Factorial Design and Simulation for _ Extractive Eth Ferm
Transcript of Factorial Design and Simulation for _ Extractive Eth Ferm
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Process Biochemistry 37 (2001) 125137
Factorial design and simulation for the optimization anddetermination of control structures for an extractive alcoholic
fermentation
Aline C. Costa a,*, Daniel I.P. Atala b, Francisco Maugeri b, Rubens Maciel a
a Department of Chemical Engineering, School of Chemical Engineering, State Uni6ersity of Campinas, P.O. Box 6066, 13081-970, Campinas,
SP, Brazilb Department of Food Engineering, School of Food Engineering, State Uni6ersity of Campinas, P.O. Box 6121, 13081-970, Campinas, SP, Brazil
Received 21 August 2000; received in revised form 13 March 2001; accepted 31 March 2001
Abstract
The design, optimization and control of an extractive alcoholic fermentation were studied. The fermentation process was
coupled to a vacuum flash vessel that extracted part of the ethanol. Response surface analysis was used in combination with
modelling and simulation to determine the operational conditions that maximize yield and productivity. The concepts of factorial
design were used in the study of the dynamic behaviour of the process, which was used to determine the best control structures
for the process. A good choice of the operational conditions was important to enable efficient control of the process. The
performance of a DMC (Dynamic Matrix Control) algorithm was studied to control the extractive process. 2001 Elsevier
Science Ltd. All rights reserved.
Keywords: Response surface analysis; Factorial design; Optimization; DMC control; Ethanol
Nomenclature
Dynamic matrix in the DMC algorithmA
Coefficients in the step-response modelb
Heat capacity, Kcal/(kg. C)Cp
Dilution rate, h1D=F/V
weighting factor in the DMC algorithmf
F Feed stream flow rate, m3/h
Fc
Cell suspension flow from centrifuge, m3/h
Cell suspension flow to treatment tank, m3/hFc1Light phase flow rate to flash tank, m3/hFE
FL Liquid outflow from the vacuum flash tank, m3/h
FLR Liquid phase recycling flow rate, m3/h
Liquid phase flow to rectification column, m3/hFLSFresh medium flow rate, m3/hF0
Fp Purge flow rate, m3/h
Fr Cell recycling flow rate, m3/h
Vapor outflow from the vacuum flash tank, m3/hFVFw Water flow rate, m
3/h
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* Corresponding author. Tel.: +55-19-788-3971; fax: +55-19-788-3965.E-mail address: [email protected] (A.C. Costa).
0032-9592/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved.
PII: S 0 0 3 2 - 9 5 9 2 ( 0 1 ) 0 0 1 8 8 - 1
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A.C. Costa et al. /Process Biochemistry 37 (2001) 125137126
I Identity matrix
Performance indexJ
KdP Coefficient of death by ethanol, m3/kg
Coefficient of death by temperature, h1KdTEquilibrium constantKeiSubstrate inhibition constant, m3/kgKi
Ks Substrate saturation constant, kg/m3
Constant in Eq. (6)m
Ethanol production associated to growth, kg/(kgh)mp Maintenance coefficient, kg/(kgh)mxConstant in Eq. (6)n
NC Control horizon in the DMC algorithm
Prediction horizon in the DMC algorithmNP
p Pressure, Pa
Vapor pressure, Pap isat
P Product concentration into the fermentor, kg/m3
Feed product concentration, kg/m3PFPLR Product concentration in the light phase from centrifuge, kg/m
3
Product concentration in the vapor phase from the flash tank, kg/m3PVProduct concentration when cell growth ceases, kg/m3Pmax
Product concentration in the cells recycle, kg/m3Prr=FLR/FL Flash recycle rate
Kinetic rate of death, kg/(m3h)rdKinetic rate of product formation, kg/(m3h)rpKinetic rate of substrate consumption, kg/(m3h)rsKinetic rate of growth, kg/(m3h)rx
R=Fr/F Cells recycle rate
Substrate concentration into the fermentor, kg/m3S
SF Feed substrate concentration, kg/m3
Substrate concentration in the light phase from centrifuge, kg/m3SLRS0 Inlet substrate concentration, kg/m
3
Substrate concentration in the cells recycle, kg/m
3
SrT Temperature into the fermentor, C
Feed temperature, CTFLight phase temperature, CFLRResidence time, htr
T0 Inlet temperature of the fresh medium, C
Cells recycle temperature, CTrTotal Reducing Sugars, kg/m3TRS
Temperature of vapor from the flash tank, CTVWater temperature, CTw
V Reactor volume, m3
Component i concentration in the light phase, mol%xEi
