Insights into the Supercritical CO₂ Extraction of Perilla Oil and Its Theoretical Solubility

Abstract

In the current research, the supercritical carbon dioxide (_SCCO₂) procedure was used to extract volatile oils from perilla leaves. The yields of the volatile oils and the four main constituents, limonene, perillaldehyde, β-caryophyllene, and (Z,E)-α-farnesene obtained by the _SCCO₂ procedure were 1.31-, 1.12-, 1.04-, 1.05-, and 1.07-fold higher than those obtained by the hydrodistillation technique, respectively. Furthermore, the duration and temperature of extraction were 40 min and 45 °C lower, respectively, in the former procedure compared to the latter technique. These advantages reveal that _SCCO₂ not only obtains high-quality extracts, but also meets the requirements of green environmental protection. The theoretical solubilities of the volatile oils acquired by the _SCCO₂ dynamic extraction at various temperatures and pressures were 1.385 × 10⁻³–8.971 × 10⁻³ (g oil/g CO₂). Moreover, the three density-based models were well correlated with these theoretical solubility data, with a high coefficient of determination and low average absolute relative deviation.

1. Introduction

Perilla frutescens (L.) Britton is a famous edible and medicinal plant that belongs to the Lamiaceae family [1,2]. Due to its special flavor, perilla leaves have a special flavor, they are often eaten directly as fresh vegetables or used as food additive material or in sushi. Furthermore, perilla leaves are a widely used traditional medicinal material because of their rich and diverse pharmacological properties, such as anticancer, antioxidative, neuroprotective, anti-inflammatory, and antimicrobial activities [2,3,4]. Essential oil has been reported to be an important bioactive ingredient in perilla leaves [5]. Perilla essential oil is not only used as a food and nutritional additive, but also has been extensively researched for its anticancer, antioxidative, neuroprotective, anti-inflammatory, and antimicrobial effects [3,6]. The chemical composition of perilla essential oil varies according to the variety, geographical factors, climatic conditions, and planting and harvest times. However, for red-leafed varieties of P. frutescens, the main volatile component has been found to be perillaldehyde [3,6]. Gas chromatography was used to study essential oils obtained from perilla leaves, providing qualitative and quantitative analyses with sufficient accuracy for the aforementioned components [5].

Hydrodistillation (HD) and steam distillation (STD) have been widely used to separate essential oils from P. frutescens because of the use of water as the solvent and simple operation [7,8,9]. However, these traditional procedures require the use of high temperatures; they often cause the degradation of heat-sensitive ingredients, thus affecting the quality of essential oils. Moreover, the procedures often cause the mixing of water-soluble components and essential oils, and further separation procedures cause the loss of essential oils. However, the long extraction time is the most frequently criticized drawback of these traditional procedures.

Because of the unique properties of supercritical carbon dioxide (_SCCO₂), such as a low critical point (7.4 MPa, 31.1 °C), chemical inertness, and high penetration and diffusion capabilities, _SCCO₂ extraction can perfectly solve the shortcomings of traditional procedures [10]. This is mainly due to the low critical point of CO₂, it does not need a very high temperature to achieve good extraction results, so it does not cause degradation of heat-sensitive components. Additionally, _SCCO₂ does not react with the constituents of the extract, so the _SCCO₂ procedure obtains a highly stable extract. Furthermore, after the extraction process is decompressed, CO₂ and the extract can be completely separated, so there is no concern about solvent residue in the extract. Based on the abovementioned advantages, _SCCO₂ extraction can obtain excellent quality extracts that are very suitable for the food, functional nutrition, cosmetics, and pharmaceutical industries. In addition, because of the high penetration and diffusibility of _SCCO₂, it effectively promotes the penetration of the solvent through the plant substrate, thereby accelerating the desorption and release from the substrate of the analyte, which then diffuses into the solvent, thus shortening the extraction time [11,12,13]. Therefore, _SCCO₂ extraction meets the requirements of economic efficiency in the industrialization process.

