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Chemical Engineering and Processing 44 (2005) 581592
Simulation of vegetable oil extraction in counter-current
crossedflows using the artificial neural network
G.C. Thomasa, V.G. Krioukova,, H.A. Vielmoba Department of
Technology, UNIJUI Northwest Regional University of Rio Grande do
Sul, PoB 560, 98700-000 Ijui, RS, Brazil
b Mechanical Engineering Graduate Program, UFRGS Federal
University of Rio Grande do Sul, 90050-170 Porto Alegre, RS,
Brazil
Received 10 June 2003; received in revised form 24 June 2004;
accepted 24 June 2004
Abstract
A new mathematical model of processes in a Rotocell extractor
was developed. The model considers: a two-dimensional approach
ofcounter-current crossed flows (CCC) with oil diffusion for
miscela; mass transfer between the bulk, pore and solid phases; the
effect of theexisting processes in the drainage and loading
sections; oil losses; and variation in the miscela viscosity and
density. The model leads toa comparedw e transientr
K
1
dototrtesteSsor
oreider-fer
ng of
rawolidwas
rdlyes thedataiffer-icsedde-e oilhe
ndedthector
0d
system of coupled partial and ordinary differential equations,
whereupon is transformed in the neural network. The solution isith
experimental data and with the method of ideal stages. The
numerical simulations reveal the extraction field properties in
th
egimes.2004 Elsevier B.V. All rights reserved.
eywords:Rotocell extractor; Counter-current crossed flow;
Miscela
. Introduction
The mathematical modeling of processes in nutritious in-ustry is
a subject that receives continuing attention in thepen literature.
In the present work, this approach is applied
o industrial extractors that are extensively employed in
sugar,il and coffee processing. In general, they are managed by
he principle of counter-current crossed flows (CCC) of theaw
material (a porous medium that contains the substanceo be
extracted, for instance, oil) and the miscela. Inside thextractor,
the flows of miscela and the raw material interacto that, in the
outlet, the raw material has low oil concentra-ion, and miscela has
high oil concentration. The most usedxtractors are: Rotocell,
De-Smet and Crown-Model[1,2].everal multi-stage methods are being
used to predict andimulate the extractor processes[3]. In this
method, uniformil concentrations in percolation sections and the
equilib-ium between the bulk and pore phases are assumed. But,
as
Corresponding author. Tel.: +55 55 3332 7100; fax: +55 55 3332
9100.E-mail address:[email protected] (V.G.
Krioukov).
indicated in[4], presently is necessary the modeling mdetailed
with the space concentration distributions, consing diffusion
extraction field, non-equilibrium mass transbetween phases,
etc.
Several articles considered the mathematical modelivegetable oil
extraction. The first works in this area[5,6]present a physical
outline of the oil extraction from thematerial, which is composed
of laminated flakes. The spart is treated as an inert component.
Oil inside the flakedivided into two areas: slow extraction, from
where oil hacomes out, and fast extraction, where the solvent
replacoil and is not drained. In these works, the experimentalwere
presented for different oleaginous species with dent flake
thicknesses. Karnofski[7] proposed a semi-empirmodel of the oil
extraction in industrial extractors that is baon the following
considerations: the oil retention time istermined by the solution
rate; and the resistance to thdiffusion through the flake borders
is relatively small. Tmodel employed experimental results, which
were extefor the prediction of oil losses in industrial extractors.
Inpaper[8], the coupled mathematical model of an extra255-2701/$
see front matter 2004 Elsevier B.V. All rights
reserved.oi:10.1016/j.cep.2004.06.013
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582 G.C. Thomas et al. / Chemical Engineering and Processing 44
(2005) 581592
Fig. 1. Processes diagram of a Rotocell extractor. (1) Miscela
inlet in theloading section; (2) wagons inlet; (3) raw material
inlet; (4) solvent inlet tube;(5) concentrated miscela outlet; (6)
drained wagon; (7) typical wagon underpercolation; (8) wagon to
fill out raw material and concentrated miscela;(9) miscela
reservoirs; (10) pumps; (11) flakes outlet; (12) drainage
section;(13) flow of miscela inside the wagon; (14) miscela flow
after drainage; (A,B, C, D) miscela distributors.
with other plant equipment (dissolventizer, miscela separa-tor,
etc.) was presented. The model included algebraic equa-tions for
each flow component (marc, water, oil and solvent)that considers
the balance between the phases. The extractosub-model was based on
the multi-stage method that uses experimental data, and does not
have the objective of presentingoil concentration distribution in
the extraction field.
A significant step was achieved in[9], which developedthe oil
extraction model in a fixed bed of expanded flakes[2], which,
contrary to the laminated flakes, present the bestextraction
properties. This system was treated as a porousmedium with two
porosity types (bulk and pore). The equi-librium constant concept
was used between the solid and porephases. To describe the oil
transfer between the phases, theformulaQpB = kfap(Cp C) was
applied. Also the oil dif-fusion was considered in the bulk phase.
