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:kriukov@admijui.unijui.tche.br (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

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

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.

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).

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

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)

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

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

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.

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)

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