xi Component i concentration in the liquid, mol%Dead biomass concentration into the fermentor, kg/m3XdDead biomass concentration in the feed stream, kg/m3XdFBiomass concentration when cell growth ceases, kg/m3XmaxTotal biomass concentration into the fermentor, kg/m3Xt=X6+Xd
X6
Viable biomass concentration into the fermentor, kg/m3
Viable biomass concentration in the feed stream, kg/m3X6F
Xc Biomass concentration in the heavy phase from centrifuge, kg/m3
Biomass concentration in the light phase flow rate to flash tank, kg/m3XEXF Feed biomass concentration, kg/m
3
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Biomass concentration in the light phase from centrifuge, kg/m3XLRCell recycling concentration, kg/m3Xr
y Controlled variable in DMC algorithm
Component i concentration in the vapor, mol%yiYield of product based on cell growth, kg/kgYpx
Yx Limit cellular yield, kg/kg
Reaction heat, kcal/(kg TRS)DH
Variation in the manipulated variable in DMC algorithmDm
k Ratio of concentration of intracellular to extracellular ethanol, kg/m
3
Activity coefficient of component iki
Maximum specific growth rate, h-1vmaxz Ratio of dry cell weight per wet cell volume, kg/m3
Density, kg/m3zm
1. Introduction
Brazil is the world main ethanol producer as the
result of a political strategy initiated in 1975 by the
government to cope with the sharp increase in oil
prices. Programmes in the USA in 1978 and, more
recently, in Canada, followed this strategy [1]. Because
of the relative stabilization of the petroleum prices at a
low level, most of the incentives to the alcohol indus-
tries were withdrawn and there was a great interest in
the optimization of all the stages of the ethanol produc-
tion process. Nowadays, with a further increase in
petroleum prices and productivity improvements at-
tained in alcohol production there is again a good
outlook for this industry. However, ethanol will only
substitute gasoline as a fuel if its production becomes
economically competitive.The operation of the alcoholic fermentation process
in a continuous mode is desirable, since higher produc-
tivity, improved yields and better process control are
attained [2]. However, the industrial implementation of
a continuous process requires a previous study of the
process behaviour and its use in the development of an
efficient control strategy. The influence of temperature
in the kinetic parameters must be considered, as there is
difficulty in maintaining a constant temperature during
industrial alcoholic fermentation. This is an exothermic
process and small deviations in temperature (2 4 C)can dislocate the process from optimal operational
conditions.
As the conventional process is inhibited by ethanol,
the selective extraction of this product during fermenta-
tion is essential to enhance process performance. Sev-
eral schemes combining fermentation with a separation
process have been developed, such as fermentation
under vacuum [3,4], pervaporation [5], solvent extrac-
tion [6], ultrafiltration [7], fermentation combined with
a flash vessel operating under atmospheric pressure [8],
fermentation combined with a vacuum flash vessel
[9,10] and CO2 gas stripping [11]. Silva et al. [10] have
shown that the scheme using the vacuum flash vessel
presents many positive features and a better perfor-
mance than an industrial conventional process [12].
Another important aspect to be considered in the
optimization of the alcoholic fermentation is the devel-
opment of an efficient control strategy, as it minimizescosts by maintaining the process under optimal condi-
tions. The choice of the control structure is an impor-
tant step in the development of a control strategy.
In this work the performance of a continuous extrac-
tive alcoholic fermentation scheme based on that pro-
posed by Silva et al. [10] is studied. A mathematical
model considering effect of temperature on the kinetic
parameters is developed based on experimental data to
describe the fermentation process. Response surface
analysis is used in a simulation study to determine the
operational conditions that lead to high yield and pro-ductivity. The concepts of factorial design are used in
the study of dynamic behavior of the process in order
to choose the best control structures for efficient con-
trol of the process and the performance of a DMC
(Dynamic Matrix Control) algorithm is tested to con-
trol the extractive process.
2. Extractive alcoholic fermentation
A general scheme of the extractive alcoholic fermen-tation proposed by Silva et al. [10] is shown in Fig. 1.