The mathematicalmodel included EDPs (one-dimensional, transient)
that weresolved by the finite elements method. Based on[9], and
con-sidering the same phenomena, in[10], a model for crossedflows
of expanded flakes and solvent in one percolation sec-tion was
presented. The model described the processes ina percolation
section of industrial extractors and includedPDEs (two-dimensional,
transient) that were solved by themethod of lines[11].
However, it is not available in the literature, a coupledm s ofo
andd andd
ex-t -p kes,t diumm d by
two types of porosity,b (the external porosity of the
chan-nelled spaces) andp (the internal porosity of the
cavityspaces), and is modeled as porous particles with diameterdp.
The solid part of the particles, named as solid phase, canalso
contain an oil portion. Miscela is a liquid that, in con-tact with
flakes, extracts oil. In spacesb, miscela is calledbulk phase and
in spacesp, it is called pore phase. In theextractor inlet, the
miscela has a very small oil concentration(Cin), and is called
solvent or weak miscela. In the outlet, it iscalled concentrated
miscela (for the oil concentration is muchhigher). The oil
initially is contained in the raw material; theobjective of the
extraction process is to transfer this speciesto the miscela.
The main elements of the Rotocell extractor are shown inFig. 1.
For operational reasons, the extractor is separated intothree
areas: loading 8, extraction (space between wagons8 and 6) and
drainage 12. In the loading area 8, the wagonis loaded with both
raw material and concentrated miscela.The wagons move evenly from
direction 2 to 11, returning toposition 2 to complete the cycle. As
observed, the extractoris rounded. The extraction area is divided
into percolationsections; each section corresponds to two wagons.
The wagonmoves under the vertical flows of miscela that extract the
oilfrom the flakes. Miscela passes from tube 4 to 5 in
counter-current crossed flow (relatively to the raw material flow),
andi f thec ted att gons,a lations le isr ns thes
2
l (at es,o ee :
teral
s; on
ludest
tionionodel of CCC flows that considers: spatial distributionil
concentration in the extraction field; mass transferiffusion; and
the presence of trays, and of the loadingrainage areas.
In this paper, a model was developed for a Rotocellractor whose
scheme is presented inFig. 1. The main comonents involved in the
extraction are: the expanded fla
he miscela and the oil. The raw material is a porous meade of
grains (for instance, soy), which is characterizer-s enriched by
extracted oil. Therefore, in the beginning oycle, the miscela is
weak, and then becomes concentrahe end of the process. The miscela,
after crossing the waccumulates in tray 9 and then enters into
another percoection (through pumps and distributors), and the
cycepeated. In the drainage area 12, weak miscela abandopacesb of
the flakes.
. Mathematical modelling
The target of the model is to predict:
two-dimensionax-ndz-directions) distributions of concentrationsC
andCp in
he extraction field in both stationary and transient regimil
losses (in outlet 11,Fig. 1) and oil concentration in thxtractor
outlet. In this case, the model should consider
the miscela and raw material flows in CCC pattern;oil transfer
between solid, pore and bulk phases;the processes in drainage and
loading areas;the existence of trays and wagons with impermeable
lawalls;the division of extraction field into percolation
sectionoil diffusion throughout the bulk phase; andthe possibility
of the miscela overflowing from a waginto two different trays at
the same time.
The physical scheme created in these conditions inche following
assumptions:
1. The extraction field is formed by a group of percolasections,
with the miscela flow in the vertical direct
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G.C. Thomas et al. / Chemical Engineering and Processing 44
(2005) 581592 583
Fig. 2. Extractor dimensional scheme for the mathematical model,
ABCD extraction field; A coordinates origin (z, x); Vv wagon
volume;LS wagon height;XR wagon medium width.
and motion of the wagons with flakes in the
horizontaldirection.
2. Each wagon is represented by a group of vertical
(con-ditional) columns (Fig. 2) having widthx, and the uni-form raw
material flows in batch periods by analogy withthe work[4]. These
periods are defined by the formula:t = x/u, whereu is the wagon
horizontal speed.
3. An analysis of experimental data[6] and of the
extractoroperational regime[2] shows that, together with the
exitoil from the solid and pore phases, an opposite transferof
solvent in almost equivalent volume occurs. With thisassumption,
the miscela volumetric flow in the extractor(Qr) is constant, and
does not depend on the processesof oil transfer between the
phases.
4. It is supposed that the operational regime is transient
andthat the concentrationsC andCp in the extraction fieldand in the
loading and drainage areas vary with the time.
5. In the upper part of each column, enters the miscela
thatescapes from the located distributor in the previous
per-colation section.
6. Diffusion is only considered along each column.7. In the
loading area, the miscela of the (mS+1)th tray
occupies the spacesb between the particles and part ofthe
spacesp inside the particles.
8. During the raw material loading, the equilibrium be-N p
holetant
9. Outside the extraction field, the mass transfer betweenthe
pore and bulk phases do not occur.
10. In the drainage stage, every bulk phase escapes in
collec-tion and after that passes through the solvent inlet. Theoil
contained in the pore and solid phases is consideredlost.
11. The horizontal areaAv of the wagons is constant. Forthis
reason (considering that the flowQT is constant),the velocityV is
also constant.
