Optimization and Extrapolation to Pilot Scale of Essential Oil Extraction from Pelargonium Graveolens, by Steam Distillation

Essential oil extraction of Pelargonium graveolens that uses the extraction by steam distillation principle was studied at two scales: Laboratory scale and pilot scale. Firstly, a simple mathematical model was considered in order to optimize the effect of parameters that can influence the yield at the initial stage. This mathematical model is in the form of first polynomial degree with 3 variables for which the coefficient evaluation is done by multilinear regression. In order to reduce errors between calculated and experimental values, an optimal design was realized then followed by corresponding experiments to the plan. The complete factorial design 23 was used. The obtained model is as shown: Y = 2,156 - 0,183X1+0,060X2 - 0,038X3 - 0,012X1X2 +0,035X1X3 +0,037X2X3 Plant mass, extraction time and condensation output displayed interesting effect on extraction yield. Secondly, an empiric model was considered to extrapolate this result at different scales. The state of the gaseous fluid inside the conducting tube was taken into account. In order to get fluids with similar characteristics, the value of the charge loss was conserved within the two scales. Actually, the charge loss determines the balance state of the fluids in the tube. Then, this was combined with a kinetic model of first order, a law concordant well between experimental and calculated results was found.


Introduction
The geranium or Pelargonium graveolens is an aromatic plant highly used in cosmetics, in sanitary products and also in food preparation. The exploitation of natural products, like essential oils are privileged compared to synthetic products. The later being more toxic often causes inauspicious secondary effects. In addition, these chemical products are some times less efficient than natural products. In developing countries like Madagascar, problems of process optimization are often forgotten. This leads to relatively high cost price of the finished products while labor cost remains very low. In spite of the permanent increase in demand for essential oils, extraction yield is low. For geranium, this yield is about 1, 5‰ [1].
Few theoretical tools are currently available for studying scale change in the extraction process of essential oil that uses steam distillation principle.
A study on extraction yield improvement for Pelargonium graveolens essential oil using steam distillation and extrapolation of the results obtained from laboratory experiment to pilot scale. This yield noted Y is defined as: The first step of the work consists in representing this Y function by one simple mathematical equation of the first order based on different parameters that influence this yield. These different variables were taken from in the literature. Experiments were planed according to a complete factorial plan 2 3. In order to insure the quality of the obtained oil, a quality control by Gazeous Phase Chromatography [GPC] was undertaken and was compared with reference samples.
The second step allowed the extrapolation to the pilot scale by considering empirical appropriate equations. Actually, the steam passing through the tube is very important and defines the equilibrium state of the steam, consequently, the extraction yield [2].
We think that the quantity of introduced plant presents some importance on the extraction yield. In fact, when the quantity of introduced plant is too high, the steam at the bottom of the tank has difficulty to go up the conducting tube. This leads to a reduction of the extraction yield and can cause burning. A too low mass of plant is not recommended because the quantity of oil will be too small and this will influence profitability compared to the quantity of energy spent.
In the case of Madagascar, labor cost is reasonable. Local companies cannot afford sophisticated machines. It is then difficult to obtain the same quantity of plant materials in a repetitive way. Therefore we have maintained the division factor similar to the industrial plant material division.
Therefore, it is not enough to calculate the yield, because the quality of the obtained oil is not known. To solve this doubt, the quality control of the oil was done using GPC.
The second step allows associating the mathematical model with empirical equations in order to extrapolate the results to the pilot scale. The steam contained in the conducting tube can have some charge loss. A too low value of the later leads to an even lower extraction yield. A greater charge loss can produce a partial decomposition of the main product and leads to burning or an essential oil of mediocre quality [2].

First step: Mathematical treatment
We will represent the extraction yield Y by a simple mathematical equation in order to show the effect of the different factors on the response function. The factorial plan at 2 levels noted 2 k (K= number of variables) suits well our expectation in solving the problem.
The principle is to give to each factor two reduced centered levels noted -1 and +1. The lower level for each factor corresponds to -1 and the higher level to +1. In order to study the 3 variables (K=3), the complete factorial design presents 2 3 = 8 lines and 3 columns for each factor.