The process consists of four interlinked units: fermentor
(ethanol production unit), centrifuge (cell separation
unit), cell treatment unit and vacuum flash vessel (etha-
nol-water separation unit). This scheme attempts to
simulate industrial conditions [12], with the difference
that only one fermentor is used instead of a cascade
system and the flash vessel is used to extract part of the
ethanol. In fact, in an industrial conventional process
the usual arrangement is to have four interlinked fer-
mentors with the measurements made at the entrance of
the first unit and at the exit of the last tank [12].
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In the cell treatment unit, the cell suspension is
diluted with water, and sulphuric acid is added to avoid
bacterial contamination. The flash vessel is operated in
a temperature range between 28 and 30 C, which is
chosen in order to eliminate the necessity for a heat
exchanger. This reduces drastically the fixed and
maintenance costs of the process, since heat exchangers
are expensive items of equipment in an alcoholic fer-
mentation plant [12]. The associated pressure is in therange of 45.33 kPa.
The process was shown to be able to maintain suit-
able conditions for the growth of Sacharomyces cere-
6isae, by maintaining a constant temperature, which
may be controlled without a heat exchanger [10]. The
vapourized stream leaving the flash vessel is sent to a
rectification column with part of the liquid stream,
while the other fraction of the liquid returns to the
fermentor. This is adjusted to maintain the ethanol
concentration in the fermentor in such a value that it
acts as antiseptic. According to practical knowledge in
industrial units, this alcohol concentration is around 40kg/m3, which has low inhibitory effect for fermenting
yeast but is highly inhibitory for most contaminating
microorganisms [10].
3. Mathematical modelling
In order to determine the feed rate and feed concen-
tration of the fermentor, mass balances on the global
process are necessary. The following considerations
were made: The concentrations of substrate and product leaving
the centrifuge are equal to the concentrations leaving
the fermentor;
The concentration of biomass in the cells recycle
stream is fixed. To maintain the concentration in a
fixed value, the flow rate of the water that dilutes the
ferment (FW) is adjusted. The cell recycle flow rate
(Fr) is maintained at a value fixed by the cell recycle
rate (R) by adjusting the flow rate of the purge (Fp).
The purge permits cell renovation and the with-
drawal of secondary products accumulated into the
fermentor.To be able to obtain the kinetic parameters as func-
tions of temperature, experiments were performed at
temperatures between 28 and 40 C in a system with
total cell recycling by tangential microfiltration. The
substrate used was sugar-cane molasses [13].
An intrinsic model, which takes cell volume fraction
into account, was used, as suggested by Monbouquette
[14]. The ethanol mass balance accounts for both intra-
cellular and extracellular product, as suggested by the
same author [15]. As the experimental data showed a
loss of cell viability with an increase in the fermentation
time, it was assumed that the total biomass comprises aviable (active) phase X
6and an inactive (dead) phase
Xd.
Assuming constant volume, the mass and energy
balance equations for the fermentor using the intrinsic
model are as follows:
viable cells:dX
6
dt=rxrd
F
V(X
6X
6F) (1)
dead cells:dXd
dt=rd
F
V(XdXdF) (2)
substrate:
d1Xtz SVndt
=F(SFS)Vrs (3)
Fig. 1. Extractive alcoholic fermentation.
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Table 1
Kinetic Parameters as functions of the temperature (in C).
Expression or valueParameter
vmax 1.57exp(41.47
T)1.29.104exp(
431.4
T)
Xmax 0.3279.T2+18.484.T191.06
Pmax 0.4421.T2+26.41.T279.75
2.704exp(0.1225.T)Yx
Ypx 0.2556exp(0.1086.T)4.1Ks1.393.104exp(0.1004.T)Ki0.1mp0.2mx1m
1.5n
7.421.103.T20.4654.T+7.69KdP
KdT 4.1013exp 41947
1.987.(T+273.15)
z 390
0.78k
FExEi=FVyi+FLxi (11)
The vapour-liquid equilibrium of the ethanol-water
mixture was calculated by Eq. (12), the value of p isat
was calculated by Antoines equation (the assumption
was made that the light phase was a binary mixture of
ethanol-water) and the value of ki was calculated using
the NRTL model (Non-random Two-Liquid) [10].
Kei=yi
xi=ki
pi
sat
p (12)
Eq. (1) to Eq. (12) were solved using a Fortran
program with integration with an algorithm based on
the fourth order Runge-Kutta method.
4. Process optimization
The extractive alcoholic fermentation process may be
optimized using response surface methodology, which is
a procedure that does not require model simplificationsand the explicit formulation of an objective function.