12. In the trays, the oil concentration is uniform, but
changeswith time.
In Fig. 2, an outline of the extractor dimensions is pre-sented.
Two wagons correspond to one percolation section,while the last
section corresponds to just one wagon. Themodel components of the
extraction field are numbered fromthe left to the right according
to: the wagons of 1 up to 2mS +1; the sections from 1 up tomS + 1;
the columns from 1 untilMC = (2mS + 1)p (wherep is the number of
wagon columns)and the trays from 2 to (mS + 1). The tray of the
last sectionis not numbered because it serves as the concentrated
mis-cela collection in the extractor outlet. But a fictitious tray
isincluded with numberm= 1, representing the solvent inlet inthe
extractor together with the drainage miscela.
Because of the use of two time scales (continuous andd uraln m-b
is ac ter itfA , out-l onst delst s noto ealf l int s ofs rms.T
sc si ntedi tiona
w nedb
tween the concentrations in solid (C ) and pore (C )phases is
established that is maintained during the wextraction process. The
volumetric equilibrium cons(Evd) is defined by the formula:
Evd =CN
Cp
= Ed[
s
he+ Cp(ol he) + EdCp(s ol)]
(1)
which can be obtained by the formulaEd = gN/gp re-placing the
mass fractions (gN, gp) by the volumetricfractions (CN, Cp).iscrete
according to the assumption 2), the artificial neetworks (ANN)
approach is applied in this work in coination with the flow
continuous model. This approachoncept that was developed for
biological models, and laound many applications in engineering
areas[12,13]. In theNN scheme, some original concepts are used:
neuron
et function, activation function, discrete time,
connectiraining, etc. The elaboration of the mathematical mohrough
ANN enables the application of the same modelnly in simulation but
also in the operational control of r
acilities. However, to conceive the mathematical modehe form of
ANN, it is necessary to build up sub-modelome of the extractor
components in continuous flow tehe main sub-models are:Extraction
field sub-model:The extraction field ABCD i
omposed byMC virtual columns with widthx; processenside thejth
column are described by the equations presen [9], which are
modified in accordance with the assumpdopted in the physical
scheme:
Cj
= VCj
z+ ES
2Cj
z2+
(1 bb
)kfap(C
pj Cj);
j = 1, . . . , MC; (2)
Cpj
= kfap
p + (1 p)Evd(Cpj Cj) (3)
hereES is the dispersion coefficient, which was determiy [14]:
ES = 0.7DAB + 2.0VdP.
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584 G.C. Thomas et al. / Chemical Engineering and Processing 44
(2005) 581592
The Sherwood number (Sh) needed to define the coeffi-cientkf is
given by[15]:
(a) Sh= 2.4Re0.34Sc0.42 in 0.08< Re < 125; (4)
(b) Sh= 0.442Re0.69Sc0.42 in 125< Re < 5000 (5)
where Re = (Vdp) / () ; Sh= (kf dp) / (DAB) ; Sc=() / (DAB)
.
Eqs. (2) and (3)are linked to the equations for othercolumns
through the boundary conditions presented below.The amount of
equations to model the real extraction fieldis large. If, for
instance,p =10 andmS = 8, the sub-modelrequires 340 partial
differential equations with two variables(, z). Using the method of
lines[11], these equations aretransformed in ODEs, dividing each
column in then lay-ers with thicknessz= LS/n and substituting the
derivatives/z, 2/z2 for the finite differences.
Concentration equations in trays:The equation for themth
situated tray under the extraction field is derived (con-sidering
the hypothesis 12) from the conservation law for theoil species,
and is given by:
dCmd
= VAvbVb
1p
j=2(m1)pj=2(m2)p+1
Cj(LS, ) 2Cm() ;
e:t dc hefit
Q
o
Q
a
Q
w hee
Fig. 3. Scheme of pore phase filling stages. (a) Filling
starting; (b) end offilling; (c) end of the mixture process.
The concentrationCin is related to the concentrationCD
(ac-cording toFig. 2) by:
Cin =CDQD + Chein qs
(qs +QD) . (11)
Loading sub-model:The purpose of this sub-model is todetermine
the initial oil concentration in the pore phase (CPin)as well as
the miscela flow (Qp) that is necessary to fill outthe spaces (b,
p) in the raw material located in the loadingsection (wagon 8,Fig.
1). The raw material in the extractorinlet contains oil only in the
solid phase N with the initial massconcentrationNv and volumetric
concentrationCe, which isdefined by:
Ce = NvMvVvol(1 p)(1 b) (12)
In the sub-model, it is considered that the concentrated
mis-cela (with concentrationCms+1 fills out the spaces (Fig.
