(symbols)
concentrations
of starch
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 rand 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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