18th European Symposium on Computer Aided Process Engineering – ESCAPE 18
Bertrand Braunschweig and Xavier Joulia (Editors)
© 2008 Elsevier B.V./Ltd. All rights reserved.
Modeling and Identification of the Bio-ethanol
Production Process from Starch: Cybernetic vs.
Unstructured Modeling
Silvia Ochoaa, Ahrim Yoob, Jens-Uwe Repkea, Günter Woznya, and Dae Ryook
Yangb
a
Department of Process Dynamics and Operation, Technical University of Berlin, Sekr.
KWT 9, Strasse 17. Juni 135, Berlin 10623, Germany.
b
Department of Chemical & Biological Engineering, University of Korea, Seoul, Korea.
Abstract
In this work, an unstructured and a cybernetic model are proposed and compared for the
Simultaneous Saccharification - Fermentation process from Starch to Ethanol (SSFSE),
in order to have good, reliable, and highly predictive models, which can be used in
optimization and process control applications. The cybernetic is a novel model, which
especially considers i) the starch degradation into both glucose and dextrins, and ii) the
dynamic behavior of the concentration of the main enzymes involved in the intracellular
processes, giving a more detailed description of the process. Furthermore, a new
identification procedure based on a sensitivity index is proposed to identify the best set
of parameters that not only minimizes the error function, but also contains a fewer
number of parameters depending on the initial conditions of the process. Finally, an
application of the two models for controlling the SSFSE process using an NMPC
(following an optimal reference trajectory for the ethanol concentration) is presented,
showing the potential and usefulness of each type of models.
Keywords: Cybernetic Model, Ethanol, Sensitivity Analysis, Parameter Identification,
NMPC.
1. Introduction
During the last years, significant improvements have been done in the bio-ethanol
industry in order to make it economically more competitive, such as, in purification
technologies for ethanol dehydration as well as in the genetic modification of microbial
strains. However, the economical feasibility of the bio-ethanol industry is still
questioned, and therefore much effort should be oriented to the optimization and control
of the process. It is well known that a suitable model of the process should be available
for developing optimization and control tasks and that although in chemical processes
this is currently not a problem, the complexity of biological systems makes its modeling
a difficult task. Bioprocess modeling is usually addressed from two different points of
view: the structured and the unstructured modeling frameworks. Structured models
(such as cybernetic models) try to describe in detail the intracellular behavior, and
although they are more complex (i.e. higher number of ODE and AE with more
parameters), they can predict more accurately the actual behavior of the process states.
Parameter identification of biochemical models by error minimization is a nonlinear
optimization problem that contains multiple local minima. In those cases, stochastic
2
S. Ochoa et al
optimization methods are more convenient because they usually present a better
performance in comparison to gradient search based methods which frequently lead to
local solutions, especially if the model contains a large number of parameters and
sufficient experimental data are not available. Therefore, trying to avoid local solutions
while at the same time finding a minimum number of parameters dependent on the
initial conditions of the process, in Section 3 an identification procedure based on a
Simulated Annealing method coupled with a sensitivity analysis is presented. The main
purpose of this paper is not to answer the question regarding to which kind of model is
better or worse; the purpose is to show that depending on the application, these two
models can even be used in a synergistic manner. Unstructured models are more
suitable for online applications where the simplicity of the model plays an important
role especially for saving computation time while the model predictions are still good.
In contrast, cybernetic models are preferred for offline applications in which very
accurate predictions are needed no matter the computation time. As an example of the
potential usefulness of the two types of models, a Nonlinear Model Predictive Control
(NMPC) for the fed-batch SSFSE process was implemented for controlling an optimum
ethanol concentration profile that guarantees maximal productivity. The unstructured
model was run online as the predictive model that is part of the NMPC; whereas the
cybernetic was used offline for finding the optimal ethanol profile defined as the
reference trajectory on the NMPC calculations. Additionally, the results of the
controlled fed batch process are compared to a batch SSFSE process, simulated using
the model presented in (Ochoa et al, 2007), in order to show that the productivity
reached in the controlled fed batch process is higher than in the batch.
2. Modeling of the SSFSE Process
The process modeled on this section is a fed batch process in which two reactions take
place simultaneously in the same vessel: i) the enzymatic conversion of starch into
glucose (by means of glucoamylase and -amylase), and ii) the fermentation of glucose
to ethanol by means of yeast. A genetically modified Saccharomyces cerevisiae strain is
used in the process (as described by Altintas et al, 2002), which is able of both,
secreting the required enzymes for the starch saccharification and producing ethanol by
glucose fermentation.
2.1. Cybernetic Model
The cybernetic modeling framework has been developed by Ramkrishna’s group and
presented in several papers. The most remarkable of those is the paper by Varner and
Ramkrishna (1999), in which the guidelines for developing cybernetic models of
bioprocesses are given, according to the type of pathway that is taking place. Following
Ramkrishna’s ideas and the metabolic pathway shown in Figure 1, the cybernetic model
for the fed batch SSFSE process is proposed in this section.
e5
e1
Starch (S)
e2
e3
Ethanol (E)
Glucose (G)
e4
Yeast (X)
Dextrin (D)
Figure 1. Metabolic Pathway for ethanol production from starch.
The cybernetic model for the fed batch process is obtained from the mass balances for
Starch (S), Glucose(G), Dextrins (D), Cells (X), Ethanol (E), Glucoamylase (e 1= e2), amylase (e3), hypothetical enzyme 1 (e4) and hypothetical enzyme (e5), as shown in
Figure 2. The expressions for the kinetics ri and the cybernetic variables i (enzyme
Modeling and Identification of the Bio-ethanol Production process from Starch…
3
activity) and ui (enzyme synthesis) are given in Figure 3. A detailed description of the
nomenclature used in this work can be found in Ochoa et al. ( 2007).
F S  S 
dS
 (r1v1  r3v3 ) X  in in
dt
Vol