3a)between the flakes (forming the bulk phase) and soaks in
theflakes (that have porosityp), therefore occupying part of
thepores (m). At the same time, due to the extraction force,
thesolid phase oil comes out to the phase pore, occupying theother
part ofp with an equivalent amount ofpm (Fig. 3b).After this
process, the uniform oil mixture is quickly set upiic thec
:een
s
C
e
C
o ser-v
C
w
m = 2, . . . , mS. (6)
Drainage sub-model:It includes formulas to determinhe drained
flow (QD), total flow (QT), the average draineoncentration (CD),
the oil concentration in the solvent in trst section entrance (Cin)
and oil losses (Q
pol,Q
Nol). From
he assumptions 9, 10:drainage and total outflow:
D = Vvbtv
; QT = QD + qs; (7)
il losses in the pore phase:
pol =
Vv(1 b)ptvLS
LS0
Cpj (z, )dz; j = 1; (8)
nd in the solid phase:
Nol =
Vv(1 b)(1 p)EvdtvLS
LS0
Cpj (z, )dz; j = 1; (9)
heretv = XR/u is the time of a wagon entrance in txtraction
field; the equation for the concentrationCD:
dCDd
= QDLSVD
LS0
Cj(z, )dz QDCDVD
; (10)n these spaces and, as a result, a concentrationCpin (Fig.
3c)s formed. It is also assumed that some amount of oil
(CNin)ontinues in the solid phase and is in equilibrium
withoncentrationCpin.
This process is described by the following equationstotal
balance of oil in the solid and pore phases betw
tages (a) and (c):
e(1 p) + Cms+1m = Cpinp + CNin(1 p) (13)
quilibrium in the stage (c)
Nin = EvCpin (14)
il conservation in the pore phase, which imposes oil conation in
the pore phase between stages (b) and (c):
ol(p m) + Cms+1m = Cpinp (15)
hereCol is the pure oil concentration (i.e.Col = 1.0).
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G.C. Thomas et al. / Chemical Engineering and Processing 44
(2005) 581592 585
The formula to calculateCpin follows directly from theabove
equations:
Cpin =
Ce(1 p) +(Cms+1p
)/(1 Cms+1
)(Cms+1p
)/(1 Cms+1
)+ p + Evd(1 p) . (16)A formula to defineQv was obtained
considering that themiscela, with a concentration ofCms+1, fills
the spacesbandm in the loading zones:
Qv = Vvtv
[b + (1 b)
p(1 Cpin)(1 Cms+1)
]. (17)
Starting from this, the concentrated miscela flow in the
ex-tractor outlet was also defined (Fig. 2) asQS = Qr Qv.
The miscela oil concentration in the extractor outletCuwas
determined by:
Cu() = 1p
j
Cj(LS, ), j = (MC p+ 1), . . . , MC.
(18)
Boundary conditions:According to the counter-currentcrossed
flows design (Fig. 2), the boundary conditions forthe equations in
each column are:
Cj(z, ) = Cin(), for j = 1, . . . , 2p, z = 0,
C
C
2
uslyi o-t enti -c (1p s ofA ns-f es ofn ), andd ete).I s be-t
eme.
The equations that describe the states, inlets, outlets and
ac-tivation functions form the extractor mathematical model.
In particular, neuron N1 corresponds to the solvent inletwith
parameters:qs, Chein ; neuron N2 to the raw material inletwith
parameters:(Mv/tv), Nv; neuron N3 to the concen-trated miscela
outlet with parameters:QS,Cu; neuron N4 tothe marc outlet with
parameters:QNol,Q
Pol. Also, the neurons
block BN6 reflects the processes in the columns, and eachone
includesnneurons of types N11 and N12 using space dis-cretization
(i = 1 . . . n) of Eqs. (2) and (3). Neurons N11(i, j)and N12(i, j)
are in theith cell of thejth column. Each neuronN11holds two inlets
and two outlets. Based on the sub-modelsequations, the following
formulas can be derived:
for the continuous inlet:
EC11(i, j) =VCi1,jz
+ ESz2
(Ci1,j
+Ci+1,j) +(
1 bb
)kfap(C
pij Cij) (23)
for the continuous outlet:
SC11(i, j) =(
V
z+ 2ES
z2
)Cij (24)
for the discrete inlet value:
ED (i, j) = C (qt)xz (25)f
S
w ce-m
-t
b-t
S
f
E
f
S
nf
ckB
0; (19)
j(z, ) = Cm(), for j = (2p(m 1)+ 1), . . . , 2pm,m = 2, . . . ,
ms, z = 0, 0; (20)
j(z, ) = Cms+1(), for j = (2pmS + 1), . . . , MC,z = 0, 0;
(21)
Cj(z, )
z= 0, for j = 1, . . . , MC, z = LS,
0. (22)
.1. Model in terms of artificial neural networks
The aforementioned sub-models group acts continuon each time
intervalt when the raw material is not in mion. Between the
intervalst, an instantaneous displacemn distancexoccurs, i.e. the
content of thejth column (misela and raw material) is replaced by
the content of thej +)th column. These displacements are shown
inFig. 4(stip-led lines), where the extractor outline is shown in
termNN. The solid lines in this net reflect the continuous tra
ers. The net is heterogenous (it includes several typeurons),
complex (it includes a subsystems of neuronsynamical (with two time
scales: continuous and discr
n Fig. 4, each neuron, block of neurons and connectionween them
reflect some component of the physical sch11 b i,j+1
or the discrete outlet value:
D11(i, j) = bCij((q+ 1)t)xz (26)hereq is the number of
instantaneous column displaents.The neuron state N11(i, j) is
described byCij , whose ac
ivation function is:
dCijd
= EC11(i, j) SC11(i, j) (27)
For the neuron N12, the following equations can be oained:
for a continuous outlet:
C12(i, j) =
kfap(Cpij Cij)
p + (1 p)Evd(28)
or a discrete inlet value:
D12(i, j) = Cpi,j+1(qt)(1 b)pxz (29)
or a discrete outlet value:
D12(i, j) = Cpi,j((q+ 1)t)(1 b)pxz (30)
The neuron state N12 is described byCpij, whose activatio
unction is:
dCpi,jd
= SC12(i, j) (31)
The neurons N11(n, j) located in the bottom of each bloN6
deliver the information to the neurons N10 (m+ 1), while
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586 G.C. Thomas et al. / Chemical Engineering and Processing 44
(2005) 581592
Fig. 4. Extractor scheme in ANN form: (a) BN6 blocks fragment;
(b) ANN fragment of drainage zone.