Based on the foregoing description, it is clear that _SCCO₂ is an excellent extraction solvent for nonpolar to low-polar components. Therefore, _SCCO₂ extraction has been widely used to extract volatile components from different substrates [14]. However, literature reports on the extraction of perilla oil with _SCCO₂ are scarce. In addition, the solubility of the analyte in _SCCO₂ is one of the important data for judging whether the _SCCO₂ extraction procedure is feasible and even good or bad in progress. Furthermore, the solubility data of the analyte are an indispensable parameter for subsequent pharmacokinetic experiments.

Although the diverse uses and pharmacological activities of perilla oil have been widely reported, data on its solubility in _SCCO₂ remain very limited. Therefore, this study primarily uses the _SCCO₂ dynamic extraction of perilla oil and carefully explores the effects of the CO₂ flow rate, temperature, and pressure on the yield to obtain the highest yield and best quality of the oil. Furthermore, three density-based correlation models with excellent accuracy are used to correlate the solubility of perilla oil obtained through experiments to expand the solubility data for subsequent pharmacokinetic experiments.

2. Materials and Methods

2.1. Raw Materials and Reagents

Dried P. frutescens leaves (the red-leaf form) were purchased from different local herbal shops (Kaohsiung, Taiwan) and then authenticated, triturated, sieved (W.S. Tyler, Mentor, OH, USA, 0.36 mm), and deposited [15]. Subsequently, the moisture content of the herb sample measured by volumetric Karl Fischer titration was 8.71% [16]. Helium (99.99%) and carbon dioxide (99.99%) were purchased from the Yun-Shan Gas Co. Ltd. (Tainan, Taiwan). Perillaldehyde, β-caryophyllene, (Z,E)-α-farnesene and limonene were obtained from Sigma Chemical Co. (St. Louis, MO, USA); n-hexane was bought from Merck Co. (Darmstadt, Germany).

2.2. Supercritical Carbon Dioxide (_SCCO₂) Extraction

A semibatch flow extraction procedure (Isco 260D, Lincoln, NE, USA) was used for _SCCO₂ extraction [17]. The extraction procedure was carried out by adding 20 g of plant sample (0.36 mm) into a stainless steel vessel (SS304, i.d. of 22 mm and length of 300 mm), which was later immersed in a large stainless steel water bath (SS304, length: 300 mm, width: 200 mm, height: 500 mm). After reaching the desired temperature and pressure, a static extraction stage (for 30 min) followed by a dynamic extraction stage (5–210 min) was carried out [18]. The oils were collected in two consecutive separators. The first separation tank is operated at 4 °C and 9 MPa, while the second separation tank is operated at 4 °C and 0.15 MPa.

2.3. Essential Oil Extraction by Hydrodistillation (HD)

In brief, 100 g of an herbal sample (0.36 mm) was placed in a 1.5 L distillation flask (3 holes), a certain amount of distilled water was added, and the device was connected with a Clevenger condenser. Subsequently, the distillation flask was immersed in a temperature-controlled water bath (Haake F3-K, Haake, Karlsruhe, Germany). After the desired temperature (100 °C) was obtained, a 4-h static stage extraction was performed for the HD procedure. The essential oil was further separated by the action of gravity. Anhydrous sodium sulfate was used to dry the obtained oils [19,20].

2.4. Gas Chromatographic (GC) Analysis

GC analyses of the essential oils were performed using a GC/flame ionization detector (FID) system (Shimadzu, model CG-14A, Kyoto, Japan) equipped with a DB-5 silica capillary column (30 m × 0.25 mm × 0.25 μm, J&W Scientific, Folsom, CA, USA) [21]. The quantities of the four main constituents, limonene, perillaldehyde, β-caryophyllene, and (Z,E)-α-farnesene were evaluated by comparing their peak areas to those of the calibration curves of the standards of constituents.

