Factorial Design and Simulation for _ Extractive Eth Ferm

8/2/2019 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

www.elsevier.com/locate/procbio

* 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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A.C. Costa et al. /Process Biochemistry 37 (2001) 125137 127

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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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


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


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


11/13


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.


12/13


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


13/13


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.

References

[1] Wheals AE, Basso LC, Alves DMG, Amorim HV. Fuel ethanol

after 25 years. Tibtech 1999;17:4827.

[2] Kargupta K, Datta S, Sanyal SK. Analysis of the performance

of a continuous membrane bioreactor with cell recycling during

ethanol fermentation. Biochem Engng J 1998;1:317.

[3] Ramalinghan A, Finn RK. The vacuferm process: a new ap-

proach to fermentation alcohol. Biotechnol Bioeng 1977;19:583

9.

[4] Cysewski GR, Wilke CR. Rapid ethanol fermentation using

vacuum and cell recycle. Biotechnol Bioeng 1977;19:112543.

[5] Christen M, Minier M, Renon H. Ethanol extraction by sup-

ported liquid membrane during fermentation. Biotechnol Bioeng

1990;3:11623.[6] Minier M, Goma G. Ethanol production by extractive fermenta-

tion. Biotechnol Bioeng 1982;24:156579.

[7] Sourirajan S. An approach to reverse osmosis/ultrafiltration.

Membrane design and development. Membrane 1987;12:3679.

[8] Ishida K, Shimizu K. Novel repeated batch operation for flash

fermentation system: experimental data and mathematical mod-

elling. J Chem Technol Biotechnol 1996;66:3406.

[9] Maiorella BL, Blanch HW, Wilke CR. Biotechnology report-

economic evaluation of althernative ethanol fermentation pro-

cesses. Biotechnol Bioeng 1984;26:100325.

[10] Silva FLH, Rodrigues MI, Maugeri F. Dynamic modelling,

simulation and optimization of an extractive continuous alco-

holic fermentation. J Chem Tech Biotechnol 1999;74:17682.

[11] Taylor F, Kurantz MJ, Goldberg N, Craig JC. Kinetics ofcontinuous fermentation and stripping of ethanol. Biotechnol

Letters 1998;20:6772.

[12] Andrietta SR, Maugeri F. Optimum design of a continuous

fermentation unit of an industrial plant for alcohol production.

In: Adv. Bioprocess Engng, 1994:47 52.

[13] Atala DIP, Costa AC, Maciel R, Maugeri F. Kinetics of ethanol

fermentation with high biomass concentration considering the

ffect of temperature. Accepted for publication in Applied

Biochem. Biotechnol., 2001.

[14] Monbouquette HG. Models for high cell density bioreactors

must consider biomass volume fraction: cell recycle example.

Biotechnol Bioeng 1987;29:107580.

[15] Monbouquette HG. Modeling high-biomass-density cell recycle

fermentors. Biotechnol Bioeng 1992;39:498503.[16] Kalil SJ, Maugeri F, Rodrigues MI. Response surface analysis

and simulation as a tool for bioprecess design and optimization.

Process Biochem 2000;35:53950.

[17] Box GEP, Hunter WG, Hunter JS. Statistics for experimenters.

New York: John Wiley and Sons, 1978.

[18] Cutler CR, Ramaker BL. Proc. Joint Auto Control Conf. 1980,

Paper WP5-B, San Francisco.

[19] Luyben WL. Process modeling, simulation and control for chem-

ical engineers, 2. McGraw-Hill, 1989.

[20] Morari M, Lee JH. Model predictive control: past, present and

future. Comp Chem Engng 1999;23:66782.

.

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