the upper neurons in the same block obtains the informationfrom
the neurons N10(m). A wagon is represented in the ANNscheme byn
pneurons of the type N11 and N12.
By analogy, the inlets, outlets, states and neuron
activationfunctions are applied to: the trays (N10 (m)), the
loading zone(N13, N14), the weak miscela inlet (N5), the drainage
zone(N8), the oil losses (N15) and the BN9 block, which reflectsthe
processes in the extraction field of the inlet column.
The calculation algorithm is determined by the structureand
properties of the mathematical model in ANN terms;that is, in the
intervalst, the neuron states evolution is de-termined by
continuous connections and is described (forinstance, for the
neurons N11 and N12) by ordinary differ-entialEqs. (27) and (31);
in the interval limitst, there areinstantaneous alterations of the
states induced by discreteconnections that are equal to the changes
of the ODE initialconditions.
Then, the algorithm includes two alternate fragments:
integration of the ODEs in the first intervalt; alteration of
the ODE initial conditions; integration of the ODEs in the second
intervalt; alteration of the ODE initial conditions, and so on
until the
end of the integration.
The ODEs system is integrated by RungeKutta explicitmethod of
the fourth order and with four stages.
3. Model and code verification
The mathematical model and the code (ROTO1) were ver-ified
through:
(a) alteration of elementary cell sizes;(b) test of the oil
species conservation law;(c) verification of uniqueness of the
extraction field station-
ary state independently of the initial distribution of
con-centrationsC,Cp, Cm,Cin;
(d) comparison with experimental data.
The data for verification of the numerical simulations(Table 1)
were chosen based on the real characteristics ofthe Rotocell
extractor, solvent and expanded flakes that weretaken
from[9,14,15,16].
The miscela properties, are functions of the concen-tration, and
are described by polynomials:
= 5.57 103C2 0.73 104C + 0.373 103;(32)
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G.C. Thomas et al. / Chemical Engineering and Processing 44
(2005) 581592 587
Table 1Data the for numerical simulations
n 30p 10mS 7tv 150DAB 109 1.3qs 103 12.5ol 914.8Evd 0.36s 1180Mv
1784Av 1.56Vb 0.2LS 2.3ap 57Nv 0.18dp 0.005b 0.4p 0.3Chein 0.001he
661.7
= 35C2 + 261.28C + 661.68, forC 0.4 (33)which were obtained by
interpolating the data found in[17].
The size of the cells is controlled byn (the number ofhorizontal
layers in the extraction field) andp (the quantityof columns in a
wagon). The integration step in the timeintervalt in the ODEs was
determined by the formulah =t/3. Numerical simulations showed that,
to avoid numericaldivergence, it is necessary to assure that the
Courant numberis satisfied in the vertical direction:Sk = Vh/z<
1.
In the stationary regime, oil flows in the extractor inlet
andoutlet have to obey the following relation:
NvMvoltv
+ Chein qs = QSCu +Qpol +QNol. (34)
Numerical simulations forSk < 1 showed thatEq. (34)
issatisfied with an acceptable precision, that is:
f = 1(QSCu +Qpol +QNol)oltv
NvMv + Chein qsoltv 0.1% (35)
Verification of the independence of the stationary state withthe
extraction field initial state were accomplished for dif-ferent
trends of the initial concentration distributionsC andCp on-c tc
sot es
byK thep h di-r theA ntal
Fig. 5. Concentrations distributionCm along the extractor:()
codeROTO1; (- - - -)ideal stages; () experimental data.
data). As the outlet signal, the total oil losses (QNol
+QDol)were chosen. As the training parameter, the specific
contactareaap was applied. In the training result, it was
determinedthatap 57 (m1) when the total losses in the model
P tol =(Qpol +QNol)oltv
(1 Nv)Mv (36)
matched the losses observed in the real extractor (Pexol 0.5%)
[16].
