18th European Symposium on Computer Aided Process Engineering – ESCAPE 18
Bertrand Braunschweig and Xavier Joulia (Editors)
© 2008 Elsevier B.V./Ltd. All rights reserved.
Computer aided modeling of an extractive
fermentation process for bioethanol production:
Outlook for development of reaction-separation
process
Rafael Ramos de Andradea, Elmer Ccopa Riveraa, Daniel Ibraim Pires Atalab,
Rubens Maciel Filhoa, Francisco Maugeri Filho, Aline Carvalho da Costaa
a
School of Chemical Engineering, State University of Campinas, P.O. Box 6066,
13081-970, Campinas, SP, Brazil
b
School of Food Engineering, State University of Campinas, P.O. Box 6121, 13081970, Campinas, SP, Brazil
Abstract
The modeling of a vacuum flash vessel and hollow fiber membrane which are part of an
extractive fermentation process were performed. In the flash vessel, the vapor-liquid
equilibrium in binary mixtures was considered. This approach uses the Predictive Soave
Redlich-Kwong equation of state, with original and modified molecular parameters. The
membrane system is represented by a resistance model that allows the evaluation of its
resistance periodically by a management software to determine the necessity of
backflushing. For kinetic phenomenological model, it was developed a computational
methodology of parameter estimation based on Quasi-Newton algorithm.
Keywords: Bioethanol, extractive fermentation process, optimization, modeling.
1. Introduction
Among the improvements of bioethanol production is the use of an extractive
fermentation process, which consists of three interlinked units composed by a bioreactor
(ethanol production), a flash vessel (for ethanol removal) and a hollow fiber membrane
system (for cells recycling). One of the advantages of this process is the non-necessity
of heat exchangers for bioreactor cooling, considering that the flash separation is held
responsible for heat removal from the fermentative broth when operated at 33C. This
reduces utilities use, decreasing maintenance costs. The continuous removal of ethanol
from the broth enables higher productivity than in common continuous processes, as it
avoids inhibition on S. cerevisiae growth; also, it allows the use of higher molasses
concentration on the feed stream, leading to less vinasse generation and lower costs with
effluent treatment.
Optimal operational conditions for this process and their modeling have not been
investigated so far. It is highly influenced by the operational conditions of the flash,
such as temperature and pressure, although these have not been completely defined. The
modeling of the flash vessel considers ethanol and congeners and is useful to investigate
the process behavior, as well as for allowing the dynamic study. The modeling of the
hollow fiber membrane module was performed based on a resistance model, as well the
backflushing strategies for filtration regeneration due to several phenomena such as
membrane blocking, cake formation models and standard pore blocking. The estimation
of parameters for a mixture of fermentative broth with S. cerevisiae is useful to predict
2
R. R. Andrade et al.
the behavior of the permeate flow through the membrane by computer simulation at
several trans-membrane pressures, and the determination of the necessity of
backflushing intervals in order to recover the membrane system to obtain better
performance conditions. The backflushing strategy can be experimentally managed by a
routine developed in LAbVIEW, using the model.
2. Modeling of flash vessel through Predictive Soave-Redlich-Kwong
(PSRK) equation of state
The idea of combining simple cubic equations of state with excess Gibbs free energy
(gE) models in order to describe the intermolecular interactions derived from the
behavior of the liquid and vapor phases is well known. Huron and Vidal (1) published
their mixing rule for the attractive parameter “a” of a cubic equation of state (EoS).
The excess Gibbs free energy given by an equation of state is a function of pressure,
whereas in the most common gE models, it is assumed that the excess volume is zero
(VE =0). For this reason, all the approaches use limiting values for the pressure (P→∞
or P→ 0) to obtain a gE mixing rule for the mixture parameter “a”. The relation between
the excess Gibbs free energy and the activity or fugacity coefficients is:
ln  i 
gE
 xi ln  i*   xi ln  i  RT
(1)
The PSRK model was first proposed by Holderbaum and Gmehling (2) and considers
the Soave-Redlich-Kwong equation of state and the UNIFAC model for the excess free
energy and the activity coefficient in the mixing rules, as shown below:
P
2
2
RT
a
RT
; ai  0.42748 R Tc i  (T ) ; bi  0.08664 c,i

v  b v (v  b )
Pc i
Pc,i
(2)
For polar components, the expression proposed by Mathias and Copeman (3) is used to
evaluate (T) in the PSRK equation:

 (T )  1  c (1  T )

2
 (T )  1  c1 (1  Tr0.5 )  c2 (1  Tr0.5 ) 2  c3 (1  Tr0.5 ) 3 ; for Tr  1
(3)
; for Tr  1
(4)
1
0.5
r
2
Tr and Tc the reduced and critical temperature, c1, c2 and c3 are empirical parameters.
The mixing rules are given by:
gE
a  b

 A1
 x1 bii
a

RT
A1
b
 xi ln bi 
(5)

where A1 is a constant equal to -0.64663. Eq. 6 is used with the UNIFAC model for gE
and the classical mixing and combination rule for the volume parameter “b” is assumed:
b
N
N
 xi x j bij ; bij 
i 1 j 1
bi  b j
2
;
(6)
In these equations, ai and bi are the pure component constants, as defined by Eq. 6.
Applications to mixtures such as those discussed in this paper were not discussed by
authors.
Computer aided modeling of an extractive fermentation process for bioethanol
3
2.1. Modified PSRK Model
The PSRK model includes two molecular parameters, a volume parameter, r, and a
surface area parameter, q. In this work, these molecular parameters are modified for
ethanol, and are adjustable. Data for binary ethanol + congener mixtures were used to
obtain optimum values of r and q. This empirical approach tries to explain the
modification of the molecular physical structure of ethanol mixed with some congener.
An analogous empirical approach was applied for temperature-dependent variables in
UNIFAC-Dortmund.
Data for the pure component, such as M (molecular weight), Tc (critical temperature),
Tb (normal boiling temperature), Pc (critical pressure), Vc(critical volume), and 
(acentric factor) were obtained from Diadem Public (4). The experimental data used in
the study (yi and T), were taken from Gmehling et al. (2).
The deviations for the temperature, %T, and for the vapor-phase concentration,
%yi, between predicted and experimental values (Eq. 7) are shown in Table 1.
% y i 
100
N

