HYBRID ARTIFICIAL NEURAL NETWORK APPLIEDTO MODELING SCFE OF BASIL AND ROSEMARY OILS

HYBRID ARTIFICIAL NEURAL NETWORK APPLIEDTO MODELING SCFE OF BASIL AND ROSEMARY OILS¹

Giane STUART², Ricardo MACHADO³, José V. de OLIVEIRA², ^*, Angela C. ULLER², Enrique L. LIMA²

SUMMARY

This work presents the results of a Hybrid Neural Network (HNN) technique as applied to modeling SCFE curves obtained from two Brazilian vegetable matrices. A series Hybrid Neural Network was employed to estimate the parameters of the phenomenological model. A small set of SCFE data of each vegetable was used to generate an extended data set, sufficient to train the network. Afterwards, other sets of experimental data, not used in the network training, were used to validate the present approach. The series HNN correlates well the experimental data and it is shown that the predictions accomplished with this technique may be promising for SCFE purposes.

Keywords: SCFE, Neural Networks, Modeling, Basil oil, Rosemary oil

RESUMO

REDES NEURAIS HÍBRIDAS APLICADAS À MODELAGEM DA EXTRAÇÃO SUPERCRÍTICA DE ÓLEO ESSENCIAL DE ALFAVACA E ALECRIM. Neste trabalho são apresentados os resultados obtidos na modelagem da extração supercrítica de óleo essencial de alfavaca e alecrim usando uma rede híbrida neuronal. Utilizou-se uma rede híbrida na configuração em série para estimar os parâmetros do modelo fenomenológico empregado para descrever o processo de extração, o modelo de Sovová. Um pequeno conjunto de dados experimentais, para cada matriz vegetal, foi usado para gerar um conjunto estendido de dados, suficiente para a etapa de treinamento da rede. A validação da presente proposta foi efetuada através da comparação entre os resultados preditos e aqueles obtidos experimentalmente que não constaram do processo de treinamento da rede. Demonstra-se que a rede híbrida neuronal correlaciona e prediz satisfatoriamente os dados experimentais, mostrando-se portanto promissora no campo da modelagem do processo de extração supercrítica.

Palavras-Chave: Redes Neuronais, modelagem, extração supercrítica, óleos essenciais

1 — INTRODUCTION

Recently, much attention has been paid to modeling SCFE of natural products from a variety of plants. Most models are based on a simplified phenomenological description of the process making use of severe assumptions [11]. Then, a couple of parameters are fitted using a set of experimental data and, generally, the obtained model is not capable of extrapolating experimental information with good accuracy, which is an undesirable feature from an engineering point of view. Some researchers have recently proposed the application of Artificial Neural Networks (ANNs) for modeling chemical engineering processes, especially those presenting high non-linear behavior [7,13].

An ANN is a structure composed of nonlinear processing elements called neurons. Since 1943, when the first computacional model of a neuron was proposed by McCullock and Pitts [6], the most adopted structure has been the so called BPN (Backpropagation Neural Network) or FANN (Feedforward Artificial Neural Network). Backpropagation networks have been thoroughly studied since the pioneer work by Romelhart and McClelland [6], and many applications in chemical engineering have been found. A detailed discussion about this topic can be found in the literature [5,10].

Despite ANNs present some advantages, like low computing time and prediction power, they often suffer from some drawbacks, such as inconsistency of the outputs (in "black box" ANNs) and the need of a reasonable set of experimental data, which is not always available.

In order to overcome the inconsistency problem, Hybrid Neural Networks have been proposed in the literature, since they ensure the physical meaning of the outputs by incorporating the process constraints and the knowledge of a physical model established a priori. In a parallel construction, the network estimates the prediction errors between process and physical model outputs, and in a series structure it estimates the parameters of the chosen model. Nevertheless, as in the case of black box networks, it is required an appreciable amount of experimental input-output data for training the HNNs.

Supercritical Fluid Extraction (SCFE) is an interesting field for the application of HNNs due primarily to the high sensibility of the model with regard to small changes of the process variables. In this work, a series HNN modeling using an extended data set and the model proposed by Sovová [12] is shown to be a good technique for correlating and predicting the extraction curves from SCFE of Brazilian Rosemary oil (Rosmarinus officianalis L.) and of Brazilian Basil oil (Ocimum basilicum L.) [2,3].

