Supercritical CO2 Extraction of Extracted Oil from Pistacia lentiscus L.: Mathematical Modeling, Economic Evaluation and Scale-Up

In this study, the extracted oil of Pistacia lentiscus L. the Tunis region was extracted using supercritical carbon dioxide (SC-CO2) extraction containing different major components in the oil such as α-pinene (32%) and terpinene-4-ol (13%). The investigation of the effect of different variables on the extraction yield with 5% level of confidence interval showed that the CO2 pressure was the main significant variable to influence the oil yield. In order to better understand the phenomena, three parameters were considered to adjust all parameters of broken and intact cell (BIC) model: grinding efficiency (G), the internal mass transfer parameter (kSa0), and the external mass transfer parameter (kfa0), which were estimated by experimental extraction curves to calculate the diffusion coefficient. From an economic point of view, we found out that the high cost of production of the extracted oil was due to the low mass of extracted oil obtained from this type of plant.

The essential oil can be extracted from specific plants by several extraction techniques: hydro-distillation [21], Soxhlet extraction [22] and supercritical carbon dioxide (SC-CO 2 ) extraction [23][24][25]. The major objective of the extraction process is to provide a more concentrated form of the desired material. Although the cost never compromises the quality, it can be a decisive factor in choosing an adequate process. However, the extraction effectiveness and the safety process must be priorities. The extract was collected as a function of time during the process through valves located at the base of the separators. The samples were weighed after 30 min of collection to avoid measuring CO2 remaining in the bottle.
The temperature of extraction was maintained constant in all the experiments (40 °C) to prevent the heat degradation of thermolabile components in the extracted oil. Table 1 shows the experimental conditions of the SFE unit where P is CO2 pressure, is CO2 flow rate, dP is the average particle size of the leave, is CO2 density, and is CO2 velocity. Observing Table 1, we noted that the conditions of extraction used during these experiments show that the CO2 flow was manually controlled, and the estimated variance of the experiments is between 2.5% to 5% of the average flow. Referring to a previous publication [29] and in order to ensure the solubility of major compounds [36][37][38][39], the collection of extracted oils and waxes was conducted using separators. The first separator was maintained at a low temperature (−5 °C) with the same extraction pressure as the experiment to precipitate waxes while the second separator was maintained at 30 °C and 40 bar for oil extract collection.
The bulk density of milled Pistacia leaves was about 291 kg m −3 , and the void fraction of the bed was equal to 0.53. Glass beads were placed on the bottom of the extractor, the powder of Pistacia leaves (23 ± 0.05 g) was placed above them and another layer of glass bead was put on the top. In addition, two filters (frits <15 µm) were used in both the inlet and the outlet of the extracting vessel. The extract was collected as a function of time during the process through valves located at the base of the separators. The samples were weighed after 30 min of collection to avoid measuring CO 2 remaining in the bottle.
The temperature of extraction was maintained constant in all the experiments (40 • C) to prevent the heat degradation of thermolabile components in the extracted oil. Table 1 shows the experimental conditions of the SFE unit where P is CO 2 pressure, Q CO 2 is CO 2 flow rate, d P is the average particle size of the leave, ρ CO 2 is CO 2 density, and µ CO 2 is CO 2 velocity. Observing Table 1, we noted that the conditions of extraction used during these experiments show that the CO 2 flow was manually controlled, and the estimated variance of the experiments is between 2.5% to 5% of the average flow. Referring to a previous publication [29] and in order to ensure the solubility of major compounds [36][37][38][39], the collection of extracted oils and waxes was conducted using separators. The first separator was maintained at a low temperature (−5 • C) with the same extraction pressure as the experiment to precipitate waxes while the second separator was maintained at 30 • C and 40 bar for oil extract collection.
The bulk density of milled Pistacia leaves was about 291 kg m −3 , and the void fraction of the bed was equal to 0.53. Glass beads were placed on the bottom of the extractor, the powder of Pistacia leaves (23 ± 0.05 g) was placed above them and another layer of glass bead was put on the top. In addition, two filters (frits <15 µm) were used in both the inlet and the outlet of the extracting vessel.

