Supercritical Fluid Extraction of Peruvian Schinus molle Leaves: Yield, Kinetics, Mathematical Modeling, and Chemical Composition

Abstract

According to the literature, Schinus molle (SM) is an important source of bioactive phytochemicals, but the phytochemical content and composition of this species, which grows in high Andean geographic zones such as Tarma (Peru), is not known. In an effort to fill this gap, our work investigated the supercritical carbon dioxide extraction of SM leaves at three temperature levels (35, 45, and 55 °C) and three pressure levels (150, 250, and 350 bar). The results revealed the highest yield of extract at 150 bar, 45 °C, and 3.28 g CO₂/min. Under these conditions, the overall extraction curves (OEC) were modeled using the Spline, logistic, and Esquível models, allowing the generation of mass transfer parameters for SFE at the optimized conditions, resulting in a similar correlation with experimental data. Twenty-six compounds were identified in the SFE extract of SM leaves. The most abundant compound classes were sesquiterpenoids (57.17%), sesquiterpenes (24.50%), and triterpenoids (10.48%); of each class, the most abundant compounds were shyobunol (33.60%), bicyclogermacrene (12.68%), and lupeone (6.58%), respectively. The compounds detected possess bioactive properties that support further studies on the application of SFE extracts of SM as a functional ingredient in commercial products.

1. Introduction

Schinus molle L. (SM) is an aromatic arboreal species found in the Peruvian Andes and other regions of South America [1]. Although there is a large number of scientific reports on the bioactive potential of the phytochemicals produced by this species, there are still limited studies of plants growing in the high Andean zones of Peru.

It has been reported that SM contains essential oils, which are traditionally extracted by hydrodistillation from its aerial parts [2,3], leaves [4], fruits [4,5], and resins [6]. SM essential oil has potential applications, such as insecticide [7], antioxidant [8,9], bactericide [10,11], herbicide [2,6], anti-corrosive [12], and fungicide [13]. The bioactive properties of SM essential oil have demonstrated potential in the production of biocidal microcapsules [14] and intelligent/active food packaging films [15]. According to scientific reports, the chemical composition of essential oils in SM parts differs in terms of the concentration of major compounds present. For instance, in SM leaves the compounds detected include α-phellandrene (29.8%), β-phellandrene (21.1%) and elemol (13.0%) [16]; α-phellandrene (20.3%), d-limonene (16.4%), germacrene-D (15.5%), and bicyclogermacrene (12.3%) [6]; 1R-α-pinene (15.5%), camphene (14.0%), β-myrcene (11.5%), and o-cymene (29.0%) [11]; 1-tetradecene (43.3%) and 1-dodecanol (22.8%) [7]; limonene (22.9%), α- and β-terpinene (12.0%) [4]; there are other compositions reported by other authors [8,9,10,13,17,18]. However, the major compounds in SM essential oil extracted from resin included caryophyllene (18.3%), bicyclogermacrene (9.2%), and germacrene-B (20.2%) [6]. In the essential oil extracted from SM fruits, the major compounds found were limonene (22.9%) [4], β-myrcene (35.8%), α-phellandrene (20.6%), and D-limonene (19.4%) [15]. The differences in the chemical composition of SM essential oils reported are attributed to the geographical area and growing conditions of the crops produced [5] and the method of extraction [8].

