Modeling and simulate alcohol fermentation process by Simulink
KHOA HỌC
CÔNG NGHỆ
P-ISSN 1859-3585 E-ISSN 2615-9619
MODELING AND SIMULATE ALCOHOL FERMENTATION
PROCESS BY SIMULINK
MÔ HÌNH HOÁ VÀ MÔ PHỎNG QUÁ TRÌNH LÊN MEN CỒN TRÊN SIMULINK
Tran Van Tai, Nguyen Truong Giang,
Nguyen Duc Trung*
1. INTRODUCTION
ABSTRACT
Ethanol fermentation is widely used in the production of foods like alcoholic beverages. In previous
Fermentation is a key process stage
in ethanol production. For improving
the cost efficiency, production
efficiency and obtaining desired
product, the research to optimize the
fermentation process for defining the
best operating parameters is needed.
Fermentation is a multivariable control
system with complex nonlinear kinetics
[1]. There are multiple modeling
methods but with complex technical
systems models, the nonlinear system
of differential equations often used.
Simulation and optimization of
fermentation conditions for the
production of ethanol has gained great
importance in the manufacturing
practice. Effective and reliable
research, the production of ethanol by batch fermentation and continuous fermentation process was
examined. Continuous fermentation is a complex process consisting of many alterations of energy and
matter flows. For improving the overall fermentation process efficiency, a rigorous analysis to determine
optimal values for operation variables is needed. Simulation of the process is a recognized way for doing
such an analysis. In this study, a MIMO (Multi Input, Multi Output) nonlinear multivariable predictive
controller was developed for an alcoholic fermentation process. Effect of agitation rate and heat exchange
in bioreactors during ethanol fermentation wasn’t analyzed. Mathematical models were used to predict
the influence of operating parameters on cell concentration, substrate utilization rate and ethanol
production rate. The basic principle used in this model is a concept of balance theory of mass and
energy.Parameter were estimated from experimental data. The kinetic model with its parameters was
applied in the simulation of a continuous fermentation process for ethanol production. Simulations for
multiple scenarios were carried out using software tool Simulink using block diagrams, overlaid on the
Matlab R2016a programming language. Results was obtained in the simulation is the basis for the
preliminary evaluation of results in optimization, identification and linearization and can be used for
design of the control systems as well as the operating mode prediction.
Keywords: Continuous ethanol fermentation process; dynamic simulation; kinetic model; MIMO; Simulink.
assessment
continuous alcohol
utility
for
TÓM TẮT
fermentation
Hệ thống lên men cồn được ứng dụng nhiều trong công nghiệp thực phẩm. Các nghiên cứu về chúng
thường là khảo sát các hệ thống lên men gián đoạn (theo mẻ) hoặc liên tục, quá trình lên men liên tục
được mô hình hóa động học và mô phỏng trong nghiên cứu này. Đây là một quá trình phức hợp gồm
nhiều quá trình biến đổi của các dòng năng lượng và dòng vật chất. Quá trình lên men liên tục được nhìn
nhận với tư cách một đối tượng điều khiển là một mô hình động học phi tuyến đa biến với các tương tác
chéo của các tín hiệu vào và các tín hiệu ra (hệ đa biến - MIMO). Quá trình khuấy trộn và quá trình truyền
nhiệt không được tập trung đi sâu phân tích trong nghiên cứu. Mô hình hóa động học được xây dựng chi
tiết làm cơ sở cho mô phỏng quá trình lên men liên tục. Cân bằng năng lượng và cân bằng vật chất là hai
nguyên lý căn bản được sử dụng trong mô hình hóa. Thiết kế mô phỏng dựa trên công cụ đồ hình của
phần mềm Simulink được đóng trong gói Matlab R2016a. Kết quả của các trường hợp hoạt động sản xuất
khác nhau có thể được đưa ra từ sơ đồ mô phỏng này. Đây là cơ sở cho việc đánh giá sơ bộ các kết quả
nghiên cứu về tối ưu, nhận dạng và tuyến tính hóa phục vụ thiết kế hệ thống điều khiển hệ thống cũng
như dự báo chế độ vận hành.
process was established in this study.
In the mathematical model used in
simulation, in addition to the detailed
kinetics
model
also
includes
computational equations describing
heat transfer, temperature dependence
of kinetic parameters, oxygen transfer
as well as the effect of metal
concentration and temperature on
mass transfer. The kinetic equations
used in the mentioned bioreactor
model are modifications of the Monod
equations based on the Michaelis–
Menten kinetics, proposed by Aiba.
Từ khóa: Lên men liên tục, mô phỏng động học, mô hình động học, MIMO, Simulink.
