Simulation of the Essential oil extraction kinetics of Xylopia aethiopica fruits from Congo Brazzaville. Fick diffusion, Peleg sorption and Michaelis-Menton enzymatic models

 

Jean Bruno Bassiloua^1,2, Thomas Silou^1,2, Hubert Makomo¹

¹Ph.D. Program (T2A) Food Chemistry and Technology, Faculty of Sciences and Techniques (UMNG)

BP: 69 Brazzaville, Congo.

²Higher School of Technology “Les Cataractes” (EPrES) BP: 389 Brazzaville, Congo.

*Corresponding Author E-mail: thsilou@yahoo.fr

 

 

INTRODUCTION:

Xylopia aethiopica (Dunal) A. Rich is a very important multi-use tree in village communities in Africa. It is an excellent quality firewood. Its fruit provides vegetable oil, essential oils and various other metabolites with food, medicinal and cosmetic uses^1-11. In its program to fight climate change, the Congo-Brazzaville has selected Xylopia aethiopica for the reforestation of the coastal savannahs of Pointe Noire and the "interland" plateau. To prevent its valorization by the extracted products from its biomass we have undertaken a systematic refining work with successively the desorption of water (drying), the extraction of vegetable oils and the extraction of essential oils.

 

In a near future other metabolites will complete this list, namely: polyphenols because of their antioxidant properties. All these operations can be modeled using the same basic scheme which is the extraction of a metabolite from a solid plant matrix supported by the So and Macdonald phenomenological approach¹². After preliminary studies carried out on the fruit drying and essential oil extraction^2,13, the present work aims to evaluate the explanatory and therefore predictive power of the main models met in the literature for the essential oil extraction: first and second kinetic models^14-19, Peleg sorption model²⁰, Langmuir gas adsorption isotherm model²¹ and Michaelis-Menton enzymatic model also called Monod model²².

 

MATERIAL AND METHODS:

1. Plant material:

The Xylopia aethiopica fruits, coming from an experimental plantation in Congo-Brazzaville, were harvested at maturity and shade-dried for 2 weeks (25-30°C) according to local practices.

2. Determination of dry matter:

A portion of m₁ g was oven-dried at 105°C to a constant mass: m₂ g, the dry matter mass (DM).

 

3. Extraction kinetics:

A portion of 300 g of dried fruits (m₁, dry basis-db-) were placed in a 500 mL round bottomed flask and boiled. The distillate is recovered in different distillation times : 15, 30, 45, 60, 90, 120 and 180 minutes. For each fraction, the organic phase was separated from the aqueous phase with diethyl ether and dried over sodium sulphate. The essential oil was recovered after evaporation of the solvent (m₂) and extraction yield is given by:

Y(%)db = (m₂/m₁)100

 

RESULTS AND DISCUSSION:

1. Extraction curve characterization:

The essential oils of Xylopia aethiopica fruits (3 trees), extracted by hydrodistillation, lead to the data gathered in Table 1 and to curves shown in Figure 1. These lasts have the general shape of extraction curves of metabolites from plant matrices, as suggested by Peleg²⁰ with an hyperbolic variation or by Chan et al.²³ with an asymptotic variation. These curves highlight a two step mechanism: one fast and the other slow. They can therefore be considered as evidence of a two-step extraction mechanism, involving extraction on two sites : broken and intact cells^{11, 18, 19}. The first and second order kinetic laws were used to test the validity of the Milojevic-Sovova and Peleg-Bucic models.

 

Table 1: Yield (%) of essential oil extraction of Xylopia aethiopica from Congo-Brazzaville (3 samples from 3 different trees)

 

Figure 1: Essential oil extraction curves of Xylopia aethiopica

The hyperbolic Michaelis-Menton model, reported in the literature as relevant to the extraction of essential oils and their constituents was also tested^24-27.

 

Xavier et al.²⁸ assums a two step curve: the first step corresponding to the initial time is linear and the second step controlled by the intra cell diffusion is curvilinear:

 

Y_t/Y_∞ = (K₁/Y_∞)(1/t) + (1- exp(-K₂t))

 

With Y_t and Y_∞ = the extraction yields at times t and t_∞, K₁ and K₂ respectively of the kinetic constants of steps 1 and 2. (Figure 2)

 

The extraction rate constant at the beginning of the process is equal to the slope of the quasi-linear initial portion of Y_t = f(t) : 0.1602 % min^-1 (Figure 2).