SM is also an interesting source of non-volatile bioactive compounds, such as alkaloids, and flavonoids [19,20]. These compounds can be present in the aerial part [21], fruits [22], husks [22], unpeeled fruits [22], stem bark [23], flowers [24], leaves [19], and seeds [20,25], which have been extracted with solvents like water [26,27], aqueous ethanol [21,28], hexane [25,29], dichloromethane [25,30], ethyl acetate [30], methanol [19], aqueous methanol [20], petroleum ether [24], acetone [24], diethyl ether [24], and solvent mixtures [31]. Solvent extraction of SM parts has been performed using traditional methods, such as maceration [23,24], boiling [26], infusion [32], and immersion warming [21]. The extracts obtained with the reported methods presented the following properties: wound-healing [21], antimicrobial [21,23], antiviral [27], antioxidant [28], antidiabetic [32], anti-inflammatory [28,33], antinociceptive [33], anticancer [24,29], antimalarial [20], antidiarrheal [19,34], analgesic [35], cytotoxic [31], gastroprotective [25], and hepatoprotective [19]. Besides the bioactive properties of SM extracts, the chemical composition of SM allowed its processing into nanoparticles with antioxidant [30] and anticancer [26] potentials. The diverse properties already reported are attributed to the wide range of molecules found in SM, including alkaloids [35], flavonoids [35], tannins [29], triterpenes [25], sequiterpenes [29], and other chemical components [20].

Currently, several emerging and eco-friendly technologies have been implemented for the extraction of bioactive compounds to overcome the time and solvent-consuming attributes of traditional methods [36]. The potential of supercritical fluid extraction (SFE) as an eco-friendly method for selecting bioactive compounds to replace petroleum-derived solvents and producing extracts without contamination has been demonstrated [37,38]. The SFE of bioactive compounds from SM has been studied in mixtures of leaves and branches [39,40] and leaves [41], utilizing carbon dioxide (CO₂) as the primary supercritical fluid.

Barroso et al. [39] reported that for the SFE of SM (2 mm average particle diameter) at the conditions of 9–20 MPa, 50 °C, and CO₂ flow rate of 8.3 g/min, the higher yield was obtained at 15 MPa, and the quality of extracts consisted of high proportions of limonene (41.4%), (E)-caryophyllene (15.6%), and bicyclogermacrene (11.6%). Marongiu et al. [40] reported α-phellandrene (26.5%), limonene + β-phellandrene (22.2%), elemol (10.8%), and α-eudesmol (6.0%) as major compounds of SM leaves extracts obtained at 9 MPa, 50 °C, and 16.7 g/min. According to our literature review, the extraction of bioactive compounds using supercritical fluid extraction (SFE) with CO₂ is promising. However, additional studies are required to investigate a wider range of thermodynamic parameters, as these can influence yield and composition, as observed in other raw materials [42,43]. Mathematical modeling of the overall extraction curves (OEC) generated from supercritical fluid extraction (SFE) is useful for process design and optimization, as it enables the assessment of kinetic behavior, aiding in the decision-making process for selecting the optimal processing parameters to achieve optimized extract quality and processing time. The OEC of the SFE process of clove and sugarcane residues at the laboratory and pilot scales were adequately described [41]. Studies on the characterization and potential applications of SM grown in the geographical area of Tarma, Peru, are scarce, to the best of the authors’ knowledge. For this reason, the goal of this work was to evaluate the recovery of extracts from SM leaves collected in Tarma Province, Peru, using supercritical fluid extraction (SFE) via a 3²-factorial design and mathematical modeling of overall extraction curves (OEC) using empirical models. The chemical composition of extracts obtained under best yield conditions was evaluated using gas chromatography-mass spectrometry (GC–MS) to assess the bioactive potential of the extracts.

2. Materials and Methods

2.1. Raw Material

Samples of SM were collected for botanical identification (collection coordinates: 11°27′32″ S and 75°40′49″ W) and extraction experiments (collection coordinates: 11°26′20″ S and 75°41′30″ W) in the district of Tarma, Junin, Peru. Dr. Carlos Reynel Rodríguez identified the species, and a botanical sample was deposited in the herbarium located at the Faculty of Forestry Sciences in the Universidad Nacional Agraria la Molina (Peru), with the sample code 52114. The use of this species for scientific investigation was authorized by the Servicio Nacional Forestal y de Fauna Silvestre—SERFOR (RA Nº D000260-2024-MIDAGRI-SERFOR-ATFFS-SELVA CENTRAL).