Analysis
Gas Chromatography-Flame Ionization Detector/Mass Spectrometry (GC-FID/MS) GC-FID analysis was carried out with a Shimadzu GC2010 Plus (Nancy, France), equipped with an HP-5 capillary column (Shimadzu, Nancy, France, with dimension: 30 m × 0.25 mm, film thickness Molecules 2020, 25, 199 4 of 19 0.25 µm). The injector and the detector were set at 250 and 300 • C. The temperature column was programmed at 50 • C for 1 min then gradually increased to 270 • C at 3 • C/min. Next, it was held for 5 min then increased to 300 • C at 20 • C/min and subsequently held for 5 min. The split ratio was 5:1 whereas the split flow was equal to 10 mL/min. Nitrogen was used as a carrier gas with a constant pressure of 100 kPa. The GC was also equipped with an Auto-Injector (Shimadzu, Nancy, France, AOC-20i) and the injected volume was equal to 1 µL.
For GC-FID-MS analysis, a Shimadzu GCMS-GC2010-QP2010 Plus equipped with a DB5-MS capillary column (Shimadzu, Nancy, France, with dimension: 30 m × 0.25 mm, film thickness 0.25 µm) was exploited. The injector and the detector were set at 250 • C. The oven temperature was programmed at 50 • C for 1 min, gradually increased to 250 • C at 5 • C/min. It was held for 10 min then increased later to 270 • C at 5 • C/min then held for 5 min. After that, it was increased to 280 • C at 5 • C/min and held for 10 more minutes. Although the split ratio was 10:1, the split flow was equal to 10 mL/min. In this process, helium was used as a carrier gas with a constant speed of 1.69 mL/min. The GC was also equipped with an Auto-Injector (Shimadzu, Nancy, France, AOC-5000) and the injected volume was equal to 1 µL. Mass units were monitored from 35 to 400 m/z at 70 eV. The mass spectra of the components were identified using data from the NIST Library (NIST08s).

Response Surface Methodology (RSM)
Response surface methodology was used to study the influence of supercritical operating extraction parameters such as CO 2 pressure (P), CO 2 flow rate (Q CO 2 ), and average particle size of the leaf (d P ), on the extract oil yield. These three response variables were coded as x 1 , x 2 , and x 3 , respectively. The range and levels of independent factors were chosen based upon the results of preliminary tests and are gathered in Table 2. The individual and interactive effects of these parameters on the dependent variable were studied. Equation (1) represents the linear model with interactions for the three operating conditions, where Y D represents a dependent variable (the yield of extract oil), a 0 is a constant, a 1 , a 2 , and a 3 are individual linear coefficient, a 12 , a 13 , and a 23 are the interactive linear coefficient, and x 1 , x 2 , and x 3 are the coded values of independent factors (pressure, CO 2 flow rate, and average particle size respectively). Nemrod-w software package was used for the regression analysis of the experimental data obtained [33]. Fit quality of the mathematical model equation was expressed by the determination coefficient R 2 , and its statistical significance was checked by an F-test. The significance of the regression coefficient was tested by a t-test. Significance level was given as *** p < 0.001, ** p < 0.01, * p < 0.05. Differences with p-value superior to 0.05 were not considered significant. For our experimental design validation, optimum conditions were fixed based on the data obtained from the experimental design.