2.5. Statistical Analysis

All yields are estimated on the basis of plant dry weight, which is expressed using the average and standard deviation (SD) of three experimental results. The SD was calculated as follows:

$$SD=\sqrt{\frac{{\displaystyle \sum _{i=1}^n{(y_{e,i}-y_m)}^2}}{n-1}}$$

(1)

where y_e,i is the experimental value, y_m is the mean value, and n is the number of experimental runs [22].

To evaluate correlations in the applied models, the two objective functions average absolute relative deviation (AARD(%)) and coefficient of determination (R²) were determined using the predicted and experimental values. These parameters were calculated using Equations (2) and (3).

$$AARD(\%)=\frac{100\%}{n}{\displaystyle \sum _{i=1}^n\left|\frac{y_{p,i}-y_{e,i}}{y_{e,i}}\right|}$$

(2)

$$R^2=1-\frac{{\displaystyle \sum _{i=1}^n{(y_{e,i}-y_{p,i})}^2}}{{\displaystyle \sum _{i=1}^n{(y_{e,i}-y_m)}^2}}$$

(3)

where y_p,i is the predicted value corresponding to point i.

3. Results and Discussion

3.1. Essential Oils Obtained by HD

Hydrodistillation (HD) and steam distillation (STD) are well-known standard procedures for extracting essential oils from natural sources. Therefore, to evaluate the performance of the _SCCO₂ extraction, this study first used the HD procedure for 4 h to extract the essential oil from P. frutescens leaves. The obtained essential oil has a pale yellow color and a strong fragrance. The yields of the essential oil and its four main components are shown in

Table 1. Comparison of the extraction conditions and yields obtained by hydrodistillation (HD) and supercritical carbon dioxide (_SCCO₂) extraction.

	HD	SCCO2 Extraction
Sample of P. frutescens leaves	P1	P1
Mean particle size (mm)	0.36	0.36
Plant weight (g)	100	20
Static extraction time (min)	—	30
Dynamic time (min)	—	170
Extraction time (min)	240	200
Extraction temperature (°C)	100	55
Extraction pressure (MPa)	—	33.0
CO2 flow rate (g/min)	—	0.37
Yields
oil (%, w/w) 1	1.02 ± 0.02	1.33 ± 0.04
limonene (%, w/w) 2	10.59 ± 0.50	11.81 ± 0.45
perillaldehyde (%, w/w) 2	39.07 ± 1.62	40.52 ± 1.50
β-caryophyllene (%, w/w) 2	9.14 ± 0.33	9.57 ± 0.36
(Z,E)-α-farnesene (%, w/w) 2	4.95 ± 0.21	5.30 ± 0.20

¹ 

Values are written as the mean ± SD (g of oil/g of dry plant weight) of the extracted oils.

² 

Values are written as the mean ± SD (g of constituent/g of oil) of four replications.

. The yields of essential oils and individual components were expressed in terms of the mass percent of the essential oil per gram of dry plant (%, g of oil/g of dry plant) and the mass percent of each component per gram of essential oil (%, g of component/g of oil), respectively.

3.2. Influence of the CO₂ Flow Rate

The extraction kinetic curve of the natural solid substratum using the _SCCO₂ dynamic procedure is usually called the overall extraction curve (OEC), which is often expressed as a graph of extraction yield versus extraction time or the mass of spent CO₂ for the extracting conditions (T, P, CO₂ flow rate, and cosolvent) [23]. The OEC not only predicts the extraction capacity of the procedure but also indicates the composition and physicochemical and biological characteristics of the extract. Furthermore, based on the experimental data of the OEC, a mathematical model of the extraction procedure can be derived to establish the parameters required by the extraction procedure, which can then be used as the basis for establishing optimized industrial procedures. Experimental OEC data fitted to a spline using two straight lines can usually be clearly divided into three stages: the constant extraction rate (CER), decreasing extraction rate and diffusion period [24,25,26]. Consequently, according to the kinetic parameters obtained in the CER period, such as the duration, mass transfer rate, and yield, the analyte concentration in the solvent phase at the vessel outlet (Y_CER) is further calculated. At a certain temperature and pressure and the most appropriate CO₂ flow rate, the Y_CER value will approach the maximum value (Y_CER *), which can be considered the theoretical solubility of the analyte in _SCCO₂. The proper CO₂ flow rate have to be sufficiently low to guarantee that the _SCCO₂ is saturated with solute at the outlet of the vessel, but it cannot restrict the mass transfer of the extraction process. Therefore, the CO₂ flow rate is one of the most crucial factors for determining the solubility of the solute in the supercritical solvent phase via the _SCCO₂ dynamic extraction method.

