Corymbia citriodora acclimatized in Congo was on an average 4% oil content and belongs to the citronellal chemotype (60% - 80%) [3] [5] . The pilot extraction was carried out at the Center of Valorization of Non-Timber Forest Products (CVPFNL) on raw plant material harvested on the Centre’s plantations in Pointe Noire.

50 kg of leaves and 100 litres of water were introduced into a 300-litre distiller fitted with a grid to separate the water from the plant matter. This first trial was repeated 2 times. The third trial involved 16 kg of leaves and 30 litres of water. The distillate was collected separately in different flasks at 15, 30, 45, 60, 90, 120, 180 minutes. Let m₁ be the mass of plant material on dried matter basis (db) and m₂ the quantity of essential oil collected at time t, the extraction yield is given by:

Y_t(%) = (m₂/m₁)100 (1)

In all cases, the extractions were carried out in a locally built distiller, at atmospheric pressure with water in the steam and liquid states (steam-hydrodistillation).

Different models were used in the literature to simulate essential oil extraction by hydrodistillation; two of these, used in this study were previously presented [10] - [12] .

The first-order diffusional model [13] - [15] and the Peleg model [16] through their simple graphical resolution respond well to the context of the study, namely extraction in rural areas at small scale using atmospheric pressure hydrodistillation. Table 1 summarizes the mathematical equations and the meaning of the terms used in this study.

Statistics and graphs were carried out on Excel 2019 software.

Table 2 reports the extraction data using a rural distiller. Experiments 1 (run 1) and 2 (run 2) were carried out with 50 kg of plant raw material and experiment 3 (run 3) with 16 kg. The first two experiments relating to the extraction of 50 kg of leaves lead to different yields (1.08% et 1.78%); thus confirming the heterogeneity of used raw material. Experiment 3 with a filling rate 3 times lower (16 kg) leads to the highest yield of 3 extractions (1.91%). On the other hand, examination of the curves Y_t/Y_∞ = f(t) ( Figure 1 ) which represents the fraction of oil extracted as a function of time leads to three superimposable curves and corresponding to an extraction in two steps with different durations. They are identical to those obtained previously in the laboratory scale [10] .

In first approximation, Y_∞ was substantially equal to Y₁₈₀, taking into account the asymptotic ending of the extraction.

[17] hypothesis considers the first step of the process as linear and the second, curvilinear:

Y_t/Y_∞ = (k₁/Y_∞)t + (1 − exp(−kt)) (2)

In Figure 2 , the break is around 45 min of the distillation time. The linear part was noted:

Y_t/Y_∞ = (k₁/Y_∞)t (3)

with a slope (k₁/Y_∞) leading to k₁: the rate constant of the fast washing step.

The initial (0 < t < 45 min) straight line equation: Y_t/Y_∞ = 0.024x + 0.0033 (R² = 0.9998) leads to following value of k₁ ( Figure 2 )

k₁/Y_∞ = 0.024

k₁ = 0.024Y_∞ = 0.024 × 1.08 = 0.026 min⁻¹

[18] adopts the symmetric hypothesis and considers the washing step as curvilinear and the diffusion step as linear ( Figure 3 ; 45 min < t < 180 min)

Y_t/Y_∞ = b + kt (4)

with b as the characteristic parameter of the first stage and corresponding to the fraction of the oil extracted during this stage; this is the parameter f of [13] .

Table 3 summarizes the information for the two steps of the pilot-scale extraction of essential oil from the leaves of Corymbia citriodora.

Table 3 shows that: 1) the kinetic rate constant of the washing step is on average 0.0233 ± 0.0006 min⁻¹ and that of the diffusion step, 0.0021 ± 0.0002 min⁻¹, leading to an average rate ratio of 11 in favor of the washing step; 2) the fraction of extracted essential oil via the washing step is 74% on average.

* [17] ; ** [18] , ***R: k_washing/k_diffusion; EO: Essential oil.

Finally, despite the heterogeneity of raw material and filling ratio of the distiller, the extraction takes place according to the same mechanism for the 3 experiments.

The two-steps (two-sites) diffusional model (broken and intact cells) of [13] postulates that the extraction yield can be described by the expression:

q_t/q_∞ = fexp (−k₁t) + (1 − f)exp(−k₂t) (5)

with f, the oil fraction extracted in the washing step.

When the extraction is done without a washing step, i.e. f = 0 [15] , this expression is reduced to:

q_t/q_∞ = 1 − exp(−kt) (6)

leads to a linear form:

ln(1/(1 − y)) = kt (7)

with

y = q_t/q_∞ = Y_t/Y_∞ (8)

The validation of the model can therefore be done graphically by this last equation.

Table 4 gathers the data necessary for the validation of the two models tested.

The data in Table 4 have enabled the first-order diffusional model to be validated by the line ln(1/(1 - y)) = kt ( Figure 4 ).

The curve ln[1/(1 − y)], a straight line with a slope = 0.0308, leads to a kinetic rate constant of essential oil extraction by steam-hydrodistillation: k = 0.0308 min⁻¹ and t_1/2 = 0.69/k = 22.62 min ( Figure 4 ). The fraction of essential oil released by washing step is 74%, accounts for the low duration ratio of the two extraction steps (R = 11).

The pseudo first order kinetic constant obtained is within the same variation range as that observed by [19] for Cymbopogon citratus (0.0286 - 0.0411 min⁻¹) using the line log(q₀ − q_t) = f(t), with q the extraction yield.

Figure 5 represents the validation lines of the Peleg model. The ordinate at the origin lead to the kinetic rate constant of Peleg (order 2), the slope and the Peleg constant of extraction capacity.

The Peleg model which considers the extraction as a desorption of a metabolite from a plant matrix postulates a hyperbolic evolution of the process given by following equation:

q_t = q₀ + t/(k₁ + K₂t) (9)

which leads to the following linear form:

t/q_t = k₁ + K₂t (10)

Here, it takes following form:

t/Y_t = k₁ + K₂t (11)

The results obtained on Run 1; for example, lead to the following equation for the overall duration of the experiment ( Figure 5 ):

t/Y_t = 0.8215t + 17.346 (R² = 0.9931)

From this equation we deduce the extraction capacity:

K₂ = 0.8215%⁻¹

We can finally access the kinetic rate constant of extraction (order 1):

k = K₂/k₁ = 0.8215/17.346 = 0.04736 min⁻¹

This value is of the same order of magnitude as that obtained above with the diffusional model which is 0.0308 min⁻¹.

In addition, we can get from K₂, the quantity of essential oil extracted at equilibrium, Y_∞ (end of extraction):

Y_∞ = 1/K₂ = 1/0.8215 = 1.22%

This maximum value of the essential oil extraction yield during experiment 1 is consistent with the value of 1.08% accepted as a first approximation and which corresponded to 180 min of extraction time, taking into account the asymptotic end of the process. This validates a posteriori the approximate method for calculating the fraction of recovered essential oil as a function of time Y_t/Y_∞.

Table 5 groups the parameters of the Peleg model obtained during these 3 experiments.

This table shows that 1) the second-order kinetic rate constant k₁ varies from 10.369 to 17.346 min%⁻¹ with an average of 13.3 ± 3.6 min%⁻¹ and the extraction capacity constant K₂ varies from 0.4547% at 0.8215% with an average of 0.6% ± 0.2%; which leads to a first-order extraction kinetic constant k = 0.0474 ± 0.002 min⁻¹ and a maximum extraction yield Y_∞ = 1.8% ± 0.5%, on average.