dG
rv
rv
FG
 (r1v1YG / S  r2v2YG / D  4 4  5 5 ) X  in
dt
YX / G YE / G
Vol
 

dD
F D
 (r3v3YD / S  r2v2 ) X  in
dt
Vol

d ei / eimax X
 max   i Cs X
ei
F e / e max
 ei
ui   i max
X  in i i
dt
K ei  C s
Vol
ei
dX
F X
 r4v4  K d X  in
dt
Vol

dE
F E
 r5v5 X  in
dt
Vol
Figure 2. Cybernetic model for the fed-batch SSFSE: Mass balances for the state variables


r1




r1
G

 
v1  

r
r


 max r1 , r2  max  1 , 3  


G D



(e / e max ) D
r2
r2  max,2 1 1
v2 
K2  D
max r1 , r2 
r3
max,3 (e3 / e3max ) S
D
r3 
v3 
K3  S
 r1 r3 
max  , 
G D
r4


 max, 4 (e4 / e max
)
G
E
4
X
1 

r4 
v

4
2
 K

G
 r4 r5 
Pini, 4 

G  K4 
max  , 
K Sini, 4
X E
r5

 max, 5 (e5 / e5max )G 
E
1  E 
r5 
v5 
G 2  K Pini,5 
 r4 r5 
G  K5 
max  , 
K Sini,5
X E
r1 
max,1 (e1 / e1max ) S
K1  S
 r1 

 r 
u1   1   G 
r

r
 1 2   r1  r3 
G D
r
u2  2
r1  r2
r3
u3  D
r1 r3

G D
r4
u4  X
r4 r5

X E
r5
u5  E
r4 r5

X E
Figure 3. Kinetic expressions and cybernetic variables for the SSFSE process
Altintas et al. (2002) developed a cybernetic model for the same SSFSE process tackled
here; but the authors did not consider the starch degradation into dextrins, which is
considered in the present work (see Figure 1). The main advantage of including this in
the model is that more accurate predictions of the process variables can be made,
especially for the starch and for the ethanol concentration, being the latter the most
valuable product of the process. This fact is corroborated by the results presented in
section 3 (see Figure 7).
2.2. Unstructured Model
The unstructured model developed here considers that the starch is composed of two
fractions, one susceptible (faster hydrolyzed, represented by Ssus), and one resistant
(Sres) as described in Kroumov et al. ( 2006). Although the saccharification is carried out
using glucoamylase and -amylase, the model considers that this two-enzyme action
can be simplified and represented by an additive enzyme activity (Enz) (Kroumov et al.,
2006). The kinetic expressions used for describing the fermentation, take into account
substrate and product inhibition in both cell’s growth and ethanol production rates. The
model for the fed batch SSFSE process is given in Figure 4, while the corresponding
kinetic expressions are given in Figure 5.
dE
F E
F S
S 
F S
S 
dS
dS
dS
F S  S 
 qX 
 R S 
 R S 
dt
  RSus S Sus Rres S res 
in
in
Sus
in
dt
Vol
Sus sus
sus, in
sus
Vol
dEnz
F Enz
 REnz     Enz  in
dt
Vol
dX
F X
 (   K d ) X  in
dt
Vol
in
res
res
dt
res
res , in
in
res
dt
Vol
Vol
 X   qX  Fin G
dG
 1.111 ( RSusSSus  RRes S Res )  
  
 
dt
 YX / G   YE / G  Vol
Figure 4. Unstructured model for the fed batch SSFSE process.
RSus 
k sus Enz
2