The input variables considered for the optimization
were the ones whose influence on yield and productivity
were determined as relevant by Silva et al. [10]. A
factorial design 24+star configuration with a central
point was performed to determine two quadratic mod-
els with inlet substrate concentration (S0), cells recycle
rate (R), residence time (tr) and flash recycle rate (r) as
inputs and yield and productivity as outputs.
In the following simulations the fresh medium flow
rate (F0) was considered constant, so that variations in
residence time led to variations in the reactor volume.The reactor volume was calculated as follows:
V=F.tr (13)
in which tr is the residence time and the feed flow rate
was calculated as:
F=F0+FLR
(1R)(14)
in which FLR is the liquid phase recycle flow rate from
the flash vessel and R is the cell recycle rate.
Yield and productivity were defined as follows:
yield=F6.P
6+FLS.PLR
F0.S0.0.511(15)
prod=F6.P
6+FLS.PLR
V(16)
Table 2 shows the coded factor levels and the real
values for the input variables. The mathematical model
was used to simulate the extractive process.
The software Statistica (Statsoft, v. 5.0) was used to
analyze the results. The quadratic models obtained for
yield and productivity as a function of the more signi fi-
cant variables were:
product:d1
Xt
z PV+Xt
z kPVndt
=Vrp+F(PFP)
(4)
dT
dt=D(TFT)+
DHrs
zmCp(5)
z and k in Eq. (3) and Eq. (4) are the ratio of dry cell
weight per wet cell volume and the ratio of concentra-
tion of intracellular to extracellular ethanol,
respectively.
The values of the constants in the energy balance Eq.
(5) are given by [10]: DH=51.76 kcal/(kg TRS); zm=1000 kg/m3 and Cp=1 kcal/(kg C).
The kinetic rates of growth, death, ethanol formation
and substrate consumption are as follows:
rx=vmaxS
Ks+Sexp(KiS)
1
Xt
Xmax
m1
P
Pmax
nX
6
(6)
rd=(KdTexp(KdPP))X6 (7)
rp=Ypxrx+mpX6 (8)
rs=rx
Yx+mxX6 (9)
The parameters were adjusted as functions of temper-
ature from the experimental data and are given in Table
1. The proposed model described the dynamic be-
haviour of the alcoholic fermentation [13].
The dynamics of the flash tank are much faster than
that of the fermentation process, so a pseudo steady
state was assumed for the flash tank. The mass balances
over the flash tank are given by
FE=FV+FL (10)
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Table 2
Coded factor levels and real values for factorial design
tr (h) R rS0 (kg/m3)
2.5Level +2 0.5280 0.6
2.125 0.425230 0.5Level +1
1.75 0.35Central point (0) 0.4180
1.375 0.275130 0.3Level 1
1.0Level 2 0.280 0.2
An analysis of the response surfaces plotted using
Eq. (17) and Eq. (18) shows that S0, R, tr and r have
opposite effects on yield and productivity, which means
that the values that increase yield decrease productivity
and vice-versa. It shows also that there are many
combinations of values that lead to high yield and
productivity. The choice of the best values for the input
variables is easier if one takes advantage of previous
knowledge of the process. For example, according toAndrietta and Maugeri [12], R cannot be much higher
than 0.3 because otherwise it would increase the re-
quirement for centrifuges capacity. Centrifuges are very
expensive and so are their maintenance costs. Another
consideration is about the reactor volume. If F0 is fixed
(F0=100 m3h), the reactor volume decreases as tr, R
and r decrease. If R is fixed, then, low values of tr and
r that lead to high yield and productivity should be
chosen. Figs. 24 show the response surfaces for yield
and productivity as functions of S0 and r for tr=1.2,
1.4 and 1.6 h, respectively. R is fixed as 0.3. The
surfaces are plotted together to facilitate visualization.
Yield is shown as a surface area and productivity as
lines. It can be observed that tr seems to have more
influence on productivity than on yield (for example,
for tr=1.2 h productivity above 26.7 kg/(m3h) and
Yield=82.9913.35.S02.54.S02+5.15.tr+7.40.R
+9.14.r+2.66.S0.tr+3.12.S0.R+5.87.S0.r
(17)
Prod=14.67+6.44.S00.9.S025.52.tr+1.58.tr 2
4.32.R4.9.r+0.94.S0.r1.18.r.R (18)
Table 3 depicts the analysis of variance (ANOVA)
for yield and productivity. Both responses present a
high correlation coefficient and the model can be con-
sidered statistically significant according to the F-test
with 99% of confidence, since the calculated values were
more than 17 times greater than the listed value. As a
practical rule, a model has statistical significance if the
calculated F value is at least 3 5 times greater than the
listed value [16].