2 — MATERIALS AND METHODS

The experiments were performed in the laboratory-scale unit presented in Figure 1, which consists of a CO₂ reservoir, a small vessel maintained at low temperatures, two thermostatic baths, a metering pump (TSP constaMetric 3200), a 0.2 dm³ jacketed extraction vessel, an absolute pressure transducer (Smar, LD301) equipped with a portable programmer (Smar, HT 201) with a precision of ± 0.012 MPa, a collector vessel with a glass tube, a cold trap and a mass flow meter (Sierra, 821-1).

Typically, amounts of around 40g of rosemary and basil leaves, supplied by Duas Rodas Industry - Brazil, were introduced into the extraction vessel. Then, carbon dioxide (99.9% purity, White Martins) was delivered and put in contact with the vegetable inside the extractor for at least one hour. The micrometering valve was then opened for 30 minutes accounting for the mass of carbon dioxide by means of the flow meter. After that, the mass of extracted oil was weighed, the glass tube was connected to the equipment and this procedure was performed up to no significant mass was extracted or, as in some cases, the extraction period exceeded a preestablished limit. The experiments were accomplished isothermally at constant pressure. The variations of the solubilities and yields around the average values were about 2%.

FIGURE 1.
Schematic diagram of the SCFE apparatus.A- CO₂ reservoir; B- cooler; C,H- Thermostatic baths; D - high pressure pump E- extraction vessel; F- collector vessel with a glass tube; G- mass flow meter; I- absolute pressure transducer; J- electrical heater.

The values of all properties concerning the solid samples and solvent are shown in Table 1, along with the characteristic parameters of the bed under the conditions studied in this work. The solvent densities were estimated by the Angus [1] correlation.

TABLE 1.
Characteristic parameters employed in this work.

Run	Plant	T (K)	P (bar)	Particle size (Mesh)	rs (g/cm3)	e	u (cm/min)
1	rosemary	310.15	100	20-32	0.4896	0.5573	0.178
2	rosemary	310.15	120	20-32	0.4896	0.5573	0.137
3	rosemary	310.15	140	20-32	0.4896	0.5573	0.139
4	rosemary	310.15	160	20-32	0.4896	0.5573	0.135
5	rosemary	320.15	100	20-32	0.4896	0.5573	0.244
6	rosemary	320.15	120	20-32	0.4896	0.5573	0.160
7	rosemary	320.15	140	20-32	0.4896	0.5573	0.143
8	rosemary	320.15	160	20-32	0.4896	0.5573	0.147
9	basil	302.15	69.8	16-32	0.5864	0.7248	0.457
10	basil	302.15	69.8	32-48	0.7791	0.5413	0.398
11	basil	305.15	79.7	16-32	0.5864	0.7248	0.088
12	basil	305.15	79.7	32-48	0.7791	0.5413	0.124

3 — HYBRID ARTIFICIAL NEURAL NETWORK MODELING

We have adopted the phenomenological model proposed by Sovová [12] to represent the experimental extraction curves. A detailed derivation of this model has been presented in the literature [12]. After some simplifications, the material balances for an element of the bed are given by:

(1)

(2)

The boundary and initial conditions are, respectively:

y(h=0,t) = 0 (3)

x(h,t=0) = x_o(4)

According to Sovová [12], the J(x,y) term has two possible expressions:

, for x > x_k (5)

, for x £ x_k (6)

The extraction curves were then determined by the following equation:

(7)

We assumed that x_o was 1% and 2%, and x_k was 0.5% and 0.7%, for rosemary and basil leaves, respectively. The physical model used in this work requires the process inputs and the parameters k_fa_o and k_sa_o to construct an extraction curve and, of course, predictions can be accomplished but leading, in some cases, to poor results.

The use of the HNN approach to capture non-linear behavior and to serve as a model has been extensively researched by several workers [4,13]. As pointed out by Thompson and Kramer [13] two types of combination can be drawn: the process model in parallel to HNN and the model in series to HNN. As mentioned before, the first strategy only corrects model deviations while the second one estimates the parameters of the model. In this work we have adopted the series HNN structure, as presented schematically in Figure 2.

It can be observed from this figure that the neural network estimates the parameters of the model from operating conditions (input variables). Though this methodology has proven to be capable of modeling processes with a high non-linear behavior, its utilization is so far limited due to the need of a big set of experimental information to train the network.

FIGURE 2. Hybrid Neural Network structure.