Modeling of the Supercritical Extraction Process
Stastováet et al. [30] made several simplifications on Sovová's model [29] by introducing two parameters: the grinding efficiency (G) and the dimensionless time (ψ), where t is the extraction time, Q represents the solvent mass flow rate, y s is the oil solubility in the solvent, N is the initial mass of the solid, and x 0 is the initial oil concentration in the solid. The mass of extracted oil (E) can be calculated by the following Equation (3)- (7): Inside the interval of dimensionless time, two regions exist between G/Z and ψ k , where There is a region definition in dimensionless coordinate, namely h k .
The dimensionless quantities Z and Y are proportional to the mass transfer coefficients according to the first and second extraction period, where k f and k s are the external and the internal mass transfer coefficients respectively, a 0 is the particle specific interfacial area, ρ f stands for the solvent density, ρ s represents the solid density, and ε is the bed void volume. The model was implemented in MATLAB TM . Three adjustable parameters were considered: the grinding efficiency (G), the internal mass transfer parameter (k s a 0 ), and the external mass transfer parameter (k f a 0 ). Equilibrium type "A" model was considered according to Sovová [28]. Since the external mass transfer parameter (k f a 0 ) had no sensitivity [40,41], Fiori et al. [39] suggested an approach to determine this parameter referring to the literature correlations-Sherwood (Sh), Reynolds (Re) and Schmidt (Sc) numbers of experimental runs. CO 2 physical properties were evaluated according to NIST database [42] and the oil extract properties were assumed to be related to the major compound found in GC-FID/MS analysis, α-pinene [43,44]. Binary diffusion coefficient (D AB ) between the CO 2 and the major compound was obtained by correlations. In the case of the supercritical fluid extraction, Sherwood number (Equation (8)) is a function of only Reynolds and Schmidt when natural convection is not significant [45][46][47], where, c 0 , c 1 and c 2 are the adjustable parameters. According to the most-proposed correlations in the literature [45][46][47], c 0 should be higher than 1, c 1 is constrained between 0.5 and 0.8, and c 2 = 1/3. Catchpole et al. [48] and Lito et al. [49] used the approach to estimate only two adjustable parameters (G, and k s a 0 ) directly using the experimental kinetic curve, and they calculated the other parameter (k f a 0 ) using the Sherwood correlation because they considered that it was not significant. However, in our approach, we estimated not only these two parameters (G and k s a 0 ), but also the external mass transfer parameter (k f a 0 ) using the experimental curve for more accuracy.
The relevance of the model fitting to the experimental data was assessed considering two statistical criteria, namely the coefficient of determination R 2 detrmined using Equation (9) and the root means square error (RMSE) given by Equation (10), where n represents the number of available experimental data, and y exp and y model are the experimental extraction yield and the extraction yield predicted by the model, respectively.