Table 3
Analysis of variance
Mean squareSum of squares F-valueSource of variation Degrees of freedom
Yield Prod. Yield Prod. Yield Prod.
2303.9 723 288Regression 90.4 8 66.8 66.5
1.36 16Residual 69.0 21.7 4.31
2372.9 744.7Total 24
Correlation coefficient 0.9710.971
F listed value: F8,16=3.89 (99%)
Fig. 2. Response surface for R=0.3 and tr=1.2 h.
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Fig. 3. Response surface for R=0.3 and tr=1.4 h.
Fig. 4. Response surface for R=0.3 and tr=1.6 h.
yield above 90.7% can be reached and for tr=1.6 h the
highest values for productivity and yield reached are
above 22.2 kg/(m3h) and 90.7%). It can also be seen
from the figures that high yield is attained for low
values of S0 and r does not influence yield much. In this
way, it is possible to choose a relatively low value of S0
to maximize yield and a low value of r to increaseproductivity. The value of tr should be relatively low to
maximize productivity and minimize reactor volume. It
is worthwhile mentioning that too low values of tr,
however, led to low yield. After analysis of the simula-
tions results using the mathematical model, the follow-
ing values were chosen: S0=130 kgm3, tr=1.3 h,
R=0.3 and r=0.25. The values of yield and productiv-
ity attained were 82% and 21 kg/(m3h). Conversion
was 96% and the reactor volume 257.4 m3. A simula-
tion using the input variable values determined by Silva
et al. [10], S0
=180 kgm3, tr
=1.2 h, R=0.35 and
r=0.4, gave yield, productivity and conversion of 81%,
22 kg/(m3h) and 96%, respectively. The volume of the
reactor, however, was 339.8 m3, 32% higher than the
obtained in the present work.
The conversion and yield attained for the two sets of
input variables were low when compared to previously
published values, conversion of 99% and yield of 86.3%
[16]. These values can be increased, but for a lowincrease in conversion and yield there is a great de-
crease in productivity and a great increase in reactor
volume. For example, the conditions to reach conver-
sion of 98% and yield of 86.4% (S0=120 kgm3, tr=1.2
h, R=0.3 and r=0.45) led to productivity of 15 kg/
(m3h) and reactor volume equal to 358.6 m3. The
productivity of the extractive process for the conditions
determined in this work or by Silva et al. [10] is much
higher than that of the conventional process. Kalil et al.
[16] optimized the industrial conventional process de-
signed by Andrietta and Maugeri [12] and obtained a
productivity of 12 kg/(m3h).
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Table 4
Coded factor levels and real values for factorial design
RS0 (kg/m3) F0 (m
3/h) r T0 (C)
0.33 110Level +1 0.275143 33
0.27Level 1 90117 0.225 27
about the effect of the interactions between the input
variables in the outputs. A two level factorial design
can be used in a dynamic behaviour study, since only a
preliminary investigation is necessary to determine if
some factors (inputs) affect the outputs.
The outputs of the extractive process are: biomass
concentration in the fermentor (Xt=X6+Xd), sub-
strate concentration in the fermentor (S), product con-
centration in the fermentor (P) and temperature in thefermentor (T). The input variables considered for ma-
nipulation are: cell recycle rate (R), inlet flow rate (F0)
and flash recycle rate (r). The input variables consid-
ered as possible load disturbances are: inlet substrate
concentration (S0) and inlet temperature (T0). Table 4
gives the coded factor levels and the real values for the
input variables. They were calculated as variations of
910% around the steady state. The steady state values
are as follows: S0=130 kgm3; R=0.3; F0=100 m
3h,
r=0.25 and T0=30 C.
As the dynamic behaviour of the process is being
studied, the output variables must be calculated as
functions of time. Thus, for each simulation, all the
output variables were calculated from 0 10 h. This
final time was chosen because after 10 h a new steady
state had been reached in all simulations. The method-
ology for the calculation of the main effects as well as
the interaction effects in a complete factorial design can
be found in Box et al. [17]. The main effect can be
interpreted as the difference (for the output variable)
between the low setting (1) and the high setting
(+1) for the respective input variable. A program in
Fortran was developed to calculate the main and inter-action effects as functions of time.