Tsen et al. [14] have recently proposed a methodology to overcome this drawback by generating an extended set of experimental data enough for the network training. Basically, it assumes that a process model is available to capture the process trends, regardless its roughness.

Let m₁, m₂, .., m_M represent the M independent input variables, f the corresponding output variable, and f^e (m^e₁₁, m^e₂₁, ..), f^e (m^e₁₂, m^e₂₂, ..) and f^e (m^e_1N, m^e_2N, ..) the experimental data set. The expression for the extended data generation, f^a(m^a₁, m^a₂ , ..), where the m^a_i’s are inputs whose output is not known, is given by:

(8)

where N is the number of the actual experimental data and w_ik is a weighing factor which is inversely proportional to the distance between extended and actual experimental points, given by:

(9)

4 — RESULTS AND DISCUSSION

We now consider the use of a series HNN to represent the extraction curves from SCFE of Brazilian rosemary oil and basil oil. It was recently demonstrated [8] that for experimental data reasonably covering the operating region, data generation can be carried out by the following simplification of Eq. (8):

(10)

From Eqs. (9) and (10) and the experimental data presented in Table 1, a set of 600 extended data was generated for training the network. In the network training the runs 2, 5, 8 and 9, were not considered, being afterwards employed to validate the network training and to check the prediction power of the present proposal. For the structure shown in Figure 2, after some trials a neural network was built and trained with 3 layers, with 6 neurons in the input layer, 10 neurons in the hidden layer and 3 neurons in the output layer.

The "real" parameters k_fa_o and k_sa_o were estimated using the Marquardt [9] least squares numerical method based on the differences between experimental and calculated e(t) and are presented in Table 2. It is also presented in this table the parameters obtained from the neural network, which are in good agreement with the" real" ones. It is worth noticing at this point the values of the predicted HNN and "real" parameters for runs 2, 5, 8 and 9.

TABLE 2.
Parameters of the Sovová model.

	Least square fitting		HNN
Run	Kf ao (min-1)	Ks ao (min-1)	Kf ao (min-1)	ksao (min-1)
1	0.005919	0.000503	0.00667	0.000212
2	0.010570	0.002178	0.00961	0.000819
3	0.008383	0.002669	0.00821	0.001153
4	0.009230	0.000799	0.00935	0.000357
5	0.080000	0.040000	0.07988	0.012900
6	0.010000	0.000046	0.00614	0.0000538
7	0.057160	0.001282	0.00658	0.0005567
8	0.008162	0.003306	0.00933	0.001560
9	0.01244	0.1x10-9	0.00844	0.0000349
10	0.03770	0.0000496	0.03745	0.0000495
11	0.03070	0.0000894	0.03070	0.0000543
12	0.01800	0.0000295	0.01802	0.0000195

Table 3 shows the experimental and calculated solubilities along with the mean deviations for e(t) curves using the Sovová model and the HNN results. Concerning the extraction curves, it can be observed from this table that the series HNN correlates the experimental data with the same accuracy of Sovová’s model. Moreover, predictions are well accomplished by the series HNN, not only with regard to the e(t) curves but also considering experimental solubilities.

It should be noted from Table 3 that the predictions obtained for runs 2, 5, 8 and 9, with the HNN methodology are very close to those from correlated results of Sovová’s model, showing the prediction power of the present approach and then its importance in engineering applications.

In Figures 3, 4 and 5 the extraction curves predicted by the series HNN and correlated by the Sovová model are compared with experimental data. As expected, based on the parameters shown in Table 2, the series HNN is capable of well predicting experimental results. The poor prediction at run 9 might be explained in terms of experimental errors, the small set of experimental data and, possibly, because of the weakness of the process model.

TABLE 3.
Experimental and calculated solubilities and mean deviations from experimental e(t).

	yr (goil/gCO2)		e (t) (AAD%*)
Run	Experimental	HNN	Sovová model	HNN
1	0.00172	0.00173	7.75	9.66
2	0.00245	0.00223	10.34	12.22
3	0.00215	0.00204	6.59	12.3
4	0.00200	0.00199	4.70	7.42
5	0.00055	0.00055	10.29	10.40
6	0.00128	0.00138	9.66	8.44
7	0.00230	0.00219	9.29	12.25
8	0.00280	0.00247	15.64	16.83
9	0.00076	0.00068	18.48	21.78
10	0.00120	0.00132	22.00	24.00
11	0.00190	0.00187	39.63	39.50
12	0.00250	0.00235	18.20	18.59

*

FIGURE 3.
Comparison between fitted Sovová’s model (correlated) and HNN predictions for run 2, for Brazilian rosemary oil.