The result is the following design
Each line corresponds to an experimental test. After the experiment realization imposed by this plan, the response function Y can be defined by a simple mathematical equation of this form: The polynomial coefficients have a simple meaning: a 0 gives the response function average, and indicates the effect of each parameter and a ij shows the interaction effects [3].
The coefficient estimation is done by multilinear regression. The principle is as following: Let's consider the model (2) ..... .... Y a a X a X a X X a X X = + = + + + + We have realized n=2 3 tests and the results were respectively y 1 , y 2 , y 3 , y 4 …., y n . The experimental matrix X of n x (k+1) is: The x ij are the values taken by the factor X 1 during the i th experiment.
The estimation Â of A is obtained through the resolution of the equation (6): • The least square constraint : E t E must be minimal So, the resolution of the two equations gives (6):

Second step: Laboratory result extrapolation to the pilot scale
In order to preview the system behavior beyond the explored field, that is the pilot scale, we based our study on the similitude principle for which, [4] the relation between one or several parameters are the same for the two scales in order to reproduce the obtained results within a greater scale.
The principle is as following: The steam coming out of the distillation balloon to the refrigerator passes through a conducting tube. In this tube, the steam might have some charge loss.
A too high charge loss may lead to partial damage of the main product and gives bad quality oil; a too low value leads to a premature condensation of the steam and consequently a lower extraction yield [5].
Therefore, to have the same fluid characteristics all the way through the trajectory in the conducting tube, we kept the value of the charge loss constant in the two scales; The empirical expression of this charge loss "regular charge loss" is given by the equation: If the steam encounters obstacles, it will have a particular charge loss which will add up to the regular charge loss. Its expression is given by (7): The charge loss was determined by using the software MATLAB-SIMULINK [6]. Matlab helps to make simple and quick simulation and it permits to solve the problem efficiently.
During the calculation step, we have marked the fluids in the laboratory with * to keep the charge loss value constant and we get [2]: ∆P* = ∆P In our laboratory experiment we used a 2 liter balloon. The geometrical similitude allows keeping the relation plant mass (m p )/ alembic volume (V alembic ) constant in the two scales. Thus we have: This expression (8) allows calculating the introduced plant mass according to the alembic capacity that is used in the pilot unit in relation with the plant quantity put in the 2 liter balloon.
We also know that the number of the Reynolds's value (R e ) determines the type of flow. When the R e value is inferior to 2000, the flow is laminar [7].
This type of flow corresponds to our case. The Reynolds's number [7] is expressed by the relation (10): . .
The charge loss coefficient for a laminar flow is given as follow: As for the condensation output extrapolation, we used equations found in the case of an agitated reactor with discontinued run in liquid phases. In fact, this extraction method displays an analogy with that type of reactor. With the aid of some hypotheses, the characteristic speed equation is given by [8][9]: By introducing the rate of condensation, one gets: The resting time to a given progress is: V being the reactor volume, N 0 the mole number at time t.
The hypotheses are: Heat repartition is considered homogenous in the two scales. The speed of the fluid remains constant during the experiment.
The reaction speed is described by the equation analogous to Van't Hoof's and it expression is as follow [9]: [X] Represents the oil concentration at time t and p the reaction order. This concentration is the quantity of obtained oil per water volume unit distilling the oil.
-We consider that the flow is continual, that means that the elementary fluid mass that flows between the tube walls is the same. In this case the mass output is given by the relation [7]: . . tan c. Condensation output: We think that this factor is interesting between 3 and 6 ml/mn. It will be noted X 3 . The condensation output determines the charge loss value. In fact, the charge loss is related to the square of the fluid speed.

Attribution of the variable levels
The experimental designs which are the translation of the reduced centered variables into real variables are given in table 2.

Experimental results
In order to estimate the experimental errors of the extraction yield, we realized five automatized repetitions in the center of the field, and the greatest difference compared to the experiment averages does not go over 3%. Each experiment imposed by the plan is repeated twice. The design used is a complete factorial design 2 3 (Table 3). It gives the model according to the equation (4) that represents the yield Y in relation with the different parameters: Where Y Is the yield directly expressed in ‰ and the parameters are the reduced centered coordinates between -1 and +1. Note that the levels -1 and +1 correspond respectively to some real lower and higher values of the parameters.

Statistical results a. Predicted coefficient -standard deviation: The MODDE
software of UMETRI AB Society was used for the calculation. The statistical study allowed to validate the model and to describe the parameter effects on the field (Table 4). Table 5 presents the statistical studies carried on to evaluate the regression significance.

c. Correlation matrix:
The correlation matrix is presented in the following table 6.

d. Individual significance of the coefficients:
The individual significance of the coefficients is presented in table 7.
e. Isoresponse curves: Considering the X 3 factor constant to -1 value and the 2 parameters X 1 and X 2 taken as variables. In these conditions the isoresponse curves take the form given in figure 2.