Fig. 5 shows the main effects of the input variables
on biomass concentration as a function of time. The
interaction effects between the input variables on this
output variable are negligible.
Fig. 5. Main effects of the input variables on biomass concentration.
5. Dynamic behaviour of the process
To choose the best control structures for a given
process, its open-loop dynamic behaviour must be in-
vestigated. The objective is to determine how the out-
put variables change with time influenced by changes in
the inputs (manipulated variables and possible distur-bances). This can be done by changing the values of the
various input variables (one by one) and observing the
change of the output variables with time. Another
approach is the use of the concepts of factorial design.
In this case, it is also possible to have information
Fig. 6. (a) Main effects of the input variables on substrate concentration. (b) Interaction effects between the input variables on substrateconcentration.
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Fig. 7. Main effects of the input variables on product concentration.
on the output variable depends also on the values of the
other factors. In this case, the main effects in Fig. 6a
were used, but it should be clear that they are approxi-
mated mean values.
Fig. 7 depicts the main effects of the input variables
on product concentration, and Fig. 8 presents the main
effects of the input variables on temperature. The inter-
action effects between the inputs on these output vari-
ables are negligible.By using the data in Figs. 5 8, a table of the effects
of the inputs on the outputs can be constructed. In
Table 5, the black area means that the input influences
the output, the white area means that the influence is
negligible and the gray area means that the input has a
weak influence on the output. Table 5 can be used to
determine the best structures for an efficient control of
the process. For example, F0 influences mainly the
substrate concentration and a loop that manipulates F0and controls S can be considered decoupled from the
other loops. If some disturbance deviates the substrate
concentration from its set point, controlling this output
through the manipulation of F0 does not affect signifi-
cantly the other output variables, which is a desirable
characteristic.
From Table 5 the following conclusions can be made:
the biomass concentration can be controlled by the
manipulation of R and disturbances in T0 have a weak
influence in this output. The best choice of manipulated
variable to control the substrate concentration is F0 and
disturbances in S0 and T0 affect this output. It is
difficult to control product concentration with the ma-
nipulated variables considered, as they have only aweak influence on this output. Thus, the variations in
the manipulated variable necessary to control this out-
put will probably be too large. Disturbances in S0 affect
product concentration. None of the manipulations con-
sidered in this work affect temperature, which can not
be controlled. In this case this is not a problem, as the
proposed scheme maintains the temperature inside a
desired range without the necessity of a control system
[10]. Disturbances in T0 affect the temperature and
disturbances in S0 have a weak influence on this output.
From the conclusions above, it can be seen thatsubstrate concentration, which is the most important
variable to be controlled in an alcohol fermentation
plant, is easily controlled. However, if it is necessary to
control product concentration, the operational point
determined in the present work is not a good choice. A
dynamic behaviour study was performed using the op-
erational conditions determined by Silva et al. [10] for
comparison. The coded factor levels and the real values
for the input variables, calculated as variations of 9
10% around the steady state, are shown in Table 6. The
steady state values are as follows: S0
=180 kgm3;
R=0.35; F0=100 m3h, r=0.4 and T0=30 C.
Fig. 8. Main effects of the input variables on temperature.
Table 5
Effects of the inputs on process outputs
Table 6
Coded factor levels and real values for factorial design
F0 (m3/h)RS0 (kg/m
3) T0 (C)r
198 0.385Level +1 110 0.44 33
0.36900.315162Level 1 27
Fig. 6a presents the main effects of the input vari-
ables on substrate concentration. In this case, the ef-
fects of interaction between some of the input variables
on substrate are important, as seen in Fig. 6b. This
means that the main effect of an input variable (factor)
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In this case, two of the manipulated variables (R and
r) have a strong influence on product concentration, as
can be seen in Fig. 9. The effects of the inputs on the
outputs are shown in Table 7. In this table shading has
the same meaning as in Table 5.
From Table 7 it can be concluded that biomass
concentration can be controlled by the manipulation of
R. The best manipulated variable to control substrate
concentration is F0, changes in S0 influence S andchanges in T0 have only a weak influence on this
output. The best choice to control P is r, as this
manipulated variable has strong influence only on this
output variable, and changes in S0 influence product
concentration. None of the manipulations considered
affect the temperature, which cannot be controlled.
