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A novel model for multicomponent supercritical fluid extraction and its application to Ruta graveolens
Accepted Manuscript Title: A novel model for multicomponent supercritical fluid extraction and its application to Ruta graveolens Author: Helena Sovov´a Marie Sajfrtov´a Roumiana P. Stateva PII: DOI: Reference:
S0896-8446(16)30295-9 http://dx.doi.org/doi:10.1016/j.supflu.2016.10.008 SUPFLU 3777
To appear in:
J. of Supercritical Fluids
Received date: Revised date: Accepted date:
9-9-2016 13-10-2016 14-10-2016
Please cite this article as: Helena Sovov´a, Marie Sajfrtov´a, Roumiana P.Stateva, A novel model for multicomponent supercritical fluid extraction and its application to Ruta graveolens, The Journal of Supercritical Fluids http://dx.doi.org/10.1016/j.supflu.2016.10.008 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A novel model for multicomponent supercritical fluid extraction and its application to Ruta graveolens Helena Sovováa,* , Marie Sajfrtováa, and Roumiana P. Statevab a
Institute of Chemical Process Fundamentals of the Czech Academy of Sciences, v. v. i., Rozvojová
135, 16502 Prague, Czech Republic b
Institute of Chemical Engineering, Bulgarian Academy of Sciences, Acad. G. Bontchev str., bl.103,
1113 Sofia, Bulgaria *
Corresponding author. E-mail address: [email protected] (H. Sovová).
Graphical abstract
Highlights
Extraction of 2 samples of rue different in contents of coumarins (C) and waxes (W)
Solubility of xanthotoxin (one of common rue furanocoumarins) in CO2 was measured
C+W mixture solubility in CO2 was modeled applying a thermodynamic framework
Extraction curves were calculated using the results of thermodynamic modeling
Abstract In this work, a multicomponent model for understanding the relationship between the chemical compositions of an extract and extracted plant is developed and presented for the first time. Its robustness and efficiency were validated on the example of furanocoumarins and waxes extracted from aerial parts of common rue with supercritical CO2 at pressures and temperatures (12-30) MPa
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and (313-333) K. For the purpose of modeling, the waxes are represented by n-tritriacontane and furanocoumarins - by xanthotoxin, the solubility of which in CO2 was measured using the dynamic method. A rigorous thermodynamic modeling framework was applied to calculate the compositiondependent solubilities of extracted compounds, which were incorporated in the kinetics model in order to calculate the extraction curves. For individual extraction curves, the average absolute deviation between the calculated and experimental extraction yields, expressed as percentage of the asymptotic extraction yield, was in the range (0.2-5.8)%.
Keywords: supercritical fluid extraction; multicomponent equilibrium; xanthotoxin; waxes; carbon dioxide 1. Introduction Most of the extracts from plants are mixtures of several tens of components and their composition varies in the course of extraction due to the different solubilities of the individual components and/or their different accessibility in the plant matrix. These changes can easily be followed in supercritical fluid extraction (SFE) where semi-continuous set-up allows a separate collection of subsequent extract fractions and their chemical analysis. For example, Reverchon et al. [1] extracted with supercritical carbon dioxide (scCO2) volatile oil from sage and measured different extraction rates of monoterpenes, oxygenated monoterpenes, sesquiterpenes, and oxygenated sesquiterpenes, decreasing in that order in a complete analogy to their decreasing solubility in scCO2. It should be also taken into account that the solubility of a minor component in the solvent can be substantially different from its solubility as a pure substance. Saldana et al. [2], who extracted with scCO2 purine alkaloids caffeine, theobromine and theophylline from herbal mate tea, observed that the solubilities in the binary CO2+purine alkaloid systems were much higher than those obtained during the extraction from plant. In another work, the apparent solubility of carotenoids extracted with scCO2 from freeze-dried tomato skin and pulp was almost one order of magnitude smaller than the solubility of individual carotenoids measured in binary system with scCO2. When co-solvents were used the apparent solubility of carotenoids was increased due to the polarity of co-solvents and perhaps also because of co-solvents’ interaction with the tomato matrix in the multicomponent complex system [3]. Mathematical models for supercritical fluid extraction usually describe the extraction kinetics only globally, regarding the extract as one pseudo-component. Still, several attempts have been made to simulate the evolution of extract composition, distinguishing between volatile oil, cuticular waxes, fatty oil, or other groups of substances in the extract. A simple way to do that is to fit calculated extraction curves separately to each examined substance or group of substances, assuming that extraction is not affected by other co-extracted substances. Such approach was tested for example in