To evaluate the influence of CO₂ flow rate on the oil yield, _SCCO₂ extraction was performed at a static stage of 30 min followed by a dynamic stage of 5–270 min at a mean particle size of 0.36 mm [27]. To establish the OEC data, the extracts were collected at equal intervals of 5–10 min, and qualitative and quantitative analyses were further performed using GC analysis. The OECs of volatile oils using _SCCO₂ dynamic extraction at a serial flow rates were expressed as the oils/dry plant mass ratio (g/g, %) as a function of the CO₂/dry plant mass ratio (Figure 1). Then, the OECs obtained at different CO₂ flow rates were fitted using two straight lines, and the Y_CER value obtained at each flow rate in the CER period (first straight line) was therefore generated, as shown in Figure 2.

Increasing the CO₂ flow rate (0.09 to 0.37 g/min) increased the contact area and collision opportunity frequency between the solvent and the plant sample, which in turn increased the value of Y_CER (Figure 2). Additionally, the greater the CO₂ flow rate is, the steeper the concentration gradient difference between the analyte and the _SCCO₂ is, which promotes the diffusion and mass transfer of the analyte and thereby enhances the value of Y_CER. However, if the CO₂ flow rate is too high (0.37 to 0.76 g/min), because of the declined extent of saturation of the supercritical solvent at higher flow rates, the value of Y_CER begins to decrease. Using _SCCO₂ extraction, a flow rate of 0.37 g/min generated the maximum value of Y_CER (Y_CER*) and was therefore determined as an appropriate CO₂ flow rate for evaluating the theoretical solubility of volatile oil in _SCCO₂.

3.3. Influences of Temperature and Pressure

Pressure and temperature are the most important factors for the performance and selectivity of _SCCO₂ extraction, and this importance has been verified for different natural species [28]. To estimate the effects of both factors on the oil yields, _SCCO₂ extraction was conducted at pressures ranging from 10.5 to 33.0 MPa and temperatures ranging from 32 °C to 55 °C, while other conditions were kept fixed as mentioned above.

Figure 3 indicates that when the pressure increases from 10.5 MPa to 33.0 MPa, the yield of volatile oil increases substantially. This result is due to the increase in the density of the supercritical CO₂ with the increase in pressure, so the solubility of the oil in the supercritical solvent increases, enhancing the yield of oil [29,30]. However, at a pressure of 33.0 MPa, the increase in the oil yield was smaller, which may be due to the decrease in mass transfer and diffusion parameters as the pressure increased.

As shown in Figure 3, the effect of temperature obviously has two opposing trends on the yields obtained by _SCCO₂ extraction at different pressures. Under the lower pressure of 10.5 MPa (Figure 3a), because it is closer to the critical pressure of CO₂ (7.39 MPa), when the extraction temperature increases from 32 °C to 55 °C, the density of supercritical CO₂ drops substantially, so the _SCCO₂ extraction capacity is reduced. However, under the four higher pressures (18.5, 23.5, 28.5, and 33.0 MPa) (Figure 3b–e), the extraction temperature obviously increases (32 °C to 55 °C), which is conducive to an increase in the extraction yield.