Cost Estimation of Processes and Scale-Up
The manufacturing cost of the supercritical extract was estimated through methodology proposed elsewhere [50,51]. Concerning material cost, electricity and labor, they were collected from regional information in Tunis (Tunisia 2016). The fixed investment cost was obtained from the literature proposed by Turton et al. [52] to evaluate the cost of manufacturing according to Equation (11) including depreciation (10% of FCI).
where COM is the cost of manufacturing of supercritical extract of Pistacia, FCI corresponds to the fixed cost of investment, C OL represents the cost of operational labor, C UT is the cost of utilities, C WT the cost of waste treatment, and C RM is the cost of raw material. According to Carvalho [53], Equation (12) can be used in order to determine the solvent flow rate required to maintain the same kinetic behavior in different SFE units (scale-up) for a given feed mass and bad geometry. Researchers [54][55][56][57] declared that the extraction time has an influence on an extraction's COM and the extraction rate increases by increasing the solvent flow rate. They also reported that oil yield in the extraction can be positively influenced by the solvent flow rate increases as the following equation: The extractor geometry data and the installed supercritical extraction cost were obtained from Núñez and del Valle [58][59][60]. In fact, a plant with two extraction vessels, each one having internal volume varying between 0.2, 0.4, 0.6 and 1.0 m 3 , was evaluated. For instance, for a plant with vessels of 1.0 m 3 , the aspect ratio was H/d = 8 (with 0.542 m × 4.334 m of inner diameter and height respectively). The wall thickness withstands 390 bar. The fixed cost of investment (FCI) of each SFE unit was determined in USD based on the values of Rocha-Uribe et al. [59]. All the values are reported in Table 3 and are calculated using the Chemical Engineering Plant Cost Index (CPECI) value for 2014 (CPECI 2014 = 580) [61].
According to Experiment (2), the relations of laboratory-scale H/d is 3.6, with the flow rate from 3.36 × 10 −5 kg/s, the bed apparent density ρ = 296 kg/m 3 , with the operational conditions of 220 bar and 40 • C for the extraction process were taken into consideration. Figure 2 shows the cycle of solvent (pure CO 2 ) during the supercritical extraction process in an operating unit. The steps are considered as being primarily solvent collection in reservoir (64 bar and 25 • C), followed by a cooling process (10 • C), pumping and pressurization of the extraction vessel (220 bar and 35 • C), followed by temperature increase (40 • C) until obtaining the desired extraction condition and finally, after this process, reducing the pressure (60 bar and 60 • C) for solute precipitation for reuse. According to Experiment (2), the relations of laboratory-scale H/d is 3.6, with the flow rate from 3.36 × 10 −5 kg/s, the bed apparent density ρ = 296 kg/m 3 , with the operational conditions of 220 bar and 40 °C for the extraction process were taken into consideration. Figure 2 shows the cycle of solvent (pure CO2) during the supercritical extraction process in an operating unit. The steps are considered as being primarily solvent collection in reservoir (64 bar and 25 °C), followed by a cooling process (10 °C), pumping and pressurization of the extraction vessel (220 bar and 35 °C), followed by temperature increase (40 °C) until obtaining the desired extraction condition and finally, after this process, reducing the pressure (60 bar and 60 °C) for solute precipitation for reuse. In this case, it is assumed that during the process of decompression, the solute is separated, and the pure solvent is returned to the system. Based on the findings of this and the mutual values found in other research papers, it is identified that extraction yields (mass extract/Pistacia load) were estimated to reach 0.3%, 0.5%, 0.7%, 1.0% and 1.5%.
The cost of 8000 h per year operational work, with continuous 24 h per day, 8 h daily shifts (2 workers/shift) was considered. The cost of labor was operationally considered to be 6.60 USD/h (1475.60 USD/month tax included). The utility cost was estimated relying on energy consumption involved in the solvent cycle CO2, cold water, and electricity [51,58]. The specific energies of CO2 for cooling, heating, and pumping in the solvent cycle were equal to −261.29 kJ/kg, 219.2 kJ/kg and 55.0196 kJ/kg, respectively. These calculations were based upon the work of Rock-Uribe et al. [59].
The electricity cost was equal to 217.10 USD/MWh (price charged in Tunis, Tunisia, tax included). Concerning raw material costs, the considered values were: 1.35 USD/kg of dried and milled Pistacia leaves, 0.15 USD/kg of CO2 and 0.97 USD/kg of ethanol for cleaning purposes [60]. It was considered that 2% of CO2 mass was lost during the extraction cycle for all the SFE process scale evaluated in this work. The cost of waste treatment was not considered because CO2 was fully recycled and Pistacia leaf can be used in soil enrichment or energy generation. In this case, it is assumed that during the process of decompression, the solute is separated, and the pure solvent is returned to the system. Based on the findings of this and the mutual values found in other research papers, it is identified that extraction yields (mass extract/Pistacia load) were estimated to reach 0.3%, 0.5%, 0.7%, 1.0% and 1.5%.
The cost of 8000 h per year operational work, with continuous 24 h per day, 8 h daily shifts (2 workers/shift) was considered. The cost of labor was operationally considered to be 6.60 USD/h (1475.60 USD/month tax included). The utility cost was estimated relying on energy consumption involved in the solvent cycle CO 2 , cold water, and electricity [51,58]. The specific energies of CO 2 for cooling, heating, and pumping in the solvent cycle were equal to −261.29 kJ/kg, 219.2 kJ/kg and 55.0196 kJ/kg, respectively. These calculations were based upon the work of Rock-Uribe et al. [59].
The electricity cost was equal to 217.10 USD/MWh (price charged in Tunis, Tunisia, tax included). Concerning raw material costs, the considered values were: 1.35 USD/kg of dried and milled Pistacia leaves, 0.15 USD/kg of CO 2 and 0.97 USD/kg of ethanol for cleaning purposes [60]. It was considered that 2% of CO 2 mass was lost during the extraction cycle for all the SFE process scale evaluated in this work. The cost of waste treatment was not considered because CO 2 was fully recycled and Pistacia leaf can be used in soil enrichment or energy generation. Table 4 shows the experimental yield results and operating conditions of supercritical extraction for the ten experiments. The experimental oil extract yield was calculated using the following Equation (13):  The yield observed for the tested conditions varied between 0.093% and 0.285%. We found that Experiment (2) with the highest pressure, lowest flow rate, and the lowest average particle diameter gave the greatest tested income extraction conditions. The replications performed at 80 bars (0.10% ± 0.0184%), which were Experiment (3) and (4), demonstrated higher variability than those performed at 180 bar (0.022% ± 0.0057%) (Experiments (8) and (9)); therefore, they have coefficients of variation equal to 17.3% and 2.5% respectively.