y cal  y exp
y exp
 Tcal  Texp 
;
 Texp

; % T  100  
N
(7)
The VLE data were analyzed using the PSRK model considering the molecular
parameters r and q as adjustable parameters. In order to evaluate these parameters, a
Genetic Algorithm optimization procedure, implemented and fully explained in Alvarez
et al. (5) was used. Thus, the optimization programs used the objective function Of:
Of 
 y1exp  y1cal 
N
(8)
2
1
In this equation, N is the number of points in the experimental data set and y1 is the
congener mole fraction in the vapor phase.
Table 1. Results of deviations for PSRK equation using original values of parameters
ethanol (2)+
acetic acid
acetaldehyde
furfural
methanol
1-pentanol
Original.
r = 2.5755,
q = 2.5880
%|T|
%|y1|
0.267
24.4
0.7
4.4
0.4
22.8
0.2
6.7
0.4
7.9
Optimized
r
2.8591
2.7217
2.4014
2.7675
2.3088
q
2.6304
2.4872
2.5911
2.6299
2.5764
%|T|
0.24
0.4
0.5
0.2
0.3
Correlation
%|y1|
22.84
4.8
14.6
5.9
9.3
%|T|
0.2
0.4
0.5
0.2
0.3
%|y1|
22.7
4.7
13.3
6.1
9.2
Results with the PSRK equation using original values for r and q for ethanol in all
mixtures congener (1) + ethanol (2) are shown in Table 1. The PSRK model presents
good predictions for the boiling temperature.
The binary systems with acetic acid, acetaldehyde, furfural, methanol and 1-pentanol
congeners were used to obtain optimized molecular parameters for ethanol. The
parameters for ethanol, r and q, were optimized for each binary system resulting in
different values for r and q, as shown in Table 1 (“optimized” columns).
In the same way the molecular parameters for ethanol, r and q, were optimized for each
binary system, and so, resulting in different values for these parameters.
Optimum parameters found for each of the five mixtures have been correlated with the
critical compressibility factor (Zc) for r and the acentric factor ( ) for q, as follows:
r  30.325166(Z c2  Z c1 ) 2  10.975229(Z c2  Z c1 )  2.548474
(9)
4
R. R. Andrade et al.
q  4.2758(2  1)2  1.4213(2  1)  2.5196
(10)
2 and Zc2 are the properties for the ethanol, and 1 and Zc1 are for each one of the
congeners.
With the proposed change, the PSRK model becomes more empirical, and improves the
model accuracy, as in Table 2 (“correlation” columns). In ternary systems, the structural
parameters r and q of ethanol were calculated with the functions:
(11)
r  1r1  2 r2 ; q  1q1  2 q2
ri is the structural parameter r for ethanol with the congener i and qi is the structural
parameter q for ethanol with the congener i. The experimental data for ternary systems
were taken from Gmehling et al. (6).
Tables 2 and 3 showed the deviations for T and congener vapor phase fraction for
binary and ternary systems. The modified PSRK model is better than the original.
Table 2. Deviations of temperature and mole fractions for binary system
ethanol (2)+
water
Original.
r = 2.5755, q = 2.5880
%|T|
%|y1|
%|y2|
0.2
3.9
2.2
Correlation
%|T|
0.1
%|y1|
2.4
%|y2|
1.4
Table 3. Deviations of temperature and mole fractions for ternary system
ethanol (2)+
water (3)
1-pentanol
1-propanol
1-furfural
Original.
r = 2.5755, q = 2.5880
%|T|
%|y1|
%|y2|
%|y3|
0.3
34.7
4.9
10.2
0.1
19.2
4.0
3.0
0.5
42.1
7.4
13.8
Eq. 11.
%|T|
0.9
0.4
1.8
%|y1|
28.7
19.9
43.4
%|y2|
4.4
3.5
4.3
%|y3|
8.2
2.6
7.3
3. Kinetic modeling and parameter estimation methodology
The mass and energy balance equations for the fermentor using the intrinsic model are:
dX v
F
 ( 1- 2 ) X v - (X v -X vF )
dt
V
dX d
F
dead cells:
  2 X v - (X d -X dF )
dt
V
viable cells:

X  
d 1  t  SV 
ρ  

substrate: 
 F(S F -S)-VX v
dt


X 
X
d 1  t  PV  t γPV 
ρ 
ρ

  VX  F(P -P)
product: 
v
F
dt
(12)
(13)
(14)
(15)
In these equations, Xv and Xd are the concentration of the viable and dead biomass
(kg/m3), respectively, Xt is the total biomass (kg/m3). S and P are the concentration of
substrate (kg/m3) and ethanol (kg/m3). The specific rates of cell growth, 1 (h-1), cell
death, 2 (h-1), substrate consumption,  (h-1), and product formation,  (h-1), are given
by Eqs. 16-19.
Computer aided modeling of an extractive fermentation process for bioethanol
1   max

Xt
S
exp(  K i S )1 
Ks  S
X
max





m

P 
1 



P
max 

5
n
(16)
 2  K dT exp( K dP P)
(17)
  Y px 1  m p
(18)

1
Yx
 mx
(19)
The parameters were adjusted from experimental data for specific molasses and
microorganism yeast, by Atala et al. (7). It is important to stress that kinetic parameters
are highly influenced by fermentation conditions (that changes periodically). Thus, in
order to represent the kinetic behavior of the process for a long time, frequent parameter
re-estimation is necessary. For this purpose, a computational method was developed,
based on Quasi Newton algorithm that minimizes the following objective function:
np
E (θ) 
 ( X n  Xen ) 2
 