The results obtained for the stationary state through ourmodel
and through the method of ideal stages (ISM) werecompared (Fig. 5)
with experimental data collected in[16].The concentrations in ISM
were calculated by formulas de-rived by KremerSoudersBrown[3]
considering thatC(x,z) = Cp (x, z), and that the miscela flow is
constant and equalto QS for all stages. As seen, both models
predict satisfac-tory results in the first stages, but for
reservoirs 6 and 7, theideal stages method leads to
concentrationsCm that are quitedifferent from the experimental
data. It is necessary to stresstwo aspects: the ideal stages method
(ISM) leads to the sameresults independently of the parametersLS,
tv,XR, b, etc.,in reality, distributionsCm depend on the alteration
of theseparameters; the model developed in this work is sensitive
tothe changes in the extractor parameters and in the raw ma-terial
characteristics. Besides, it predicts the concentrations then
4
p tot wasp ,i0oT tionC st d: stairway form (pore and bulk),
equal and uniform centrations with high values (C = Cp), uniform
but differenoncentrations:C (small value), andCp (high value). It
wabserved that, independently of the initial valuesC andCp,
he extraction field (ABCD onFig. 2) evolves into a
uniqutationary state.
In the ANN approach, net training was accomplishedF connections
(Fig. 4a) i.e. by mass transfer betweenore and bulk phases. The
training takes place througect modeling[12], comparing the outlet
signals betweenNN (mathematical model) and supervisor (experimepace
distribution in the extraction field that is shown inext section of
the work.
. Results and discussion
The numerical simulation of the transient regime uhe
establishment of steady regime of the extraction fielderformed for
the data inTable 1, with uniform, but different
nitial concentrations:C(x, zc) = Cm = 0.01; CP(x, zc) =.2. The
results are shown inFig. 6 up to 10 in the formf three-dimensional
plots:C = f (x, zc); Cp = f (x, zc).he solvent inlet zone (that is,
miscela with concentrahein 0.001) in the extractor (tube 4,Fig. 1)
correspond
o coordinates:x = 0, . . ., 6; zc = 0, while the concentrate
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588 G.C. Thomas et al. / Chemical Engineering and Processing 44
(2005) 581592
Fig. 6. (a) Extraction field of bulk phase (75 s); (b)
extraction field of porephase (75 s).
miscela outlet zone (tube 5,Fig. 1) corresponds to
coordi-nates:x = 48, . . ., 51;zc = 30. For the raw material inlet
andoutlet zones, the coordinates are, respectively,x = 51,zc = 0,.
. ., 30 andx = 0, zc = 0, . . ., 30.
Fig. 6a and b (for time = 75 s) shows that, in the in-lets of
the extractor, the initially uniform concentration fieldstarted to
deform. It is shown the existence of a concentra-tion wave (Fig.
6a) on one side of the extractor (through thefirst section), while
on the other side, an abrupt front of highconcentrationCp (Fig. 6b)
emerged from the loading zone.In most of the extraction field, it
is observed a growth of con-centrationC and a decrease of
concentrationCp due to thefast oil transfer between the pore and
bulk phases (C (x, zc) 0.03;Cp (x, zc) 0.17).
In time = 225 s (Fig. 7a and b), the plotC= f(x, zc) showsthat
the concentration wave decayed at the bottom of the firstsection
and, through the tray and tube (that links the first andsecond
sections), affected the concentration distribution ofthe second
section. In the other end of the field because ofthe raw material
motion, a small, non-uniform front appeared,since the last section
of the distributor continued injectingmiscela with a small
concentrationCm. In the graphCp (x,zc), two effects are
observed:
a decrease inCp (in the hexane inlet area:x = 0, . . ., 6,zc= 0,
. . ., 30) due to a reduction onC;
withnce o
Fig. 7. (a) Extraction field of bulk phase (225 s); (b)
extraction field of porephase (225 s).
a slope caused by oil transfer from the pore phase to thebulk
phase.
In the remaining region of the extraction field, there is
anapproach between the concentrations of the pore and
bulkphases(C(x, zc) 0,06;Cp (x, zc) 0.11, respectively).
The extraction field in time = 750 s is presented inFig. 8aand
b. The plotC = f(x, zc) shows waves passing through thesecond and
third sections, and forming steps between thesections (x= 12;zc =
0, . . ., 30). The step corresponding tox= 6,zc = 0, . . ., 30 is
steeper because in the oil distribution ofthe first section, it
strongly affected the initial concentrationCin. On the other end,
the front is moved forming, inx = 42,. . ., 50,zc = 0, . . ., 30, a
region of high concentration witha step (corresponding tox = 48,zc
= 0, . . ., 30) between thelast two sections.