Results and Discussion
By comparing all results, we observe that the present work provided different yields that were in some cases inferior to those reported by other authors [31,60]. In fact, Bampouli et al. [62] obtained an outcome from the leaves of Pistacia lentiscus (PL) var. chia (from Chios, Greece) varying between 1.6% and 5% w/w. The conditions were ranging from 100 to 250 bar and 45 • C with a flow rate of 1.5 to 3.0 kg CO 2 /h. Also, Congiu et al. [31] acquired yields between 0.25% and 0.45% for the leaves of Pistacia lentiscus (PL) coming from the regions of Costa Rey and Capoterra (Sardinia, Italy) providing 90 bar and 50 • C with a flow rate of 0.9 kg CO 2 /h.
The variation of the obtained yields must be due to the areas of cultivation processing, treatment of raw materials and experimental conditions in the extraction process. Appendix A shows the characterizations of the essential oil obtained from the leaves and carried out using GC-MS-FID. We observed that the major compounds for the extraction of Pistacia lentiscus in the Tunis region are α-pinene (32%), followed by terpinene-4-ol (13%), 1-8-cineole (6%), α-terpineol (4%), β-caryophyllene (4%) and borneol (4%), as summarized in Table 5. Furthermore, as expected, these compositions are not significantly influenced by changing the operating conditions due to the constant extraction temperature. Response surface methodology (RSM) was used to study the individual and the interactive influence of operating extraction parameters on the extract yield to find the optimal operating conditions. Table 6 shows the experimental design yield for the ten experiments. We used the analysis of variance (ANOVA) to evaluate the statistical significance of the linear model represented in Equation (1). The model can describe the variation of the results because it is significant at <5%. We, also, verified the model efficiency and the adaptability to the experimental data by estimating the coefficient of actual and predicted determination (R 2 and predicted R 2 respectively) calculated by the analysis of variance. We found out that the actual determination coefficient indicates that the fitted model explains 91.2% of the variability in the extraction yield. The predicted R 2 was 0.998 (a good agreement) indicating that our experimental design can be used for modeling the response variables employed, as shown in Figure 3. Response surface methodology (RSM) was used to study the individual and the interactive influence of operating extraction parameters on the extract yield to find the optimal operating conditions. Table 6 shows the experimental design yield for the ten experiments. We used the analysis of variance (ANOVA) to evaluate the statistical significance of the linear model represented in Equation (1). The model can describe the variation of the results because it is significant at <5%. We, also, verified the model efficiency and the adaptability to the experimental data by estimating the coefficient of actual and predicted determination (R 2 and predicted R 2 respectively) calculated by the analysis of variance. We found out that the actual determination coefficient indicates that the fitted model explains 91.2% of the variability in the extraction yield. The predicted R 2 was 0.998 (a good agreement) indicating that our experimental design can be used for modeling the response variables employed, as shown in Figure 3.   (1): the linear intercept constant (a0), the individual linear effects of the three independent variables (a1, a2, and a3), and their interactive linear effects (a12, a13, and a23). Therefore, the linear regression equation used to evaluate the experimental yield becomes (YD), This equation indicates that the main factor that significantly influences the yield was the CO2 pressure when the confidence of 5% was considered. The equation identifies the best conditions through variation of chosen parameters to maximize the extraction efficiency, which is presented in Experiment (2).   (1): the linear intercept constant (a 0 ), the individual linear effects of the three independent variables (a 1 , a 2 , and a 3 ), and their interactive linear effects (a 12 , a 13 , and a 23 ). Therefore, the linear regression equation used to evaluate the experimental yield becomes (Y D ), Y D = 0.183 + 0.084x 1 (14) This equation indicates that the main factor that significantly influences the yield was the CO 2 pressure when the confidence of 5% was considered. The equation identifies the best conditions through variation of chosen parameters to maximize the extraction efficiency, which is presented in Experiment (2).
For a better understanding of the statistical results, Figure 4 represents the 2D response surface of the experimental yields by the function of pressure, average particle size and the flow rate of CO 2 . As can be observed in Figure 4, the highest yield was obtained around the maximum point of pressure (P = 220 bar) when the flow rate of CO 2 and average particle size were around minimum points.  For a better understanding of the statistical results, Figure 4 represents the 2D response surface of the experimental yields by the function of pressure, average particle size and the flow rate of CO2. As can be observed in Figure 4, the highest yield was obtained around the maximum point of pressure (P = 220 bar) when the flow rate of CO2 and average particle size were around minimum points.