2.1.1. Preparation

SM leaves were dried and covered in Kraft paper at room temperature until they achieved a dried and brittle texture. Dried SM leaves (DSML) were vacuum-packed and stored at −20 °C (Meling Biomedical, DW-YL270, Hefei, China). The leaves were then ground using a home immersion blender (Oster FPSTHB460A-053, 400 W, China) for 60 s.

2.1.2. Particle Size

The particle size of SM was determined by inserting 30 g of dried and milled raw material into a granulometry analyzer (Retsch, AS 200 Basic, Haan, Germany) [42].

2.1.3. Colorimetric Analysis

The colorimetric analysis of DLSM was determined in the solid material before and after the SFE, with a portable colorimeter (Konica Minolta, CR-20, Japan) under the CIE L*a*b* system. With the lightness (L*) and the coordinates (a* for red (+) or green (−), and b* for yellow (+) or blue (−)), the color variations were calculated, i.e., ΔL*, Δa*, Δb* and ΔE*. The parameter ΔE* consists of the total color difference, as described in Equation (1).

$$∆E^{\mathrm{\ast }}={\left[{\left(∆L^{\mathrm{\ast }}\right)}^2+{\left(∆a^{\mathrm{\ast }}\right)}^2+{\left(∆b^{\mathrm{\ast }}\right)}^2\right]}^{0.5}$$

(1)

2.2. SFE Equipment

A bench-scale SFE equipment (Singularity Extraction Technologies, PD-Basic-2235, Campinas, Brazil) was used (Figure 1). The equipment was located at the Instituto de Investigaciones en Tecnologías Altoandinas (INITA) of the Universidad Nacional Autónoma Altoandina de Tarma (UNAAT), at an altitude of 3053 m above mean sea level (AMSL). Under the ambient conditions attributed (17 °C was considered) to the geographical zone from where the experiments were performed, the CO₂ density considered was 1.257 kg/m³, according to the NIST website [43]. The SFE unit compressor was operated with the aid of a cooling bath (Singularity Extraction Technologies, Brazil) at −2 °C and a medical-grade air compressor (SCHULZ, MSV 12, SCHULZ Compressores LTDA, Santa Catarina, Brazil) supplying air at 4 bar. The CO₂ flow was controlled with the aid of a flowmeter (MasterFlex, IL, USA). The volume of CO₂ used in each extraction was measured in cubic meters with the aid of a totalizer (LAO, G1,6, São Paulo, Brazil).

2.3. SFE Experiments

2.3.1. Experimental

Carbon dioxide (99.99% purity, Linde, Lima, Peru) was the solvent used in SFE. The experiments were carried out in an extraction vessel (100 mL, 31.38 mm diameter) loaded with 10.03 ± 0.01 g of DLSM and glass beads (3 mm diameter, ISOLAB Laborgeräte GmbH, Carsalo, Brazil) to fill the empty spaces. SFE experiments were conducted to determine the conditions of highest extraction yield, based on a 3²-factorial design, evaluating the effects of pressure (150, 250, and 350 bar) and temperature (35, 45, and 55 °C) on extraction yield. Nine experiments were performed in duplicate. A CO₂ flow rate of 3.28 g/min, a static time of 10 min, and a solvent to feed ratio (S/F, g CO₂/g feedstock) of 11.87 were selected. Global yield (or yield of extract) was determined gravimetrically, according to Equation (2), where $Y$ is the yield of extract from DLSM obtained via SFE (expressed in %, g/100 g), $E$ is the weight of extract obtained from the SFE (expressed in g), and $S$ is the weight of raw material (DLSM) used in the extractions (expressed in g).

$$Y\left({\displaystyle \frac{g}{100g}}\right)={\displaystyle \frac{E}{S}}\times 100$$

(2)

2.3.2. Overall Extraction Curves and Mathematical Modelling

The overall extraction curve (OEC) was plotted for the process conditions associated with the highest extract yield, as determined by the assays in Section 2.3.1. Duplicate OECs were performed using 10.03 ± 0.01 g of DLSM, and extracts were collected periodically for up to 140 min of extraction. For the collection of extracts, 50 mL vials were used.