 

Stanojevic et al.²⁹ adopted the opposite assumption in which a linear portion of the curve is in the end of the process preceded by a curvilinear initial portion. It leads to a slope of 7. 10^-4% min^-1(curve 3), versus 0.1602% min^-1 for the first step; with a rate ratio : first step/second step = 10⁵.

 

Figure 2: Different steps of Xylopia aethiopica essential oil extraction

 

It is possible to evaluate the importance of the fast step using the ordinate at the origin of the end straight line of the process. The first step leads to a yield of 3.558 (ordinate at the origin, figure 3) versus a yield of 3.683 % for the total process; a percentage of 97 % (Table 1, sample 3).

 

Almost all of the extraction is carried out during the quick step at the first half hour of the process.

 

2. Diffusional Model Test (order 1)

Table 2 gathered the data needed to test the different models studied in this work.

 

Table 2: Data used for 3 model validation: ln[1/(1-y_t)] = f(t), 1/Y_t = f(1/t) and t/Y_t = f(t)

 

Figure 3 shows that the equation ln1/(1/(1-y) =f(t) lead to straight lines with good coefficients of determination (R²: 0.8141-0.9702); the experimental data validate thus the first order diffusion model for the extraction of the Xylopia aethiopica essential oil.

 

Figure 3: Validation straight lines of first order diffusion model (Milojevic)

 

Table 3: Main parameters from the first order diffusion model (Xylopia aethiopica)

The ordinate at the origin for the 3 samples studied suggest the existence of another step in addition to the intra cell diffusion limiting step and their values close to 0 reflects the very high rate of this step. Table 3 summarizes the main parameters from this model for the 3 samples. The extraction kinetic constant (order 1) deduced from the slopes of the validation straight lines varies from 0.0148 to 0.0649 min^-1 with an average t_1/2 = 0.069/0.0376 = 1.84 min which makes it possible to estimate the extraction end either at 18.4 min (10 t_1/2) or at 36.8 min (20 t_1/2). Any additional extraction time does not allow a significant gain on the yield of the extraction.

 

3. Peleg model Test (order 2)

For this model the variation of the extraction yield as a function of the extraction time is:

Y_t = Y₀ ± t/(k₁ + K₂t)

which gives after linearization:

t/Y_t= k₁+ K₂t

 

The curves t/Yt = f(t) in Figure 4 are straight lines with very good coefficients of determination (R²>0.99). The experimental results validate the second order kinetic model.

 

One can therefore graphically deduce the parameter values of the model : k₁, the Peleg second order kinetic constant and K₂, the Peleg extraction capacity constant which is related to Y_∞, the maximum yield of the extraction. It can be seen that k₁ vary from 1.7602 to 2.7742 min %^-1 and K₂, from 0.1963 to 0.2602 %^-1. From these values we deduce the first order extraction constant: k = K₂ /k₁ = 0.086 - 0.148 min^-1 and the maximum extraction yield Y_∞ = 1/K₂ = 3.84- 5.09 %, (Table 4).

 

Figure 4: Validation straight lines of Peleg model

 

 

Table 4: Main parameters from the second order kinetic model (Xylopia aethiopica)

 

 

4. Michaelis-Menton model Test:

The Michaelis-Menton model, also called the Monod model, has its origin in the basic expression of enzymatic kinetics that is adapted to the metabolite extraction from a plant matrix²²:

Y_t = Y_max (t/K_m+t)

1/Y_t =(K_m/Y_max) (1/t) + 1/Y_max

These expressions have been generalized in simulation methods using nonlinear regression ^24-27:

Y = [K₁X/(K₂ + X)]+ ε

1/Y_t = (b/Y_∞)(1/t) + 1/Y_∞

 

The straight lines in Figure 5 validate the Michaelis-Menton model and lead to Y_∞ = 3.78 – 5.04 %; and at b/Y_∞ = 2.2864 -2.7352 min%^-1. These results are of the same order of magnitude as those obtained by Mejri et al. [22] for the Ruta chalepensis L. extraction essential oil with Y_max = 5.88- 16.66 mL/100g and b/Y_max = 7.29- 13, 34 min %^-1.