Study of the Y response function a. Statistical validation of the model:
The comparison of variance 1/F with F 0, 95, υ1, υ2 of SNEDECOR, reveals that the hypothesis of a biased is rejected. This means that we can conclude that the phenomenon does not present curvature [6].
The paragraph b representing the global signification of the model, explains that the regression is significant. This means that the effect of the parameters on the response is not negligible and that the model describes well the phenomenon [6].
The correlation matrix symmetry (Table 6) indicates that the factors are not correlated. Thus, the calculation of the multilinear progression is valid for presenting the phenomenon [6].

b. Interpretation display:
The relation (17) shows that the different parameter coefficients are not very high. This indicates that the parameter levels were well chosen because the optimum should be very near to the experimental field [3]. The average quantity of extracted oil is 2.156‰. This is higher than the yield observed in the literature.
The mass of introduced plant has a negative effect on the yield. This is expected: A more important quantity of plant material leads to a lower yield because the oil at the bottom of the container has difficulty to come up to the surface. The extraction time has a relatively low but significant positive impact. Actually, for an extraction of 300 g of plants under the same conditions as the experiments 1 and 5, the difference in oil weight extracted is about 67 g. Its cost is equal to the labor for 3 extraction operations.
Re -0,899 0,295 -0,184 -0,061 0,172 0,184 1  The isoresponse curves that the theoretical optimum is about 2.4 to 2.5 ‰ corresponding to the operating conditions of X 3 =-1, X 1 =-1 et X 2 = +1; which is not the experimental case. In fact, the no.2 experiment attracts particularly our attention. The extraction time at the -1 level, therefore of 3:30. The plant mass is high and the condensation rate is relatively low. Despite the low yield of 1.95 ‰, less energy is spent to collect a sufficient quantity of oil. We consider these operating conditions as optimal.
Therefore, it is no sufficient to obtain some oil and to be satisfied from the studies on the effects of the different parameters. The oil quality must be controlled and compared with the standard oil quality.

Quality control of the extracted oil
The sample no.2 will be identified with its chemical composition and its physic -chemical characters in order to insure its quality according to the AFNOR norms. The physical characteristics such as the organoleptic characteristics, the relative density and the refractory index, show that the norms were followed.
To identify the constituents of our sample, we used the GPC based on the given operation conditions. The obtained chromatogram was compared with a standard chromatogram in order to identify the oil constituents. The identification of the chromatogram picks allows finding about 95.75% of all the constituents. The oil is of good quality and the rhodinol content (citronellol + geraniol) of 44% indicates that the oil is of Bourbon type [1].

Extrapolation of the results to the pilot scale
Our objective was to establish some extrapolation rules for industrial unit designs and at the same time study the system behavior outside the laboratory field. The studied field corresponds to 350 and 1000 Liter capacity alembics.
The relation (8) gives the extrapolation law of the introduced plant mass depending on the alembic capacity. For a 350l alembic, this mass varies respectively between -1 and +1 levels from 31 kg to 73 kg. For a 1000 l alembic capacity it varies from 90.5 kg to 209.5 kg.
Extraction time is an intensive value and does not depend on the quantity of plant material. At a greater scale, this time remains between 3:30 h and 4:30 h.
The relations (12), (15) and (16) allow determining the condensation output. For the 350l alembic, the recommended output varies from 21 to 63 l/h and from 60 to 180 l/h for a 1000 l alembic.
In order to obtain the same fluid characteristics throughout its trajectory, the conducting tube should be sized.
The relations (5), (6), (7), (10), (11) allow to calculate the size of the tube and to know the value of the charge loss that should not be passed. For a conducting tube of 13 cm diameter, the conducting tube length should be 2, 30 m.
We have determined K c and p from relations (12), (15) and (17) between 3:30 h and 4:30 h times: Thus, the simulation of Pelargonium graveolens essential oil extraction was realized from the experiment n°4 at larger scale by associating two mathematical and kinetic models ( Figure 3).
We note that the difference between the calculated and experimental values is relatively low (about 2%). At the end of the extraction, one notices a slight deviation between the model and the experimental values. This confirms on one hand that we are very near the optimum because the yield is tending to stabilization, and on the other hand, the chemical reaction phenomenon is les dominant than at the beginning of the operation [9].
In spite of the optimization and sizing study process complexity, the association of mathematical and simple kinetic models has simplified the simulation of the extrapolation of the Pelargonium graveolens essential oil extraction by correctly choosing the parameters to be studied. These results reveals that the proposed models simulate well the essential oil extraction going from the laboratory phase to the pilot scale extrapolation.

Conclusion
This extraction technique is often used in Africa to extract these plants oils. The geometrical similitude and the kinetic model (5),(6), (10), (11), (12), (15) and (17) that we elaborated allow displaying the kinetic model efficacy when it is associated with simple mathematical model. In fact, the chemical reaction phenomenon is present during the extraction that uses the steam distillation. The conducting tube sizing is necessary during the extrapolation step. Former studies on material transfer model during essential oil extraction from coriander fruits confirm this thesis on the presence of the chemical reaction [8].
In addition, experimental studies allowed improving the yield at pilot scale and bringing an extrapolation theory of essential oil extraction that uses this steam distillation principle.
-Importance of the charge loss value that permits the sizing of the conducting tube, -Presence of the chemical reaction during the extraction, consequently, the speed general equation of the reactions allows extrapolating the condensation output.