Analysis and Validation of Experimental Design
The statistical analysis for the final selected model shows that the effect of the CO2 pressure is the only variable that has a significant effect on the yield, compared to the other variables that have no effects. For this reason, we analyzed the selection effect of the identification and validation points used for our experimental design. The existence of a correlation between the parameters increases the size of the confidence intervals [63], therefore we need to control the value of the correlation coefficients 2 to 2.
In our investigation, we have used the D-optimality criterion [64] to separate the experiments used for both parametric identification and validation model. This method consists of choosing a set of parametric identification points to obtain the highest determinant of the Fischer matrix information [65]. To investigate the influence of selection on the confidence intervals of each parameter, we studied the correlations between the parameters using the following matrix correlation coefficients summarized in Table 8.

Analysis and Validation of Experimental Design
The statistical analysis for the final selected model shows that the effect of the CO 2 pressure is the only variable that has a significant effect on the yield, compared to the other variables that have no effects. For this reason, we analyzed the selection effect of the identification and validation points used for our experimental design. The existence of a correlation between the parameters increases the size of the confidence intervals [63], therefore we need to control the value of the correlation coefficients 2 to 2.
In our investigation, we have used the D-optimality criterion [64] to separate the experiments used for both parametric identification and validation model. This method consists of choosing a set of parametric identification points to obtain the highest determinant of the Fischer matrix information [65]. To investigate the influence of selection on the confidence intervals of each parameter, we studied the correlations between the parameters using the following matrix correlation coefficients summarized in Table 8.  Figure 5, which represents the frequency of the correlation coefficient, mimics 87% of the correlation between the parameters pairs are in the range of 0.2 to 0.4. This indicates the use of the Detmax Fedrov algorithm [66] that has no effect on the correlation between the parameters. Therefore, the used supports of a linear model with interaction, and subsequently the experimental design, are applicable at least in this study.  Figure 5, which represents the frequency of the correlation coefficient, mimics 87% of the correlation between the parameters pairs are in the range of 0.2 to 0.4. This indicates the use of the Detmax Fedrov algorithm [66] that has no effect on the correlation between the parameters. Therefore, the used supports of a linear model with interaction, and subsequently the experimental design, are applicable at least in this study.