G  S Sus
 
K m 1 
 S Sus  S res
 K G  K Starch
REnz 
 m   S sus  S res Enzmax
K enz  S sus  S res
Rres 
k res Enz
2

G  S res
 
K m 1 
 S Sus  S res
 K G  K Starch
Figure 5. Kinetic expressions for the unstructured model.
q
qm G
k sp  G 


1  E 
G 2  Emp 
K ssp

m G
ks  G 

E 
1 

G 2  Em 
K ss
4
S. Ochoa et al
3. Identification of Parameters
Define n sets of data at
different initial conditions
Initial set of Pk parameters
Metropolis Monte Carlo Optimization:
n

min Fobj ( P)  min  MSE X ,h  MSE
.
h 1
S ,h
 MSE
G ,h
 MSE
E ,h

Caculate the sensitivity index:
S 
k
I
P0k  P k
F
obj
( P k )  Fobj ( P0k ) dP
P0k  P k
For each Parameter
Is SI < Tol?
Yes
The parameter is not Sensitive
= Fixed Parameter (P=Pns)
No
The parameter is Sensitive: P=Ps
Re-optimization of Ps for each n set of data using
the Metropolis Monte Carlo Method.
Optimal values for data set 1
Optimal values for data set 2
Optimal values for data set n
Figure 6. Developed Identification Procedure: Optimization coupled with Sensitivity analysis.
The parameters for both models were identified using experimental data reported by
Altintas et al. (2002), following the identification procedure proposed in Figure 6. The
identification procedure uses different sets of experimental data at different initial
conditions and is divided in three main steps: i) An initial optimization routine (for all
sets of data simultaneously) is run to calculate a first group of parameters for the various
sets of experiments; ii) a sensitivity index is calculated for identifying which parameters
have stronger influence on the objective function (according to a pre-established
tolerance, Tol), iii) a re-optimization is performed, this time for each set of data
independently, but only considering those parameters to which the objective function
showed a higher sensitivity. The objective function (Fobj) was taken as the sum of the
normalized squared error values for X, S, G and E (comparing to the experimental data).
The sensitivity index SI evaluates the sensitivity of Fobj to each parameter when the k-th
parameter varies between the integration limits that are defined as a function of the
optimized value for k (P0k). It is important to remark that the sensitivity is usually
analyzed as the partial derivative of Fobj with respect to the k-th parameter; however in
this case an optimum has been already found and if we use the typical sensitivity
analysis, we could find that some parameters may have a sensitivity value of zero. That
is the reason why we propose here to analyze the sensitivity using the new index shown
in the procedure described in Figure 6. Cybernetic and unstructured models presented in
Section 2 are composed of 34 and 20 parameters respectively. After analyzing the
sensitivity by means of the new sensitivity index, it was found that only 17 and 7
parameters respectively, are sensitive parameters. It is possible to state that for the set of
parameters for each kind of model, only those sensitive should be periodically adapted
using online information from the process, especially when the process conditions
change considerably. On the other hand, non-sensitive parameters can be maintained
fixed at their optimal values. As the main advantage of the identification procedure is
the reduction of the number of parameters that should be adapted online, it is important
to remark that the success of the procedure depends highly on the methods used for the
Modeling and Identification of the Bio-ethanol Production process from Starch…
5
optimization and re-optimization steps. Stochastic optimization methods are more
suitable due to their ability for escaping out of local minima. In this way, the Metropolis
Monte Carlo simulated annealing method (Kookos, 2004; Ochoa et al., 2007) is
recommended because of i) its random nature, which allows the exploration of a much
wider region, ii) its ability for avoiding getting trapped in a local optimum, which is
given by the Metropolis condition and iii) the annealing effect, which takes care of the
convergence. In Figure 7 a comparison between the predictions made by the
unstructured, the cybernetic and Altintas’ model is presented for starch and ethanol. As
can be seen, the models presented in Section 2 not only are in good agreement with the
experimental data but also give a better description of the state variables during the
whole process. In contrast, Altintas’ model fails predicting the ethanol and starch
dynamic behavior. It is important to remark that the main difference is that, in contrast
to the cybernetic presented here, Altintas’ model does not consider the conversion of
starch into dextrins. This is probably the main reason why their model predicts higher
starch concentration in the interval 20-100 h leading to a lower predicted ethanol, and a