The OEC of SM extraction was plotted considering the extraction yield (g extract per 100 g raw material) versus the solvent-to-feed ratio (S/F, g CO₂/g raw material). The kinetic behavior was studied by modeling the OEC using empirical models [38,44,45,46,47].

The Visual Basic for Applications function of Microsoft Excel was used to model the 2 straight-lines spline [38,45,46]. The solver function of Microsoft Excel estimated the adjustable parameters for logistic model, implemented by Martínez et al. [44], and Esquível et al. model [47]. The Spline model [38,46] is expressed by the Equation (3):

$$m_{EXT}=b_0+b_{1}t+b_2\left(t-t_{CER}\right)$$

(3)

where

• b₀ (g) is the linear coefficient, b₁ (or M_CER, in g/min) is the slope of constant extraction rate (CER) straight period, physically expressed as M_CER, which is the extraction rate for the CER period; b₂ (or M_FER, in g/min) is the slope of falling extraction rate (FER) straight line; m_EXT (g) is the mass of extract, t is the time of extraction (min), and t_CER (min) is CER period.

The mass of extract predicted at the CER period (R_CER, g extract/100 g raw material) was calculated by dividing the ratio between the accumulated mass of extract at t_CER and the mass of feed F₀ (g), as demonstrated in Equation (4).

$$R_{CER}=\left({\displaystyle \frac{m_{CER}}{F_0}}\right)\times 100$$

(4)

The mass ratio of extract in the supercritical phase at the vessel outlet (Y_CER, g extract/g CO₂) was calculated as the ratio between b₁ (or M_CER) and the CO₂ flow.

Martinez et al. [44] proposed a logistic model (Equation (5)) to describe the OECs, considering the mass transfer of the extract (represented by a single group of compounds) to the fluid phase.

$$m_{EXT}={\displaystyle \frac{X_0{F}_0}{\mathrm{e}\mathrm{x}\mathrm{p}\left(b{t}_m\right)}}\left\{{\displaystyle \frac{1+\mathrm{e}\mathrm{x}\mathrm{p}\left(b{t}_m\right)}{1+\left[\mathrm{e}\mathrm{x}\mathrm{p}(t_m-1)\right]}}-1\right\}$$

(5)

where m_EXT is the mass of extract (g), F₀ (g) is the input mass of raw material, X₀ is the global yield expressed in terms of m_EXT/F₀ (g/g), b (m⁻¹), and t_m (min) are the adjustable parameters.

Esquível et al. [47] proposed an empirical equation (Equation (6)) to predict the yield variation in the SFE.

$$m_{EXT}=X_0{F}_0\left({\displaystyle \frac{t}{b+t}}\right)$$

(6)

where m_EXT is the mass of extract (g), F₀ is the mass of raw material used in the SFE (g), t (min) is the time of extraction (min), and b (min) is the adjustable parameter of the model with no physical meaning.

2.4. Characterization of Extract

Gas Chromatography–Mass Spectrometry (GC–MS)

The chemical composition of the DLSM SFE extract was assessed by gas chromatography-mass spectrometry (GC–MS). The analysis service was performed by the Laboratory of Research and Certifications (LABICER) of the National University of Engineering (UNI). A gas chromatograph GC–2010 Plus (Shimadzu, Kyoto, Japan), equipped with autosampler AOC-6000 (Shimadzu, Japan), mass spectrometer GCMS-QP210 Ultra (Shimadzu, Japan), and RESTEK Rtx-5 MS column (30 m × 0.25 mm × 0.25 μm) was used. The analysis was performed following the chromatographic method developed by Bendif et al. [48], considering an interface temperature of 290 °C and 250 °C for the ion source. Before analysis, 0.1 mL of the DLSM SFE extract was diluted in 9.9 mL of n-hexane (Merck Millipore, EMSURE, Darmstadt, Germany) and filtered (0.45 μm syringe filter: Nylon Filter, TEKNOKROMA, Barcelona, Spain). Helium (≥99.99% purity, Linde Peru S.R.L., Peru) was used as carrier gas. The compounds were identified using the NIST 2014 library, which is available in the software provided with the equipment. The relative composition (expressed as percentage, %) was determined by dividing the chromatographic peak area of the single compound by the areas of all chromatographic peaks detected, followed by multiplication of the resulting value by 100.