Effect of Operating Conditions on the Mass Transfer
All experimental data were used to determine the model parameters (G, and , and ) (see Appendix B). Table 9 shows that the two adjusted parameters (grinding efficiency (G) and internal mass transfer parameter ( ), which is estimated by the experimental kinetic curves, have no significant change between the two approaches. As expected [3,13,31], the value of grinding efficiency (G) increases by decreasing the average particle size. This parameter is not only related to the particle size, but also to the shape of its distribution (normal, bimodal). As a result, it influences the curve shape due to the solvent flow asymmetry effect.
In the first approach, we applied the correlations proposed by Lito, Catchpole, and King using only the binary diffusion coefficient (CO2-α-pinene) to estimate the external mass transfer parameter ( ). On the other hand, the adjusted parameters were not only grinding efficiency (G) and the internal mass transfer parameter ( ) but also the external mass transfer parameter, which was estimated by experimental extraction curves in the second approach.

Effect of Operating Conditions on the Mass Transfer
All experimental data were used to determine the model parameters (G, and k s a 0 , and k f a 0 ) (see Appendix B). Table 9 shows that the two adjusted parameters (grinding efficiency (G) and internal mass transfer parameter (k s a 0 ), which is estimated by the experimental kinetic curves, have no significant change between the two approaches. As expected [3,13,31], the value of grinding efficiency (G) increases by decreasing the average particle size. This parameter is not only related to the particle size, but also to the shape of its distribution (normal, bimodal). As a result, it influences the curve shape due to the solvent flow asymmetry effect. In the first approach, we applied the correlations proposed by Lito, Catchpole, and King using only the binary diffusion coefficient (CO 2 -α-pinene) to estimate the external mass transfer parameter (k f a 0 ). On the other hand, the adjusted parameters were not only grinding efficiency (G) and the internal mass transfer parameter (k s a 0 ) but also the external mass transfer parameter, which was estimated by experimental extraction curves in the second approach. Table 10 shows the parameters (k f a 0 , and D AB ) for both approaches. The adjusted parameter (k f a 0 ) estimated by the experimental kinetic curves in the second approach is different than the correlated parameter proposed by Lito and Catchpole in the first approach. This parameter affects the values of the diffusion coefficient as shown in Table 10. In the second approach, the parameter values of the Sherwood number were experimentally obtained from the extraction curves and k f values. The parameter correlation suggested in the second approach was determined from c 0 and c 1 settings, resulting in the equation as shown in Table 11.
The adjusted parameters are within the range reported by [19] and their applicability for Reynolds and Schmidt values are in the ranges 2 ≤ Re ≤ 60 and 2 ≤ Sc ≤ 12. The values of the mass transfer coefficients (k f a 0 ) ranged from 1.4 × 10 −2 to 3.7 × 10 −1 for the estimation performed with the correlations of Lito and Catchpole.
Concerning the adjustment made with the three parameters G, k f a 0 and k s a 0 (the value of k f a 0 is 0.020), it ranged from 7.3 × 10 −3 s −1 to 8.9 × 10 −2 s −1 . These values are lower than those obtained by adjustment with the correlations. The parameters k s a 0 were in all cases between 1.9 × 10 −5 s −1 and 1.8 × 10 −4 s −1 .

Cost Estimation of Processes and Scale-Up
The greatest impact on the cost of manufacturing extracted oil production of P. lentiscus in Tunisia is represented by the raw material cost (RMC), followed by the fixed cost of investment and the utility cost, as indicated in Figure 6.

Cost Estimation of Processes and Scale-Up
The greatest impact on the cost of manufacturing extracted oil production of P. lentiscus in Tunisia is represented by the raw material cost (RMC), followed by the fixed cost of investment and the utility cost, as indicated in Figure 6.  Table 12 shows the manufacturing costs of the supercritical extract of Pistacia lentiscus in the US. We note that for the same yield, the lowest costs were those obtained at the highest production volume, as was expected. Concerning yield values obtained on a pilot scale (0.30%), the cost of the manufacturing process of the supercritical extract weas between 999.63 USD/kg and 813.95 USD/kg. These values are considered very high when compared to the costs of other vegetable raw materials such as rosemary extract which is worth 49.71 USD/kg [21], ginger oleoresin which costs 99.80 USD/kg [20], Curcuma longa L. extract which is worth 164.4 USD/kg [40] and habanero pepper extract with a cost of 540.19 USD/kg [33].
A yield increase in the extraction process reduces the cost of manufacturing. Thus, the high cost of production is due to the low yields gained from this kind of plant. Prices of traded extracted oils of Pistacia lentiscus sold in 5 mL, 10 mL or 30 mL vials are about 5.83 USD/g (5830.00 USD/kg). These values are obtained from the local market in Tunis, Tunisia.