Although the increase in temperature causes the density of supercritical CO₂ to decrease, the vapor pressure, diffusion coefficient, and mass transfer coefficient of the solute and solvent all increase with the temperature. The driving forces of these two different trends compete with each other; that is, the rise in the latter driving force offsets the fall in the former driving force, which benefits the improvement in the extraction capacity of _SCCO₂. The competing effects of the two apparently contradictory driving forces caused by the extraction temperature result in a crossover trend when _SCCO₂ dynamically extracts the perilla oil [31]. Similar to this phenomenon, it has also been observed that _SCCO₂ dynamically extracts different analytes, such as rice bran oil [31], crude oil [32] and coenzyme Q10 [33].

3.4. Characterization of Oils Obtained by _SCCO₂ Extraction and HD

As indicated in Table 1, the yields of oil and the main volatile components obtained by _SCCO₂ extraction for 200 min at 33.0 MPa and 55 °C were obviously higher than those of the HD procedure. The yield of volatile oils was 23.9% higher when acquired by _SCCO₂ extraction instead of HD. In addition, the contents of perillaldehyde, limonene, caryophyllene and (Z,E)-α-farnesene were approximately 1.02-, 1.12-, 1.05-, and 1.07-fold higher, respectively, when acquired by the _SCCO₂ procedure instead of HD extraction. In addition, the extracts obtained by _SCCO₂ extraction are stronger and deeper than those obtained by HD in terms of aroma and color. Therefore, it is inferred that _SCCO₂ extraction can obtain higher quality perilla oil than the HD procedure. Furthermore, the _SCCO₂ procedure reduced the time required (1.2-fold) and the operating temperature (45 °C). Therefore, these advantages of the _SCCO₂ procedure enable it to meet the green requirements.

3.5. Theoretical Solubility of Volatile Oils and Models

The OECs in Figure 3 obtained by _SCCO₂ dynamic extraction at different pressures and temperatures were further fitted to a spline using two straight lines. The slope of the first straight line (CER period) was used to calculate the theoretical solubility of volatile oil in supercritical CO₂, and the results are shown in

Table 2. Solubility data for the P. frutescens oils obtained by dynamic _SCCO₂ extraction.

T (°C)	P (MPa)	ρ (kg/m3) 1	Y*oil × 103 (g oil/g CO2) 2
32	10.5	760.051	3.787 ± 0.152
	18.5	867.666	5.199 ± 0.20
	23.5	904.672	5.835 ± 0.234
	28.5	933.114	6.625 ± 0.265
	33.0	953.445	6.898 ± 0.276
38	10.5	667.094	3.105 ± 0.124
	18.5	834.302	5.783 ± 0.232
	23.5	877.501	6.496 ± 0.260
	28.5	909.376	7.308 ± 0.292
	33.0	931.632	8.065 ± 0.321
43	10.5	578.482	2.496 ± 0.101
	18.5	804.654	6.389 ± 0.256
	23.5	854.039	7.145 ± 0.287
	28.5	889.141	7.904 ± 0.319
	33.0	913.159	8.506 ± 0.343
49	10.5	441.899	1.818 ± 0.073
	18.5	766.348	6.742 ± 0.269
	23.5	824.725	7.409 ± 0.296
	28.5	864.279	8.227 ± 0.334
	33.0	890.625	8.853 ± 0.355
55	10.5	361.884	1.385 ± 0.055
	18.5	725.117	7.358 ± 0.296
	23.5	794.638	7.970 ± 0.321
	28.5	838.944	8.759 ± 0.352
	33.0	867.733	8.971 ± 0.367

¹ 

ρ: density of the scCO₂.

² 

Y^*_oil: the theoretical solubility of volatile oil in scCO₂.

. At all five extraction temperatures, the theoretical solubility increased substantially with pressure because of the increase in the supercritical CO₂ density. This result is similar to those of most studies using _SCCO₂ dynamic extraction [33,34].