Disturbances in T0 affect the temperature.
6. Dynamic matrix control
The basic concepts of the DMC algorithm wereoriginally presented by Cutler and Ramaker [18] and
can be found in Luyben [19]. This control algorithm
has great potential for industrial application [20]. The
basic idea is to use a time-domain step-response model
of the process to calculate the future changes in the
manipulated variables that will minimize some perfor-
mance index.
The output of a SISO (Single Input Single Output)
system can be computed from its step response model,
(bi), as follows:
yol,i=y 0meas+ %
NP+1
k=0
(bi+1kb1k)(Dmk)old (19)
in which yi is the value of the output y at sampling time
i (in the future); Dmk is the change in the manipulated
variable at sampling time k (in the past) and y
meas
0 is themeasured value of y at the actual sampling time.
The DMC algorithm minimizes the square of the
deviation between the predicted output in closed loop
and the set-point values at NC future sampling periods
by solving the constrained least squares minimization
problem:
J= %NP
i=1
(y set pointycl,i)2+f 2 %
NC
k=1
[(Dmk)new]2 (20)
in which J is the performance index to be minimized;
Dm is the vector of the NC future changes in the
manipulated variable to be calculated; f is the suppres-sion factor or tuning parameter, which penalize the
objective function for changes in the inputs Dm ; NP is
the prediction horizon and NC is the control horizon.
The minimization of Eq. (20) using the least squares
method results in the following equation
(Dm)new= [ATA+f 2I]1ATy (21)
in which:
y=y set pointyol (22)
Matrix A in Eq. (21) is the dynamic matrix and iscomposed by the step-response coefficients.
The DMC controller has three parameters that can
be adjusted to good performance of the controller: NP,
NC and f. In this work the DMC algorithm was
implemented in a Fortran program.
In the following tests with the DMC control, the
operational conditions used were the determined in the
present work and the steady state conditions are given
by: Xt=30.1 kgm3, S=5.4 kgm3, P=37.7 kgm3,
T=33.4 C.
6.1. Case 1. Substrate concentration control bymanipulating F0
This control structure was chosen based on the dy-
namic behavior study results. As the inlet flow rate (F0)
influences strongly only the substrate concentration, it
is a good variable to be manipulated to control that
output variable.
In the first test of the performance of the controller,
step changes of920% were made in the inlet substrate
concentration (S0). Fig. 10 shows the open-loop re-
sponse and the result when the DMC controller is used.
The controller maintained the controlled variable near
Fig. 9. Main effects of the input variables on product concentration.
Table 7
Effects of the inputs on process outputs
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A.C. Costa et al. /Process Biochemistry 37 (2001) 125137 135
Fig. 10. Substrate concentration against time for step change of
920% in feed substrate concentration.
to the set-point value in the presence of the load
disturbances considered.
The performance of the DMC controller for the
servo problem was tested by making a step change of
950% in the set-point value. Fig. 11 presents the
results for the controlled variable when the process is
operated with the DMC controller. It can be seen that
the DMC controller presented good performance for
the servo problem.
6.2. Case 2. Product concentration control by
manipulating R
According to Table 5, the flash recycle rate (r) is the
best choice of manipulated variable to control product
concentration, as it influences only this output variable.
However, as this influence is weak, the manipulated
variable whose influence on product concentration is
the strongest was chosen (see Fig. 7), the cells recycle
rate (R). This manipulated variable was chosen only to
determine if product concentration can be controlled,but it is not a good choice, since it has a strong
influence on biomass concentration (see Table 5). Then,
the variations made in this manipulated variable to
control product concentration would affect much the
biomass concentration. Also, according to Andrietta
and Maugeri (1994), the value of this manipulated
variable can not be much higher then 0.3 because
otherwise the needs on industrial centrifuges capacity
would be increased.
Step changes of 920% were made in S0. Fig. 12a
and 12b show the behaviour of the controlled andmanipulated variables, respectively. It can be seen from
the figures that, in the case of the positive step change,
the DMC controller was able to return the substrate
concentration to the steady state. For the negative step
change, however, R reached a lower restriction (it was
Fig. 11. Substrate concentration against time for change of950% in
the set point.
Fig. 12. (a) Product concentration against time for step changes of920% in S0. (b) Cells recycle rate against time for step changes of 920 inS0.