2. A STATE - SPACE MODEL FOR AN
ALCOHOLIC FERMENTATION
Hanoi University of Science and Technology
*Email: trung.nguyenduc@hust.edu.vn
Received: 25/4/2021
Revised: 05/6/2021
Accepted: 25/6/2021
In this study, the spatial distribution
of parameters in the bioreactor wasn't
assessed. The quantities were referred
to the concentrated parameters
138
P-ISSN 1859-3585 E-ISSN 2615-9619 SCIENCE - TECHNOLOGY
mathematical model based on the model assumption of
uniform distribution (ideal stirred tank) [2].
The bioreactor is modeled as a continuous stirred tank
with constant the substrate flow. There is also a constant
outlet flow from the bioreactor that includes the product,
substrate and biomass (Fig. 2).
Ethanol production is divided into two phases:
respiration (yeast propagation under aerobic conditions)
and ethanol fermentation under anaerobic conditions:
The kinetic equations used in the mentioned bioreactor
model are modifications of the Monod equations based on
the Michaelis-Menten kinetics, proposed by Aiba et al [3].
- Aerobic conditions: C6H12O6 + 6O2 → 6CO2 + 6H2O
- Anaerobic conditions: C6H12O6 → 2C2H5OH + 2 CO2 + Q
dcX
dt
cS
pcp
mXc
eK
(1)
(2)
(3)
X KS cS
dcP
dt
cS
p1cp
μPcX
eK
KS1 cS
dcS
dcX
dcP
1
1
dt RSX dt RSP dt
Where RSX and RSP are defined asratio of cell produced
per glucose consumed for growth and ratio of ethanol
produced per glucose consumed for fermentation,
respectively.
Inorganic salts are added with the yeast. Those are
necessary compounds for the formation of coenzymes. But
the inorganic salts also have a strong effect on the
equilibrium concentration of oxygen in the liquid phase.
Figure 1. Flow diagram of transform matter in bioreactor
Effect of the ionic concentration is calculated by Eq (4):
HI HNaINa HCaICa HMgIMg HClICl
i i
(4)
HCO ICO HHIH HOHIOH 0,1274
3
3
The equilibrium concentration of oxygen depend on
temperature in distilled water is given by the empirical
equation as follows [4] :
c*O 14.6 0.3943T 0.007714T2 0.0000646T3 (5)
2 ,0
r
r
r
In the fact that salts are dissolved in the medium the
equilibrium concentration of oxygen in liquid phase is
calculated by Setchenov equation [4]:
Figure 2. The continuous fermentation reactor
HI
i i
c*O c*O ,0 10
(6)
2
2
Mass transfer coefficient for oxygen related to
temperature is determined by the following empirical
equation [5]:
Figure 3. Diagram description of a state variable xi
T 20
r
(kla) (kla)0 (1.024)
Equation for the rate of oxygen consumption is:
cO
1
2
Figure 4. Diagram description of the system state equation
rO μO
c
(7)
YO X KO cO
2
2
2
2
2
The continuous fermentation reactor is shown in Fig. 1
and 2 described as a block diagram of the input (U) and
output (Y) vectors. Dynamic response in output Y to step
change in input U ( Fig. 4).
The formula of the maximum specific growth rate
related to the growth rate that increases with the
temperature and the effect of the heat denaturation:
a1 /R(T 273))
a2 /R(T 273))
r
μX A1e(E
A2e(E
(8)
r
dX
dt
Y = G(X,U)
=F(X,U)
dxi
dt
i=1:n
= fi (X,U)
(I)
In continuous fermentation process, there are inlet and
outlet flow. Total volume of the reaction medium is:
139
Website: https://tapchikhcn.haui.edu.vn Vol. 57 - No. 3 (June 2021) ● Journal of SCIENCE & TECHNOLOGY
KHOA HỌC
CÔNG NGHỆ
P-ISSN 1859-3585 E-ISSN 2615-9619
[ Rate of change in volume] = [ Volume input rate] –
[Volume output rate]
c*O ,0 14.60.3943T 0.007714T2 0.0000646T3
dV
dt
r
r
r
2
F F
(9)
i
e
HI
i i
c* cO ,0 10
*
O2
2
Where: Fi and Fe are defined as flow of substrate
entering the reactor and outlet flow from the reactor,
respectively.