2.5. Statistical Analysis

The effect of pressure and temperature on the extraction yield was evaluated using a 3²-factorial design. The results were evaluated to determine the assumptions of normality (using the Anderson–Darling test) and homogeneity of variance (using the Bartlett test). Subsequently, analysis of variance (ANOVA) was performed at a significance level of 0.05 using Minitab software version 21.2 (Minitab LLC, USA).

3. Results and Discussions

3.1. Effect of SFE Parameters

Extractions were performed with ground DLSM with an average particle diameter of 0.82 ± 0.01 mm. An average particle diameter (2 mm) was used in the extraction of bioactive from SM samples (leaves and twigs) with supercritical CO₂ [39]. The reduction in the particle size contributes to the extraction of bioactive, because the grinding allows to break the structures of the plant material. The effects of experimental conditions on the yield of extract are shown in Figure 2. The highest yield of 1.36 ± 0.03% was observed at 150 bar and 45 °C, and the lowest yield of 0.88 ± 0.08% was observed at 150 bar and 55 °C. Interestingly, the yields obtained in this work were higher than those reported by Marongiu et al. [40], who observed yield of 0.7% after the SFE of SM leaves at 90 bar, 50 °C and 16.67 g CO₂/min, and slightly lower compared to those reported by Barroso et al. [39], who conducted SFE of a mixture of SM leaves and twigs at the conditions of 120 bar, 50 °C and 8.28 g CO₂/min per 120 min, and by Scopel et al. [49], after the SFE with pure CO₂ at 150 bar, 60 °C and 8.28 g CO₂/min for 170 min. According to Scopel et al. [49], the use of a cosolvent (water and ethanol) in SFE with CO₂ did not increase the yield of Schinus molle extract (leave + twigs). On the other hand, extraction with the use of cosolvents affects bioactive properties, such as antimicrobial activity [49]. The yield of bioactive extract obtained from DLSM observed in the present study and its difference with that reported in the literature show that the SM species growing in the high Andean region of central Peru is a potential source of bioactive. The differences observed are probably due mainly to the genetic variability of the species and the area of cultivation.

Considering the effect of temperature, it was observed that for the isotherms obtained at 35 and 55 °C, the extraction yield was higher at 250 bar. However, it was also observed that 45 °C significantly decreased the extract yield at 250 bar, which is attributed to the increased vapor pressure of target molecules present in the SM extract, leading to a decrease in the CO₂ solvation power [50]. However, after increasing the pressure to 350 bar, a considerable increase in the extraction yield was observed at 45 °C, as the system had overcome the crossover region under these conditions. The crossover region consists of the overlap of solubility of the extract in CO₂ as the temperature increases [51]. At 150 bar, it was observed that the extract yield increased after the temperature increased from 35 to 45 °C, and then decreased with further temperature increases from 45 to 55 °C. This phenomenon occurred because at pressures lower than the crossover pressure (in this work, possibly between 250 and 350 bar), the effect of CO₂ density predominates in the extraction. For instance, at 150 bar, the density of CO₂ at 45 °C is approximately 0.742 g/mL, which is next to the densities of alcohols used in conventional extraction of essential oils like methanol (0.792 g/mL), which explain the affinity of extract to CO₂ at the selected condition compared to 55 °C, where the density of CO₂ is 0.654 g/mL [52].