However, when examining the influence of temperature on the theoretical solubility of oils in supercritical CO₂, the phenomenon of retrograde solubility in the supercritical solvent was inspected at 10.5 MPa (Table 2), where an increase in temperature leads to a decrease in the theoretical solubility under a pressure below that of the crossover zone, and at a pressure higher than that of this zone, the theoretical solubility of oils increases with temperature (32 °C to 55 °C). When _SCCO₂ is used to extract different analytes dynamically, retrograde solubility behavior is often observed [33,35].

The Chrastil [36] model is the most commonly used model for correlating solubility data and describes the relationship between the solubility of the volatile oil (Y*_oil) and the density of supercritical CO₂ (ρ) as follows:

$$\ln (Y^{\ast }{}_{oil})=a_0+a_1\ln (\rho )+\frac{a_2}{T}$$

(4)

where T is the extraction temperature (K); a₀, a₁ and a₂ are the model parameters; and a₂ is further denoted as

$$a_2=\frac{-\Delta H_T}{R}$$

(5)

where ∆H_T is the total heat of the reaction or solution, and R is the universal gas constant (8.314 J/mol K).

Additionally, two models frequently utilized to correlate experimental data were proposed by Bartle [37] and Kumar and Johnston (K–J) [38]. The common features of these two models are simplicity and high accuracy. In the Bartle model, the correlation between the experimental data and the density of supercritical CO₂ is demonstrated in a semi-logarithmic relationship.

$$\ln (Y^{\ast }{}_{oil})=b_0+b_1{\rho }_{}+\frac{b_2}{T}$$

(6)

where b₀, b₁ and b₂ are the model parameters; and b₂ is further denoted as

$$b_2=-\frac{\Delta H_T}{R_{}}$$

(7)

Furthermore, in the Bartle model, in addition to the solubility data, density and temperature, the pressure parameter is added and is expressed in the following formula.

$$Ln(\frac{Y^{\ast }{}_{oil}P}{P_{ref}})=c_0+c_1(\rho -{\rho }_{ref})+\frac{c_2}{T}$$

(8)

where c₀, c₁ and c₂ are the model parameters; P_ref is 0.1 MPa; ρ_ref is a reference density with a value of 700 g/L; and c₂ is further expressed as

$$c_2=-\frac{\Delta H_{vap}}{R}$$

(9)

Then, the solubility data obtained by _SCCO₂ dynamic extraction at different temperatures and pressures (Table 2) was linearly regressed using Equations (4) (Chrastil model), (6) (K–J model) and (8) (Bartle model), as shown in Figure 4, Figure 5 and Figure 6, respectively. The coefficient of determination (R²) was high, in the range of 0.992–0.999, which means that the three models mentioned above were sufficiently accurate to illustrate the solubility of the oils in supercritical CO₂. Furthermore, Equations (4), (6), and (8) were used to perform multiple linear regression on the solubility data of the volatile oil, according to which all parameters of the three models were obtained (

Table 3. The fitted solubility parameters of three density-based models and the approximate heat of vaporization, total heat of solution and heat of solvation for P. frutescens oils obtained by dynamic _SCCO₂ extraction.

Model	n4	Parameters			AARD(%) 5	Thermodynamic Parameters
		a0:	a1:	a2:		∆HT,C (kJ/mol) 6
1 1	25	–13.29	2.52	–2750.33	1.39	22.87
		b0:	103b1:	b2:		∆HT,K-J (kJ/mol) 7
2 2	25	1.58	3.56	–3033.85	1.53	25.23
		c0:	103c1:	c2:		∆Hvap(kJ/mol) 8
3 3	25	14.19	6.97	–4701.20	3.25	39.08
						∆Hsolv (kJ/mol) 9
						–15.03

¹ 

Chrastil model: $\ln (y^{*}{}_{oil})=a_0+a_1\ln (\rho )+\frac{a_2}{T}$,

² 

K-J model: $\ln (y^{*}{}_{oil})=b_0+b_1\rho +\frac{b_2}{T}$,

³ 

Bartle model: $\ln (\frac{y^{*}{}_{oil}P}{P_{ref}})=c_0+c_1(\rho -{\rho }_{ref})+\frac{c_2}{T}$, where y* is the theoretical solubility; P is the pressure (MPa); P_ref is 0.1 MPa; ρ is the density of the scCO₂ (kg/m³); ρ_ref is a reference density (700 kg/m³); T is the temperature (K); a₀, a₁, a₂, b₀, b₁, b₂, c₀, c₁, and c₂ are the fitted parameters.