cO
1
2
r
μ
c
O
YO X KO cO
O2
2
2
2
2
μX A1e /R(T 273)) A2e(E
(Ea1
a2 /R(T 273))
r
r
A biomass balance is presented as follows:
dV
dt
dcX
dcX
dt
cS
Fe
V
pcp
eK
cX
(10)
FiFe
μXc
mXc
X KS cS
cS
Fe
V
eK c
cX
p
p
The mass balance for the product is presented by the
following equation:
dt
X KS cS
dc
cS
Fe
V
p1cp
μPcX
eK
cP
P
dcP
dt
cS
KS1 cS
Fe
V
p1cp
eK
cP
(11)
dt
dcS
dt
KS1 cS
mPcX
cS
X KS cS
cS
1
RSX
Fi
V
p
p
μXc
eK c
cS,in
A substrate mass balance is expressed by Eq. (12):
[Substrate utilization rate] = [Substrate input rate] –
[Substrate output rate] – [Substrate uptake rate for growth]
– [Substrate uptake for production formation]
1
Fe
V
p1cp
μPcX
eK
cS
RSP
(kla)(c*O cO )rO
2
KS1 cS
dcO
2
dcS
dt
cS
X KS cS
cS
1
RSX
1
Fi
V
pcp
eK
cS,in
2
2
μXc
dt
dT
rO DH
KTAT (T T )
Fi
V
Fe
(T 273) (T 273)
(12)
r
r
ag
r
2
Fe
in
r
p1cp
eK
cS
dt
dT
V
32ρrCheat,r
VρrCheat,r
μPcX
RSP
KS1 cS
V
F
KTAT (T T )
r ag
ag
ag (Tin,ag T )
ag
The concentration of the dissolved oxygen in the
reaction medium is calculated by Eq.(13):
dt
V
VρrCheat,ag
j
[Oxygen utilization rate] = [Oxygen input rate due to
the mass transfer] – [Oxygen rate consumed for
fermentation reaction]
There are numerous kinetic models for ethanol
fermentation. Mathematical models have been used to
predict the effect of operating parameters on biomass
concentration, substrate utilization rate and ethanol
formation rate. The kinetic parameters of the alcohol
fermentation were used in this study obtained from the
previous experimental data.
dcO
(kla)(c*O cO ) rO
(13)
2
2
2
2
dt
An energy balance for the fermentation process is given
as below:
For the bioreactor:
Table 1. Parameter values used for simulation
dT
dt
F
V
F
e
r
i
No Parameter
Nomenclature / Value/
(T 273) (T 273)
in
r
V
Greek symbols
Unit
9.5x108
(14)
rO DHr
KTAT (T Tag )
1 Pre exponential factors in Arrhenius
equation
A1
r
2
32ρrCheat,r
For the jacket:
VρrCheat,r
2 Pre exponential factors in Arrhenius
equation
A2
AT
2.55x1033
dTag
dt
F
KTAT (T Tag )
1, m2
4.18, Jg-1K-1
mg/L
r
ag (Tin,ag Tag )
Vj
(15)
3 Heat transfer area
VrCheat,ag
4 Heat capacity of mass of reaction
5 Oxygen concentration in the liquid phase
Cheat,r
Thus, kinetic modeling of alcohol fermentation in
continuous fermentation bioreactor is a set of
simultaneous equations:
cO
2
c*O
6 Equilibrium concentration of oxygen in
the liquid phase
mg/L
2
7 Product (ethanol) concentration
8 Substrate (glucose) concentration
9 Glucose concentration in the feed flow
10 Biomass (yeast) concentration
CP
CS
g/L
60, g/L
g/L
CS,in
CX
g/L
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P-ISSN 1859-3585 E-ISSN 2615-9619 SCIENCE - TECHNOLOGY
11 Apparent activation energy for the
growth, respectively, denaturation
reaction
Ea1
Ea2
50000 J/mol
220000 J/mol
12 Flow of cooling agent
13 Flow of substrate entering the reactor
14 Outlet flow from the reactor
15 Specific ionic constant of ion i (i = Na,
Ca, Mg, Cl, CO3, etc.)
Fag
Fi
Fe
Hi
L/h
L/h
L/h
Figure 5. Schematic diagram simulated the overall system
16 Ionic strength of ion i (i = Na, Ca, Mg,
Cl, CO3, etc.)
17 Product of mass-transfer coefficient for
oxygen and gas-phase specific area
18 Constant of oxygen consumption
19 Constant of growth inhibition by ethanol
Ii
The simulation program was designed according to
modularization as presented in Fig. 5. Each of modules
contained nonlinear and integral equations to describe a
system of equations of state - space for an alcoholic
fermentation as the following Fig. 6.