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A.C. Costa et al. /Process Biochemistry 37 (2001) 125137136
Fig. 13. (a) Product concentration against time for step changes of 920% in S0. (b)- Flash recycle rate against time for step changes of 920 in
S0.
assumed that R cannot be lower than 0.05) and the
product concentration did not return to the steadystate. As the dynamic behaviour study has shown, the
influence of R on S is weak, and, for the negative step
change in S0, the variation in R necessary to return the
controlled variable to the steady state was too large.
Tests were made using the other manipulated vari-
ables (F0 and r) to control the product concentration
and in all the cases the control algorithm failed in the
case of the negative step change.
6.3. Case 3. Product concentration control by
manipulating r (operational conditions determined by
Sil6a et al. [10])
As the dynamic behaviour study showed that it is
possible to control product concentration if the opera-
tion point is that determined by Silva et al. [10], the
performance of the DMC controller was tested for the
same disturbances considered above. In this case, the
manipulated variable chosen was r, as it influences
strongly only this output (see Table 7), which is a
desirable characteristic. Fig. 13a and 13b show the
behavior of the controlled and manipulated variables.
In this case the DMC controller was able to return theproduct concentration to the steady state for the posi-
tive and negative step changes.
7. Discussion
Despite many advantages of using ethanol produced
from biomass as a fuel (it is a high-energy, clean
burning and totally renewable liquid fuel), it will only
substitute gasoline if its production is economically
competitive. Thus, there is an increased interest in the
optimization of all the steps of ethanol production.
One way to improve the productivity of a product
inhibited fermentation such as ethanol production is thecontinuous removal of the product as it is formed.
Several attempts have been made to achieve simulta-
neous separation of ethanol using various product re-
moval methods [2]. The fermentation process coupled
with a vacuum flash vessel proposed by Silva et al. [10]
and studied in this work presented a high productivity
(21 22 kg/(m3h)) when compared to the industrial
conventional process proposed by Andrietta and
Maugeri [12]. This process was optimized by Kalil et al.
[16] and presented a productivity of 12 kg/(m3h).
A key to the successful design, optimization and
control of an appropriate industrial process is a thor-ough understanding of the systems dynamics. A math-
ematical model based on fundamental mass balances
and kinetic equations using experimental parameters
described as functions of the temperature has been used
to investigate the influence of operational variables on
yield and productivity, using the method of factorial
design and response surface analysis. Under the deter-
mined conditions the productivity attained was 21 kg/
(m3h) and the yield was 82%. The reactor volume was
254.7 m3. The operational conditions determined by
Silva et al. [10] led to productivity and yield of 22kg/(m3h) and 81%, respectively. The volume of the
reactor, however, was 339.8 m3, 32% higher than that
obtained in the present work. In both cases the produc-
tivity was higher and the reactor volume was lower
than in an industrial conventional process [12,15]. Yield
and conversion, however, were lower. Higher yield and
conversion, of 86.4% and 98%, respectively, can be
obtained, but productivity decreases to 15 kg/(m3h)
and the reactor volume increases to 358.6 m3.
The industrial operation of the extractive fermenta-
tion process requires the development and implementa-
tion of an efficient control strategy, able to keep the
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A.C. Costa et al. /Process Biochemistry 37 (2001) 125137 137
main process variables in its set points in spite of load
disturbances and/or set point changes. The DMC con-
troller has great potential for industrial application,
because this algorithm is considered robust and easily
implemented [20].
To choose the best structures for an efficient control
of the alcoholic fermentation, its dynamic behaviour
has been studied. The factorial design methodology was
successfully used to achieve this goal. It was shown thatthe operating conditions have a strong influence on the
performance of the control algorithm. If the extractive
process is operated at the conditions determined in this
work, substrate concentration is easily controlled by the
manipulation of F0. Product concentration, however,
cannot be controlled in at least one situation (distur-
bance of20% in S0). The operation of the extractive
process at the conditions determined by Silva et al. [10],
in spite of requiring a higher reactor volume, enables
the control of both substrate and product concentra-
tions. This shows the importance of the study of the
dynamic behavior of the process before designing anindustrial plant.
The methodologies used in this work (factorial design
and response surface analysis combined with simula-
tion) were adequate for the optimization and determi-
nation of control structures for the extractive ethanol
fermentation. They can be applied to any other fermen-
tation process, independently of the number of vari-
ables, provided that a representative mathematical
model is available.
Acknowledgements
The authors acknowledge FAPESP (process number
98/09198 6) and CAPES for financial support.
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