The normality analysis of experimental errors follows a normal distribution according to Anderson–Darling’s normality test at a significance level of 0.05 (p-value = 0.106 and Anderson–Darling’s statistic was 0.592). On the other hand, the analysis of the homogeneity of variances using the Bartlett statistic (α = 0.05) showed homogeneity across variances (p-value = 0.972 and Bartlett statistic = 2.25). Therefore, the results of the test of normality and homogeneity of variations suggest that it is pertinent to proceed with the analysis of variations to determine whether there is a significant effect in terms of individual or interaction of factors (pressure and temperature) on the DLSM extract yield.

Table 1. Analysis of variance (ANOVA) on the effects of temperature and pressure of SFE.

Source	DF	Seq SS	Contribution (%)	Adj SS	Adj MS	F-Value	p-Value
T	2	0.05065	14.43	0.05065	0.025325	10.03	0.005
P	2	0.06213	17.70	0.06213	0.031064	12.30	0.003
T × P	4	0.21553	61.40	0.21553	0.053883	21.34	0.000
Error	9	0.02272	6.47	0.02272	0.002525
Total	17	0.35103	100.00

T: temperature, °C; P: pressure, bar; DF: degrees of freedom; Seq SS: sequential sums of squares; Adj SS: adjusted sums of squares; Adj MS: adjusted mean squares.

presents the ANOVA results for the extract yield obtained under various experimental conditions. The results of the ANOVA, with α = 0.05, indicate that the interaction between temperature and pressure levels has a significant effect (p-value = 0.00) on the yield of the DLSM extract (Table 1). Likewise, temperature and pressure have a significant individual effect on the extract yield. The effect of the thermodynamic variables in the SFE process can vary depending on the raw material, as in the case of the extraction of oil from sucupira seeds, it was reported that the temperature × pressure interaction were not significant effect on the yield [53], a similar observation was carried out in samples of Acca sellowiana (O. Berg) Burret [54].

The dried and milled SM leaves, as well as the extract collected under optimal conditions (45 °C and 150 bar), are shown in Figure 3. The extract (Figure 3) has an amber coloration and an oily texture. The oily texture of the SM extract is due to the fat-soluble nature of its major compounds, such as the sesquiterpenoid [55]. A pale yellow color was observed in a fraction of the SM leaves extract obtained with supercritical CO₂ at 90 bar and 50 °C [40]. The fractionation of the SM extract performed by Marongiu et al. [40], could explain the difference in the color of the extract obtained by these authors and us. On the other hand, the color of leaves before and after SFE under the optimal conditions is observed in Figure 3B and C. The colorimetric analysis of SM leaves after the SFE increased the lightness (L* coordinate,

Table 2. CIELAB parameters of DLSM, before and after SFE extraction at 45 °C and 150 bar.

DLSM	CIELAB Parameters
	L*	ΔL*	a*	Δa*	b*	Δb*	ΔE*
Before extraction	39.19 ± 0.24	39.21	−4.26 ± 0.17	0.41	18.85 ± 0.15	15.48	42.16
After extraction [56]	78.40 ± 0.16		−3.85 ± 0.18		34.33 ± 0.23

), decreased the green color coordinate (a*, Table 2), and increased the yellow color (b* coordinate, Table 2). Such color variations are potentially attributed to the extraction of pigments during SFE.

3.2. Mathematical Modeling

Figure 4 shows the OCE of DLSM, plotted as cumulative yield versus extraction time and cumulative yield versus S/F. The adjustable parameters for the mass transfer models, along with the correlation factor and mean square errors (MSE) obtained for each model, are presented in

Table 3. The adjustable parameters, mean square error (MSE), and correlation factor (R²) of mass transfer models applied to the SC-CO₂ extraction of S. molle at 45 °C and 15 MPa.