 

Figure 5 : Validation straight lines of Michaelis-Menton model

 

Babu et al.²¹ obtain the same equations starting from the function of the adsorption isotherms of Langmuir gases:

y =m_t/∑m_t

y = Y_∞.t/( b+t)

1/y = (b/Y_∞) (1/t) + 1/Y_∞.

 

with m_t, the mass of essential oil collected at time t; ∑m_t, the cumulative mass of the essential oil collected for the total extraction; Y_∞, the yield of the extraction at t_∞.

 

These authors, who thus define the Langmuir adsorption model, find values compatible with ours for the extraction of Eucalyptus cinera essential oil.

 

Y_∞= 2.86 – 3.45%

b/Y_∞= 20.36-25.51 min^-1

 

DISCUSSION:

Whether diffusional or sorption, all these models are based on the So and Macdonald phenomeological approach¹², built on the Patricelli et al. works³¹. These authors consider the metabolite to be extracted as a macro-compound that can be subject to the laws of formal kinetics with the extraction yield assimilated to concentration and the extraction rate, to the progress of the process. The extraction takes place in two steps on two sites: the cells broken by the pre-extraction treatments and those that remain intact. The first fast, step, related to the washing of the metabolite located on the surface from the broken cells; it is called washing step. The second step takes into account the metabolite diffusion from the solid to the liquid; it is the diffusion step, governed by Fick's second law. This approach can explain the extraction curve shape: asymptotic, according to some authors or hyperbolic, as in the Peleg and Michelis-Menton models. To be generally relevant, the explanation of the extraction of essential oils from Xylopia aethiopica must synthesize the hypotheses of these two models, namely: diffusion of the essential oil (Milojevic-Sovova) through desorption pores (Peleg). Each of the models providing a part of the explanation. The extraction curve already provides a significant amount of information by combining the different approximations of these two models. For the extraction of the essential oil of Xylopia aethiopica, it allows (i) to estimate the relative importance of each step; more than 90 % of oil is extracted the first 30 minutes of 3 hours total extraction with a rate about 10⁵ greater the diffusion step rate. (ii) the initial rate of the process measured according to the approximation of Xavier et al.²⁸ equal to 0.1602 % min^-1 and the process end rate, according to the approximation of Stanojevic et al.²⁹ equal to 7.10^-4 % min^-1. The 3 models provide additional informations on the process details: (i) Milojevic's kinetic model (order 1) lead to the global extraction constant rate (k = 0.0148-0.0649 min^-1) and to the extraction end time: 18 minutes (10t_1/2) or 36 minutes (20 t_1/2). (ii) The Peleg model leads to a hydrodistillation constant k= K₂/k₁ = 0.086-0.148 min^-1 and to the maximum extraction capacity Y_∞ = 1/K₂ = 3.84-5.09 %. (iii) The Monod model (Michaelis-Menton) gives an evaluation of Y_∞ = 3.78 – 5.04 % very close to that obtained in the Peleg model (3.84- 5.09 %) and is consistent with the experimental values (3.7-4.6 %, after 120 min of extraction time, Table 1). The cross-referencing of the results from the different models enriches the explanation proposed for the extraction of the essential oil of Xylopia aethiopica and finally allows to deep the predictions on the process.

 

CONCLUSION:

Three models were tested for the explanation of Xylopia aethiopica essential oil extraction. Experimental data fitted the three models. Each model allows a part of the total information and different parameters of studied models lead to concordant informations. The extraction involves in two steps according to the phenomenological approach. The first rapid step (k= 0.1602 % min^-1) corresponds to the extraction of free essential oil from broken cells by washing and represents more than 90 % of total extracted metabolite. The second, which is lower (k= 7.10^-4 % min^-1) corresponds to extraction of essential oil from intact cells, by diffusion. The total hydrodistilation rates were k= 0.0148 - 0.0649 min^-1 (Diffusional model) and k= 0.086-0.148 min^-1 (Peleg model).

 

The maximum extraction yield 3.7-5.1 % (Peleg model and Michaelis-Menton models) is consistent with the experimental values (3.7-4.6 %, after 120 min of extraction time).

 

CONFLICT OF INTEREST:

The authors declare no conflict of interest.

 

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Received on 12.10.2021                    Modified on 24.11.2021

Accepted on 28.12.2021                   ©AJRC All right reserved