Kla
38, h-1
KO2
KP
8.86 mg/L
0.139, g/L
20 Constant of fermentation inhibition by
ethanol
Kp1
0.070, g/L
21 Constant in the substrate term for growth
22 Constant in the substrate term for
ethanol production
KS
KS1
1.030, g/L
1.680, g/L
23 Heat transfer coefficient
KT
3.6x105
Jh-1m-2 K-1
24 Rate of oxygen consumption
25 Universal gas constant
mg l-1 h-1
r
O2
R
8.31
J mol-1 K1
26 Ratio of ethanol produced per glucose
consumed for fermentation
27 Ratio of cell produced per glucose
consumed for growth
28 Temperature of cooling agent in the
jacket
29 Temperature of the substrate flow
entering to the reactor
RSP
RSX
Tag
Tin
0.435
0.067
15oC
Figure 6. Detailed calculation of CAL_OXY_TR_TAG
The above simulation diagram was used for multiple-
cases simulation depending on the kinetic parameters
entered via M-file as follows:
- Flow of substrate entering the reactor: Fi = 51 (l/h)
- Outlet flow from the reactor: Fe = 51 (l/h)
- Glucose concentration in the feed flow: CS,in = 60 (g/l)
- Temperature of cooling agent in the jacket: Tag= 15oC.
25 oC
30 Temperature in the reactor
31 Volume of the mass of reaction
32 Volume of the jacket
Tr
V
Vj
30 oC
50, L
100, L
- Temperature of the substrate flow entering to the
reactor: Tin= 25oC
33 Yield factor for biomass on oxygen
(mg/mg), defined as the amount of
oxygen consumed per unit biomass
produced
YO2
0.970,
mg/mg
- Simulation - time: t = 60 (h)
Simulation results obtained as follows:
- Simulation results using Runge-Kutta (4,5)[6]
- The comparison of the results between ode45 and
34 Reaction heat of fermentation
∆Hr
μO2
518 kJ/mol
O2 đã tiêu
thụ
ode23 solvers.
In the Fig. 7 showed the result of fermentation process.
In the first 1 hour, it’s the lag phase for yeast acclimate for
the environment so the reactor temperature decreased by
cooler agent. At the log phase (about 10 hours after lag
phase) where cells are rapidly growing and dividing that’s
increase temperature in the reactor and then the reactor
temperature was controlled by the cooler agent.
35 Maximum
specific
oxygen
0.5, L/h
consumption rate
36 Maximum specific fermentation rate
37 Maximum specific growth rate
38 Density of cooling agent
μP
μX
ρag
ρr
1.790, L/h
h-1
1000, g/L
1080
39 Density of the mass of reaction
The two graphs (Fig. 8) shown that using Runge-Kutta
(4,5) method(ode45) with higher convergence than Runge-
Kutta (2,3) method(ode23). A smaller calculation step given
more accurate results. The simulation results are closely
relevant with data obtained from the previous
3. RESULTS AND DISCUSSION
The presented dynamic model is simulated by using
software tool Simulink as a toolbox package in the Matlab
R2016a software.
141
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CÔNG NGHỆ
P-ISSN 1859-3585 E-ISSN 2615-9619
experimental. This simulation allows engineers to perform
different analysis in order to select the best parameter for
operating fermentation process. The application of this
simulation method will open the prospect of simulating
multiple fermentation processes in food technology and
biotechnology.
4. CONCLUSIONS
In this work, we have simulated the modelling of
alcohol fermentation process by Simulink® which a tool of
Matlab®. Accordingly, using mathematical models and
simulation tools have predicted the result and reducing
time
and
labor
experimental works. We
showed the using Runge-
Kutta (4,5) algorithm
(ode45) was better result
than Runge-Kutta (2,3)
algorithm
Choosing
(ode23).
calculation
method is also important
that effect to conclusions.
Figure 7. Simulation results using Runge-Kutta
REFERENCES
[1]. Cheng Y., T.W. Karjala, D.M. Himmelblau, 1995. Identification of
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[2]. Roels J.A., 1982.Mathematical models and the design of biochemical
reactors. Journal of Chemical Technology and Biotechnology, 32(1): p. 59-72.
[3]. Aiba S., M. Shoda, M. Nagatani, 2000. Kinetics of product inhibition in
alcohol fermentation. Reprinted from Biotechnology and Bioengineering, Vol. X,
Issue 6, Pages 845-864 (1968). Biotechnol Bioeng, 67(6): p. 671-90.
[4]. Sevella B., 1992. Bioengeneering Operations. Technical University of
Budapest, Tankonykiado, Budapest.
[5]. Godia F., C. Casas, C. Sola, 1988. Batch alcoholic fermentation modelling
by simultaneous integration of growth and fermentation equations. Journal of
Chemical Technology & Biotechnology, 41(2): p. 155-165.
[6]. Dormand J.R., P.J. Prince, 1980. A family of embedded Runge-Kutta
formulae. Journal of Computational and Applied Mathematics, 6(1): p. 19-26.
THÔNG TIN TÁC GIẢ
Trần Văn Tài, Nguyễn Trường Giang, Nguyễn Đức Trung
Viện Công nghệ sinh học và Công nghệ thực phẩm,
Trường Đại học Bách khoa Hà Nội
Figure 8. The comparison of the results between ode45 and ode23 solvers
142
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