Conclusions
Pistacia lentiscus L. plant from the Tunisian region is appeased of medicinal properties in its extract oil that can be produced using supercritical carbon dioxide (SC-CO2) extraction. In this study, we observed that the α-pinene (32%) was the major compound of the extracted oil of Pistacia lentiscus in the Tunis region. The experiment (2) having the highest pressure, lowest flow rate, and the lowest average particle diameter gave the greatest tested income extraction conditions.
We investigated the influence of CO2 pressure, average particle size, and CO2 flow rate and their interaction on the extract yield using the response surface methodology (RSM). It was observed that the main factor that significantly influences the yield was the CO2 pressure and, therefore, the best  Table 12 shows the manufacturing costs of the supercritical extract of Pistacia lentiscus in the US. We note that for the same yield, the lowest costs were those obtained at the highest production volume, as was expected. Concerning yield values obtained on a pilot scale (0.30%), the cost of the manufacturing process of the supercritical extract weas between 999.63 USD/kg and 813.95 USD/kg. These values are considered very high when compared to the costs of other vegetable raw materials such as rosemary extract which is worth 49.71 USD/kg [21], ginger oleoresin which costs 99.80 USD/kg [20], Curcuma longa L. extract which is worth 164.4 USD/kg [40] and habanero pepper extract with a cost of 540.19 USD/kg [33].
A yield increase in the extraction process reduces the cost of manufacturing. Thus, the high cost of production is due to the low yields gained from this kind of plant. Prices of traded extracted oils of Pistacia lentiscus sold in 5 mL, 10 mL or 30 mL vials are about 5.83 USD/g (5830.00 USD/kg). These values are obtained from the local market in Tunis, Tunisia.

Conclusions
Pistacia lentiscus L. plant from the Tunisian region is appeased of medicinal properties in its extract oil that can be produced using supercritical carbon dioxide (SC-CO 2 ) extraction. In this study, we observed that the α-pinene (32%) was the major compound of the extracted oil of Pistacia lentiscus in the Tunis region. The experiment (2) having the highest pressure, lowest flow rate, and the lowest average particle diameter gave the greatest tested income extraction conditions.
We investigated the influence of CO 2 pressure, average particle size, and CO 2 flow rate and their interaction on the extract yield using the response surface methodology (RSM). It was observed that the main factor that significantly influences the yield was the CO 2 pressure and, therefore, the best conditions through variation of chosen parameters to maximize the extraction efficiency were presented in Experiment (2).
We studied the influence of operating parameters on mass transfer by evaluating a process applying broken and intact cell (BIC) on the essential oil extraction curves that are acquired from the leaves of Pistacia lentiscus L. The two adjusted parameters (grinding efficiency (G) and internal mass transfer parameter (k s a 0 )), which were estimated by the experimental kinetic curves, have no significant change between the two approaches (Lito and Catchpole approach, and AYDI A approach). However, the external mass transfer parameter (k f a 0 ) proposed by AYDI A was different from the correlated parameter in the first approach that significantly influences the values of the diffusion coefficient.
The economic evaluation in the scale-up process was obtained for the SC-CO 2 extraction of these plant leaves. We indicated that the lowest costs were obtained at the highest production volume for the same yield. The manufacturing cost of oil production is reduced by a yield increase in the extraction process because of the low yields obtained from this type of plant.

Acknowledgments:
The authors are grateful for the financial support received from IPEST and LRGP.

Conflicts of Interest:
The authors declare no conflict of interest.  Table A4. Operating conditions estimated THREE parameters from best fitting and modeling errors used by AYDI A.