Model	Parameters	Result
Spline	tCER (min)	27.00
	b0 (g/min)	5.507 × 10−3
	b1 =MCER (g/min)	3.875 × 10−3
	b2 =MFER (g/min)	−3.343 × 10−3
	RCER (% g ext/100 g feed)	4.052
	YCER (g ext/g CO2)	1.178 × 10−3
	R2	0.984
	MSE	3.95 × 10−4
Esquível	b (min)	99.08
	R2	0.994
	MSE	7.6 × 10−4
Martínez	tm (min)	1.0 × 10−11
	b (min−1)	2.279
	R2	0.985
	MSE	4.26 × 10−3

. The lowest deviation between experimental and correlated data was obtained by the Spline model (Table 3). Despite the highest correlation factor (R²), the Esquível model showed the highest deviation between the experimental and predicted data, compared to the Spline, indicating that R² alone does not fully describe the model’s ability to predict the OEC. The Esquível model predicts the OEC, like the variation in mass of extract absorbed with adsorbate pressure given by the Langmuir isotherm. Martinez et al. [44] propose a model that uses the logistic growth equation to describe OECs, considering the solute as a pseudo-pure component.

The Esquível et al. [47] and Martínez et al. [44] models present a few adjustable parameters: b (min) for the Esquível model and b (min⁻¹) and t (min) for the Martínez model. For this reason, these models do not provide sufficient information to describe the types of mass transfer mechanisms involved in the supercritical fluid extraction (SFE) of solid matrices. Additionally, the lack of physical meaning of the parameters renders these types of models inapplicable for process design and scale-up, despite serving as a simple alternative to describe the evolution of the SFE process using empirical kinetic equations.

Considering the Spline model, the duration of the CER period (t_CER) was 27 min (Table 3). In the CER period, represented by the first adjusted line, occurs the extraction of the soluble material available on the surface of the plant matrix. The R_CER of 4.052 g/100 g corresponded to approximately 70% of the experimental global yield of 5.56 g/100 g obtained for the experimental OEC, which is consistent with the literature, which states that during the CER period, approximately 70–90% of the soluble material is extracted [46].

This result is relevant for the further scale-up techno-economic assessment of Schinus molle (SM) leaf extraction via SFE. Key factors such as overall extraction yield, extract quality, and processing costs are critical factors in decision making for industrial implementation. Compared to traditional methods such as distillation, these factors become even more significant. It is important to note that, although general economic trends for SFE are documented, its economic feasibility varies on a case-by-case basis, because of raw material properties, process conditions, location, and market factors [57].

The interpretation for the negative b₂ (or M_FER, in Table 3) is that neither external nor internal diffusion mass transfer mechanisms are relevant to the OEC.

3.3. SFE Extract Composition

The relative composition of DLSM SFE extract obtained at 45 °C and 150 bar is available in

Table 4. Composition of the SFE extract of S. molle leaves obtained at 45 °C and 150 bar.

RT a	Compounds a	MF	MW	Area (%) a	Some Bioactive Properties/Uses b
7.073	Alpha Phellandrene (M)	C10H16	136.23	0.19
7.983	Pseudolimonene (M)	C10H16	136.23	0.17
19.226	Gamma-Elemene (S)	C15H24	204.35	1.17	Antileishmanial activity [65]
21.050	Beta-Elemene (S)	C15H24	204.35	1.15	Antiangiogenic activity [66]
21.591	Alpha-Gurjunene (S)	C15H24	204.35	0.51
21.887	Caryophyllene (S)	C15H24	204.35	1.83	Insecticidal activity [67]
22.959	Humulene (S)	C15H24	204.35	0.63
23.194	9-epi-(E)-Caryophillene (S)	C15H24	204.35	0.34
23.828	Germacrene D (S)	C15H24	204.35	0.26
24.323	Bicyclogermacrene (S)	C15H24	204.35	12.68	Larvicide [60]
24.457	Alpha-Muurolene (S)	C15H24	204.35	0.20
24.893	Cubebol (St)	C15H26O	222.37	0.59
25.012	Not identified	-	-	4.54
25.183	6-epi-shyobunol (St)	C15H26O	222.37	4.35
25.914	Elemol (St)	C15H26O	222.37	10.42	Repellent [61] Fragrance [68]
26.416	Palustrol (St)	C15H26O	222.37	0.30
26.661	Germacrene D-4-ol (St)	C15H26O	222.37	6.31
27.124	Viridiflorol (St)	C15H26O	222.37	0.80
27.242	Not identified	-	-	0.71
27.453	Ledol (St)	C15H26O	222.37	0.48
28.193	Epiglobulol (St)	C15H26O	222.37	0.32
29.274	Not identified	-	-	0.74
29.916	Shyobunol (St)	C15H26O	222.37	33.60
32.231	Gamma-Gurjunene (S)	C15H24	204.35	5.73
33.018	Not identified	-	-	1.02
47.281	Linolenic acid (Fa)	C18H30O2	278.4	0.09
50.602	Squalene (T)	C30H50	410.7	0.36
56.688	Beta-Amyrone (Tp)	C30H48O	424.7	3.28
57.110	Beta-Amyrin (Tp)	C30H50O	426.7	0.62
57.564	Lupeone (Tp)	C30H48O	424.7	6.58
Total area				99.97