n 1 
2
Xemax

( S n  Sen ) 2
2
Semax

( Pn  Pen ) 2 

2
Pemax

np
 n (θ)
(20)
n 1
In Eq. 20,  specify the parameters vector, which the temperature-dependent
parameters, as max, Xmax, Pmax, Υx and Υpx. Xen, Sen and Pen are the measured
(experimentally) concentrations of cell mass, substrate and ethanol at the nth sampling
time. Xn, Sn and Pn are the concentrations computed by the model at the nth sampling
time. Xemax, Semax and Pemax are the maximum measured concentrations and the term np
is number of sampling points. n() is the error in the output due to the nth sample.
The objective of the optimization problem developed in FORTRAN is to find out  by
minimizing the objective function, using Quasi-Newton algorithm. The values of X, S,
and P from the model are obtained by the integration of Eqs. 12-15 with initial
corresponding parameters, applying FORTRAN IMSL routine DBCONF, based on the
fourth-order Runge-Kutta method.
4. Potentiality and model of membrane for S. cerevisiae separation
An alternative for substituting the centrifuges for cell separation in biotechnological
processes is the application of hollow fiber membrane. Among its advantages is the
flexibility of scale up, low consumption of energy at low pressures, and ease to clean.
The solution flows in parallel with the membrane surface, which is more convenient in
industrial processes (8) due to the capacity of enhancing the flux of permeate, reducing
the polarization or fouling phenomena.
The CO2 formation in the fermentative broth leads to a reduction of the fouling on the
membrane. The study of the influence of bubbles on flux was done by Lu et al. (9).
An additional strategy is relevant for optimizing the performance of the membrane for
the fermentative process, such as the backflushing technique, which consists of a
reverse injection of air to remove the cake from the surface, decreasing the total
resistance of filtration. This task is repeated at time intervals that need to be determined
for S. cerevisiae with molasses and congeners, and its application is needed in
fermentative systems to allow long time of operation in industrial plants.
The cake resistance, which influences the permeate flux, must be on-line evaluated
during operation in order to guarantee the feeding in the flash vessel, and to determine
the backflushing time. This routine (determination of cake resistance) must be updated
6
R. R. Andrade et al.
continuously considering the changes on the biomass concentration in the feed stream of
the membrane. For this purpose the resistance model is applied, as follows:
J
P
 .Rm  Ra 
(21)
In this equation, J is the permeate flux; ΔP is the trans-membrane pressure;  the
permeate viscosity; Rm is the intrinsic resistance of membrane and Ra the additional
resistance (effects of adsorption, pore blocking, gel layer and polarization).
The data of flux and trans-membrane pressure are collected by a flowmeter and pressure
sensor, respectively, installed in the process, which values are stored in a computer by a
software management developed in LAbVIEW (National Instruments, Co.). These data
enables the calculation of membrane additional resistance that is constantly updated
with time. The backflushing is performed automatically and controlled by a routine
developed in LabVIEW, when the parameter Ra reaches a high pre-determined value.
This membrane flux regeneration is important to maintain the mass flow in the flash
vessel.
5. Concluding Remarks
This proposed use of a Predictive Soave-Redlich-Kwong (PSRK) model to describe the
phase equilibria in the flash distillation, using modified molecular parameters r and q
for ethanol becomes the model more empirical, but keeps its predictive capabilities.
Furthermore, the introduction of new molecular parameters r and q in the UNIFAC
model gives more accurate predictions for the concentration of the congener in the gas
phase for binary and ternary systems.
Taking into consideration the chances of kinetic behavior of the process (with impact on
parameters), which are caused by the raw material characteristics and dominant yeast
lineage in fermentation, a computational tool for parameter estimation was presented
based on Quasi-Newton algorithm. The difficulty in this technique is the choice of a
initial estimative for parameters, although the good quality of prediction of the model.
The analysis of membrane application shows a high potentiality for extractive process
and suggests strategies for optimizing its performance through a management software.
The development presented is important to allow a better understanding of the process,
modeling, optimization and its dynamic study to develop control strategies.
Acknowledgements
The authors acknowledge FAPESP and CNPq for financial support.
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