FIGURE 4.
Comparison between fitted Sovová’s model (correlated) and HNN predictions for run 8, for Brazilian rosemary oil.

FIGURE 5.
Comparison between fitted Sovová’s model (correlated) and HNN predictions for run 9, for Brazilian basil oil.

5 — CONCLUSIONS

In this work a series HNN was successfully applied for modeling extraction curves from SCFE Brazilian Rosemary oil and basil oil. An extended data set was generated by interpolation inside the experimental data set. The results obtained here show that the series HNN is able to reproduce, with good accuracy, the experimental data and also to represent the experimental trends of the extraction curves.

6 — NOMENCLATURE

a_o Specific interfacial area, cm^-1 e(t) Mass of extract relative to N H Height of bed, cm h Axial coordinate, cm J(x,y) Mass transfer rate, g.cm^-3.min^-1 k_f Solvent-phase mass transfer coefficient, cm. min^-1 k_s Solid-phase mass transfer coefficient, cm. min^-1 N Mass of the solute-free solid phase, g P Pressure, bar T Temperature, K t Time, min u Superficial velocity of solvent, cm.min^-1 x Solid phase concentration in solute-free basis y Solvent phase concentration in solute-free basis y_r Solubility, g oil.g CO₂^-1 e Void fraction r Solvent density, g.cm^-3 r _s Density of solid phase, g.cm^-3

Subscripts

k Easily accessible solute o Overall initial concentration

7 — REFERENCES

[1] ANGUS, S.; ARMSTRONG, B.; REUCK, K.M. International Thermodynamic Tables of the Fluid State: Carbon Dioxide, Ed. Oxford: Pergamon Press, 1976.

[2] COELHO, L.A.F.; OLIVEIRA, J.V.; D’ÁVILA, S.G.; VILEGAS, J.H.Y.; LANÇAS, F.M. Journal High Resol. Chromat., in press.

[3] COELHO, L.A.F.; STUART, G.; OLIVEIRA, J.V.; D’ÁVILA, S.G. Proceedings of the III Congresso I Fluidi Supercritici e le loro Applicazioni, 1995, 115-119.

[4] CUBILLOS, F.; ALVARES, P.; LIMA, E.L.; PINTO, J.C. Powder Technology, 1996, 87(2), 153-160.

[5] CUBILLOS, F. PhD Thesis. COPPE, Rio de Janeiro, 1995

[6] DE SOUZA Jr., M.B. PhD Thesis. COPPE, Rio de Janeiro, 1993.

[7] HUNT, K.J.; SBARBARO, D.; ZBIKOWSKI, R.; GAWTHROP, P.J. Automatica, 1992, 28(6),1083-1112.

[8] LIMA, E.L.; OLIVEIRA, J.V.; STUART, G.; MACHADO, R.A.F. Proceedings of the 4th International Symposium on Supercritical Fluids, 1997, 307-310.

[9] MARQUADT, D.W. J. Soc. Ind. Appl. Math. 1963, 11, 431.

[10] POLLARD, J.F.; BROUSSARD, M.R.; GARRISON, D.B.; SAN, K.Y. Computers Chem. Engng. 1992, 16(4), 253-270.

[11] REVERCHON, E. Journal Superc. Fluids, 1997, 10(1), 1-37.

[12] SOVOVÁ, H. Chem. Eng. Sci., 1994, 49(3), 409-414.

[13] THOMPSON, M.L.; KRAMER, M.A. AIChE J., 1994, 40(8), 1328-1340.

[14] TSEN, A.Y.-D.; JANG, S.S.; WONG, D.S.H.; JOSEPH, B. AIChE J., 1996, 42(2), 455-465.

Programa de Engenharia Química/COPPE/UFRJ, Cidade Universitária, Cx. Postal: 68502 CEP 21945-970, RJ

³

Departamento de Engenharia Química/CTC/UFSC, Campus Universitário, 88040-970, SC

^*

To whom correspondence should be addressed.

¹

Received for publication in 5/8/97. Acepted for publication in 8/12/97.

²

Publication Dates

• Publication in this collection
  17 Dec 1998
• Date of issue
  Dec 1997

History

• Accepted
  03 Dec 1997
• Received
  05 Aug 1997