MF: molecular formula, MW: molecular weight, RT: retention time (min), M: monoterpene, S: sesquiterpene, St: sesquiterpenoid, FA: fatty acid, T: triterpene, and Tp: triterpenoid. ^a Paucarchuco Soto and Padilla Pacahuala [56]. ^b Reported in the scientific literature.

. In the extract chromatogram, a prominent presence of shyobunol, bicyclogermacrene, elemol, lupeone, germacrene D-4-ol, and gamma-Gurjunene was observed (Figure 5). Shyobunol was the major compound in the extract studied in this work. Interestingly, this compound was found in the lowest amounts in the SFE extracts of SM at 90 bar and 50 °C [39], and in Citrus limon (L.) Osbeck essential oil [58] and different parts of Bolivian SM [59]. Bicyclogermacrene is the second major compound in the DLSM SFE extract, whose presence was reported previously in the SM essential oils extracted via SFE from the leaves [39,41], and resin [6]. Bicyclogermacrene is a compound also found in Heracleum sprengelianum leaves, which presented larvicide activity [60]. Other important compounds found in the DLSM SFE extract include: (a) elemol, found previously in SM in essential oil [8,13,16,18,40] and SFE extract [40], which has been applied as repellant agent against ticks [61], (b) lupeone, a compound detected in the extracts of Boscia coriacea (Pax.) peels, showed anticancer potential [62], (c) germacrene D-4-ol, found in the essential oil of Artemisa species, that showed larvicide activity against Aedes aegypti L. [63], (d) gamma-Gurjunene, a compounds found at highest amount in Pluchea indica (L.) Less. tea [64]. The DLSM SFE extract obtained presents molecules with important bioactive properties and has the potential to be used as an ingredient in products for the chemical, cosmetic, and pharmaceutical industries.

4. Conclusions

This work studied the extraction of S. molle leaves using supercritical fluid extraction (SFE). The extraction yields were affected by the temperature and pressure of supercritical CO₂; the highest and lowest yields were observed under conditions of 150 bar and 45 °C, and 150 bar and 55 °C, respectively. Under the highest yield conditions, it was possible to obtain 5.69% w/w extract from the DLSM for an S/F of 54.8 and 140 min of extraction. The Spline model precisely described the OECs plotted under the conditions of best extraction yield with two straight lines. The model calculated the duration of the constant extraction rate to be 27 min, during which approximately 70% of the total extract yield was obtained. The SFE extract consisted mainly of sesquiterpenoids, sesquiterpene, and triterpenoids. The compounds identified in the present study possess diverse bioactive properties, according to the scientific literature, suggesting their potential for the functional products industry. Our results show that the SFE extract of S. molle leaves produced in Tarma, Peru, has potential to be used as an ingredient in products with functional properties.