In the distribution ofCp = f(x, zc), the pattern of front
dis-placement and of concentration increase continues. In the
firstsections, the concentration distributionCp = f(x, zc)
presentsa slope due to the decrease in the concentrationsC. In
thecentral region of the extraction field, the concentrations
ap-proximate each other, being almost the same (C(x,zc) 0.07;Cp (x,
zc) 0.09). In the plot forC = f(x, zc), it can be seenthe formation
of three steps between the first sections andtwo steps in the last
sections. They are more perceptible onthe tops (zc = 0) than on the
bottoms (zc = 30) of the sec-t nt ina front displacement (on the
opposite side) that movedthe same speed of the raw material, and
the appeara fions because of the miscela diffusion and
displaceme
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G.C. Thomas et al. / Chemical Engineering and Processing 44
(2005) 581592 589
Fig. 8. Extraction field of (a) bulk phase (750 s) and (b) pore
phase (750 s).
the horizontal direction. In the bottom of the last section
(x=48, . . ., 51,zc = 30), a maximum ofC 0.18 is created forthe
following reasons:
together with the raw material (through linex= 51,zc = 0,. . .,
30), a miscela with concentrationCms+1 < Cu entersin the
extraction field;
it corresponds to the average concentration that leaves fromthe
bottom of the next to the last section (x = 42, . . ., 48,zc =
30);
therefore, in line (x = 42,. . ., 51,zc = 30), the
distributionof concentrationsC is the following:Cms+1 (average
inline x = 42, . . ., 48,zc = 30) Cms+1 (concentration in linex =
51,zc= 0, . . ., 30). This fact forces the formation of a maximumin
line x = 48, . . ., 51,zc = 30.
In the graph forCp(x, zc) (Fig. 8b), the displacement
anddecrease front continues with the increase in the size of
slopezone. In the first sections (x = 0, . . ., 12, zc = 0, . . .,
30),concentrationsCp tend to tilt with its decrease.
In time = 975 s (Fig. 9a and b), the distributionC = f(x,zc) was
still characterized by the the same trends:
almost all steps between the sections were already formed,with
the heights of the first steps decreasing and the heights
Fig. 9. Extraction field of (a) bulk phase (975 s) and (b) pore
phase (975 s).
the maximum concentration in the last section increased(C =
0.21);
the plateau almost disappeared, except in the center ofthe
field.
In the graphCp = f (x,zc), the wave front moved in the cen-tral
part of the field and almost disappeared, but the slopeheight
increased, causing a decrease in the inclination. Thetrend of
decrease inCp with the enlargement of the first sec-tions
continued.
In Fig. 10a and b, the distributionsC = f (x, zc) andCp
= f (x, zc) are shown in time = 3600 s, which is closer tothe
stationary state. All steps are already formed, with theheights
approximately corresponding to the method of idealstages, but with
concentration spatial distributions, where areobserved: smooth in
section bottoms, existence of maximumin last section, etc. The
plateau observed in time = 975 scompletely disappeared. The
distributionCp = f (x, zc) estab-lished only a monotonic
concentration gradient. However,according to the ideal stages
method, the concentrationsCp
should present steps between sections that do not correspondto
the distributionCp of actual extractors.
The simulation was performed even = 12600 s. But, dur-ing the
interval = 3600 s/12600 s, distributionsC= f (x,zc)andCp = f (x,
zc) practically did not change, which indicatestof the last steps
increasing; he achievement of the stationary state.
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590 G.C. Thomas et al. / Chemical Engineering and Processing 44
(2005) 581592
Fig. 10. Extraction field of (a) bulk phase (3600 s) and (b)
pore phase(3600 s).
5. Conclusion
In this work, a new model was developed for counter-current
crossed flows that are present in industrial extrac-tors of the
Rotocell type. The difference between the tradi-tional ideal-stages
method and the proposed model is a two-dimensional, transient and
considers the main phenomenainvolved in the extractor: mass
transfer between the bulk andpore phases, oil diffusion through
bulk phase, existence oftrays and the influence of drainage and
loading zones in itsoperational characteristics. The new model is
sensitive to theflake properties, the extractor operational
parameters and thedimensions of the sections. It is included
sub-models for:the extraction field, trays, drainage and loading.
These sub-models were transformed in form of ANN that could
allowwith simplicity the use of two time scales (continuous and
dis-crete), accomplish connections training and apply the modelto
the design and control of the extractor. The training of thenet was
accomplished by mass transfer connections in the ex-traction field
between the pore and bulk phases, by adjustingthe area of contact
(ap).
The developed code could solve cases with up to 50,000ODE (the
number of ODE was determined by the parametersn andp of the
extraction field discretization). The algorithmwas stable, without
presenting oscillations with the mesh res-o thei con-
dition could be satisfied. Comparison with experimental dataand
species conservation law (oil) showed a satisfactory ac-curacy of
the solution. Another confirmation was achievedthrough the
simulation of different initial distributions of theconcentrationsC
andCp in extraction field, obtaining theexpected single stationary
state.
The numerical simulations revealed several interesting ef-fects
that usually occur with the application of new, moredetailed
models. Among these effects, the following can bementioned: the
waves of concentrations passing throughthe sections, the formation
of steps, the appearance and dis-placement of fronts with
subsequent formation of slopes, for-mation and establishment of the
maximum concentration, etc.
Acknowledgements
The authors thank CNPq for the financial support
(No.470458/2001-1), and the company Coimbra Clayton (CruzAlta-RS,
Brazil) for the permission to use the experimentaldata.