⁴ 

Number of data points used in the correlation.

⁵ 

Average absolute relative deviation. $AARD(\%)=\frac{100}{n}{\displaystyle \sum _{i=1}^n\left|\frac{y_{p,i}-y_{e,i}}{y_{e,i}}\right|}$,

⁶ 

Total heat of solution obtained from the Chrastil model, ∆H_{T, C} = −a₂ × 8.314 J/mol-K.

⁷ 

Total heat of solution obtained from the K-J model, ∆H_{T, K-J} = −b₂ × 8.314 J/mol-K.

⁸ 

Heat of vaporization obtained from the Bartle model, ∆H_vap = −c₂ × 8.314 J/mol-K.

⁹ 

Heat of solvation, $\Delta H_{solv}=\frac{1}{2}(\Delta H_{T,C}+\Delta H_{T,K-J})-\Delta H_{vap}$.

). Table 3 shows that all AARD(%) were less than 3.3% (1.39–3.25%), which again means that these three models reliably and accurately describe the solubility of volatile oil in supercritical solvents. In addition, using the three parameter values of a₂, b₂, and c₂, the heat of the solution (∆H_T), vaporization (∆H_vap), and solvation (∆H_solv) for the supercritical binary systems were further calculated using Equations (5), (7), and (9), respectively (Table 3). The ∆H_T values obtained from the Chrastil (∆H_T,C) and K–J (∆H_T,K-J) models were 22.87 and 25.23 kJ/mol, respectively, and the value of ∆H_vap obtained using the Bartle model was 39.08 kJ/mol. It shows that vaporization is an endothermic process for binary systems. Therefore, the value of ∆H_solv was further calculated using the following equation [39]:

$$\Delta H_{solv}=\frac{1}{2}(\Delta H_{T,C}+\Delta H_{T,K-J})-\Delta H_{vap}$$

(10)

The thermodynamic parameters in Table 3 indicate that the value of ∆H_solv is −15.03 kJ/mol, which demonstrates that solvation is an exothermic process for the oil-supercritical CO₂ binary systems. The value of ∆H_solv is negative because ∆H_vap was higher than ∆H_T in the oil-supercritical binary systems.

4. Conclusions

_SCCO₂ extraction and hydrodistillation (HD) extraction were used to separate the oils and the four main constituents in oils from Perilla frutescens leaves. _SCCO₂ extraction obtains higher yields of the oil and its four main components than the latter procedure, and uses milder operating conditions (duration time and temperature). Additionally, the theoretical solubilities of the oils obtained by the _SCCO₂ dynamic extraction at various temperatures and pressures were systematically evaluated, and retrograde solubility behavior was found in the oil-supercritical CO₂ binary systems. At a minimum experimental pressure (10.5 MPa), the density of CO₂ dominates the extraction capacity of _SCCO₂; therefore, this extraction procedure is suitable for lower temperatures. However, at higher pressures (18.5, 23.5, 28.5, and 33.0 MPa) the vapor pressure, mass transfer, and diffusion coefficients prevailed in the _SCCO₂ extraction; therefore, a higher temperature benefits the extraction process. Furthermore, the theoretical solubility was excellently correlated with three density-based models. Consequently, the heat of the solution, vaporization, and solvation for the oil-supercritical CO₂ binary systems were perfectly estimated. Because the heat of the solution and vaporization were both positive values, the entire _SCCO₂ extraction was an endothermic process. However, because the heat of solvation was negative, this step is an exothermic process.