lower starch for the period 100-140 h leading to a higher predicted ethanol.
30
15
Cybernetic
Unstructured
Altinta's Model
Experimental
Experimentaldata
data
Ethanol Concentration (g/l)
25
10
Starch Concentration(g/l)
20
15
10
5
5
0
0
0
50
Time(h)
100
150
0
50
Time(h)
100
150
Figure 7. Models Predictions for Starch (left side) and Ethanol (right side).
4. Nonlinear Model Predictive Control
In this section the usefulness of each kind of model is exemplified in the control of the
fed-batch SSFSE process. The objective of the control system is to maximize the
productivity of the process, which is calculated as the total mass of ethanol produced.
Due to its accuracy for predicting the dynamic behavior of the process, the cybernetic
model was used offline to calculate a profile for the ethanol concentration that leads to
maximal productivity; whereas the unstructured model was used in the prediction block
of the NMPC, because of its simplicity (important for a fast online solution) and still
good prediction capability. Figure 8 shows the scheme of the control system. The
dynamic behavior of the process and the NMPC performance were investigated through
simulation studies considering measurement noise with standard deviation of 3%,
0.02%, 0.01% and 0.02% for X, S, G, and E respectively. During the process, two
disturbances were simultaneously considered, i) a 10% of change in the feed starch
concentration (Sin) and ii) a 20% of change in the value of the maximum specific growth
rate um. The results for the NMPC are compared in Figure 9 to those for the nominal
case (optimal operation without disturbances) and to the batch results. The batch case
was run in open loop using the unstructured model presented in Ochoa et al. (2007).
Despite the disturbances and the model mismatch, the NMPC followed successfully the
optimal ethanol reference trajectory calculated offline. Therefore, it can be stated that
the cybernetic and unstructured models are quite useful for offline and online
6
S. Ochoa et al
applications respectively, due to the predicting capability of the cybernetic model and
the simplicity (and even good predictions) of the unstructured model. Besides, it is
important to highlight that a higher ethanol concentration (and therefore a higher
productivity) is obtained in the fed-batch process when compared to the batch process.
In the example tackled here, it is shown that by means of a conveniently controlled fedbatch process, the purity of the ethanol in the fermentation stage can be increased,
which is translated into a reduction of downstream purification costs.
d1(sin), d2 (um)
Offline Set point
Calculation (Cybernetic Model)
Eref -
NMPC (unstructured
model)
+
Fin
Process (unstructured
model + noise)
Eprocess
Figure 8. NMPC: Cybernetic and Unstructured models application.
18
16
14
Ethanol (g/l)
12
10
8
Efedbatch(NMPC)
Ebatch
6
Eref(nominal)
4
2
0
0
20
40
60
80
100
120
Time (h)
140
160
180
200
Figure 7. NMPC results. Ethanol concentration: Fed batch controlled process vs. Batch.
5. Conclusions
Cybernetic and unstructured models were proposed for the fed batch SSFSE process.
The models were compared to a cybernetic model previously reported, showing a better
performance than the previous model. The parameter identification of the models was
done by means of a new identification procedure in which stochastic optimization is
coupled to sensitivity analysis. Using this procedure, it was possible to find which
parameters should be adapted online and which could be kept at fixed values, leading to
a more robust model. The unstructured model is suitable for online applications such as
model-based control, whereas the cybernetic is the best choice for applications where
the accuracy of the model is important such as the off-line determination of optimal
trajectories to be tracked along the process.
References
M. Altintas, B. Kirdar, Z. I. Önsan and K. Ülgen. 2002, Cybernetic Modelling of growth and
ethanol production in a recombinant Saccharomyces cerevisiae strain secreting a bifunctional
fusion protein, Process Biochem., 37, 1439-1445.
A. D. Kroumov, A. N. Módenes and M. C. A. Tait, 2006, Development of new unstructured
model for simultaneous saccharification and fermentation of starch to ethanol by recombinant
strain, Biochem. Eng. J., 28, 243-255.
J. Varner and D. Ramkrishna, 1999, The non-linear analysis of cybernetic models. Guidelines for
model formulation, J. Biotechnol., 71, 67-104.
I. K. Kookos, 2004, Optimization of Batch and Fed-Batch Bioreactors using Simulated
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S. Ochoa, A. Yoo, J-U. Repke, G. Wozny and D.R. Yang. 2007, Modeling and Parameter
Identification of the Simultaneous Saccharification-Fermentation Process for Ethanol
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