Appendix A. Nomenclature
Aa in the
C di-
C (di-
C se
C ion
C
C for
C ad-
C -
C ec-
C en-
C at
C at
C nelution. However, a careful choice of the cell size and
ofntegration time step was necessary so that the Courantsv miscela
wagon transverse area (m2)p contact area between the pore and bulk
phases
raw material volume unit (m1)oil volumetric concentration in the
bulk phase (mensionless)
p oil volumetric concentration in the pore phasemensionless)
e initial oil volumetric concentration in the solid
pha(dimensionless)
in oil concentration in the solvent in the first sectentrance
(dimensionless)
j oil volumetric concentration in the miscela forjthcolumn
(dimensionless)
pj oil volumetric concentration in the pore phase
jth column (dimensionless)pin oil volumetric concentration in
the pore phase lo
ing zone (dimensionless)m oil volumetric concentration in themth
tray (dimen
sionless)D oil volumetric concentration in the drainage coll
tor (dimensionless)N volumetric concentration in the solid phase
(dim
sionless)u oil final volumetric concentration in the miscela
extractor outlet (dimensionless)Nin oil volumetric concentration
in the solid phase
loading zone (dimensionless)hein oil initial volumetric
concentration in the hexa
(dimensionless)
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G.C. Thomas et al. / Chemical Engineering and Processing 44
(2005) 581592 591
Cij activation function for N11(i, j)th neuron, concen-tration
in the bulk phase (dimensionless)
Cpij activation function for N12(i, j)th neuron, concen-
tration in the pore phase (dimensionless)dp conditional diameter
of expanded flakes (m)DAB diffusion coefficient (m2/s)EDk (i, j)
discrete inlet in neuron(i, j) of kth type (dimension-
less)ECk (i, j) continuous inlet in neuron(i, j) of kth type
(dimen-
sionless)Ed mass equilibrium constant between the solid and
pore phases (dimensionless)Evd volumetric equilibrium constant
between the solid
and pore phases (dimensionless)ES dispersion coefficient
(m2/s)gN oil mass fraction in the solid phase (dimensionless)gp oil
mass fraction in the pore phase (dimensionless)h integration step
(s)kf mass transfer coefficient among the pore and bulk
phases (m/s)LS bed height (m)mS extractor number of sections
excluding the last one
(dimensionless)Mv initial mass of expanded flake in a wagon
(kg)MC number of vertical conditional columns in extraction
n di-
N kes
NP
P
p di-
QQ let
Q for
Q
Q
QQ tor
q (di-
qS -
S -
SuV
Vb tray volume in the percolation section (m3)Vv wagon volume
(m3)VD volume for collection of drained miscela (m3)x bed
horizontal coordinate (m); bed horizontal con-
ditional coordinate for three-dimensional plots
(di-mensionless)
XR medium width of a wagon (m)z bed vertical coordinate (m)zc
bed vertical conditional coordinate for three-
dimensional plots (dimensionless)f error of calculation
(dimensionless)b raw material external porosity, bulk phase
(dimen-
sionless)m part of pore phase that is occupied by miscela
with
concentrationCmS+1 in loading zone (dimension-less)
p raw material internal porosity, pore phase
(dimen-sionless)
miscela viscosity (kg/(ms))he hexane density (kg/m3) miscela
density (kg/m3)ol oil density (kg/m3)s solid phase density (kg/m3)
current time (s)t batch period (s) (s)
SijmDiov
SNp
R
UA,
Uti-
on,cond
ex-996)
ign,field (dimensionless)number of horizontal layers in
extraction field (mensionless)
v oil initial mass concentration in the expanded
fla(dimensionless)
k symbol of thekth neuron type (dimensionless)tol theoretical
oil losses (dimensionless)exol experimental oil losses
(dimensionless)
number of wagon vertical (conditional) columns (mensionless)
D miscela volumetric drained flow (m3/s)S miscela volumetric
flow in the extractor out
(m3/s)Bol oil volumetric flow among pore and bulk phases
volume unit (s-1)pol oil volumetric losses in the pore phase
(m
3/s)Nol oil volumetric losses in the solid phase (m
3/s)
v miscela volumetric flow in the loading zone (m3/s)T miscela
total volumetric flow through extrac
(m3/s)number of instantaneous column
displacementsmensionless)
s hexane volumetric flow in the extractor (m3/s);Dk (i, j)
discrete outlet in neuron(i, j) of kth type (dimen
sionless)Ck (i, j) continuous outlet in neuron(i, j) of kth type
(dimen
sionless)k Courant number (dimensionless)
wagon speed (m/s)miscela vertical speed in the wagon (m/s)tv
wagon time passage in the percolation sectionx column width (m)z=
LS/n width of horizontal layer (m)
ubscriptsnumber of horizontal layernumber of columnnumber of
traydrainage
n initiall oil
vagon
uperscriptssolid phasepore phase
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Simulation of vegetable oil extraction in counter-current
crossed flows using the artificial neural
networkIntroductionMathematical modellingModel in terms of
artificial neural networks
Model and code verificationResults and
discussionConclusionAcknowledgementsNomenclatureReferences