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the model for scCO2 extraction of volatile oil, lipids, and piperine from black pepper seed [4]. However, the approach was developed predominantly in connection with a logistic model, which was applied by Franca and Meireles in their study on the extraction of free fatty acids, triglycerides, and carotene from palm oil fibres [5], and by Martínez et al. [6] who examined the extraction of ginger rhizome oleoresin composed of monoterpenes, sesquiterpenes, and hydrocarbons and by other authors. Chia et al. [7], who recently investigated the possibility of a separate extraction of groups of compounds, applied the above approach in modeling the scCO2 extraction of tocopherols, tocotrienols, and -oryzanol from rice brain. Another approach to modeling extraction of mixtures from plants takes the multicomponent equilibrium into account. Shen et al. [8], who also extracted rice bran oil with scCO2, evaluated the apparent partition coefficients of triglycerides and oil’s minor components. They compared the composition of the saturated oil solution in CO2, determined from initial slopes of the extraction curves of individual oil components, with the composition of oil in the rice bran determined from its nhexane extract. Gaspar [9] evaluated the selectivity of individual classes of components in the scCO2 extraction of volatile oil from oregano bracts under different extraction conditions. Sovova et al. [10] implemented the separation factor of β-sitosterol to triglycerides into a model for scCO2 extraction of sea buckthorn oil from particle surface, where the dependence of the separation factor on extraction pressure and temperature was calculated using thermodynamic models. The idea of implementing the results obtained from the application of a robust thermodynamic framework, allowing reliable calculation of the solubility of a single solid solute/solid solutes mixture, in the model for supercritical fluid extraction kinetics was further developed by Sovova and Stateva [11] in their recent contribution on the extraction of cuticular waxes. The aims of the present contribution are to: i)
outline the features of a novel model for multicomponent supercritical fluid extraction from plants, which introduces a relation that characterizes in a more realistic manner the influence of the initial plant composition changes on the solubility of the solutes in the scCO2. The new model incorporates elements of the approach developed in [11], and further improves and considerably extends its application;
ii)
validate and demonstrate the robustness and reliability of the novel model on the example of the supercritical extraction of furanocoumarins and waxes from aerial parts of Ruta graveolens.
The necessary experimental data for testing the model were obtained by supercritical fluid extraction of two samples of Ruta graveolens, also known as common rue, a plant native to the Balkan Peninsula. This plant is rich in furanocoumarins, substances which sensitize skin to light [12]. On the one hand, furanocoumarins can cause dermatitis or blisters when skin is exposed to the sun, but on the other hand they are efficient in phototherapy [13]. Like coumarin and its other derivatives, furanocoumarins are also efficient antifeedants that protect different plants against pests. The major
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coumarin of R. graveolens is rutamarin, which potential as antiviral drug and as a compound efficient against diabetes was revealed recently [14,15]. In our model, the coumarins were represented by the furanocoumarin xanthotoxin, which solubility in scCO2 was, to the best of our knowledge, measured and reported for the first time in this work. Firstly, the experiments will be presented. Then, the new model for multicomponent supercritical fluid extraction, which takes into consideration the influence of plant composition on the extraction, and the corresponding thermodynamic modeling framework (TMF) applied, will be outlined. The performance and viability of the model and the TMF are subsequently demonstrated on the simulation of coumarins and cuticular waxes extraction from rue, where each of the two groups of substances is represented by a single compound. 2. Experimental 2.1. Chemicals and materials Xanthotoxin (>98%) was purchased from Sigma-Aldrich (St Louis, MO, USA). CO2 (>99%) was supplied by Linde (Praha, CR). Common rue was harvested in two successive years. Its aerial parts were dried. Before extraction they were shortly immersed in liquid nitrogen, cut using a mill with rotating knives, and passed through a sieve with 0.6 mm openings. 2.2. Soxhlet extraction 10 g rue and 250 mL n-hexane were placed in a 500 mL flask of Soxhlet extractor and the herb was extracted for 6 h. The solvent was then evaporated in a rotary vacuum evaporator and the dry extract was weighed and stored for chemical analysis. 2.3. Supercritical extraction Different extraction equipment was used for the rue samples S1 and S2 but the extraction procedure was in both cases identical. The extraction of sample S1 was carried out in an apparatus Spe-ed SFE (Applied Separations, USA). The extraction column (volume 32 mL; inner diameter 14 mm) was filled with 12.8-16.0 g of plant particles placed between layers of glass beads serving as solvent flow distributors. The extractor was connected to the equipment with stainless steel capillaries and placed into the air-conditioned box. Carbon dioxide was sucked from a pressure container using a high-pressure pump cooled by water to 5 °C. The solution flowing from the extractor expanded to the ambient pressure in a heated micrometer valve and the extract fractions were collected in an empty glass vial at room temperature. The flow rate was adjusted to (0.87-0.90) g/min. The quantity of CO2 leaving the vial was measured using a gas meter (Pl 0,1, Spectrum Skutec, CR).
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In the case of the sample S2, the extractor of volume 150 ml with an inner diameter 30 mm was equipped with a water heated jacket. The extraction equipment consisted of CO2 compressor with pressure controller, the extractor, a heated micrometer valve with an adapter for air-tight attachment of a vial where the extract was collected, and a gas meter. The vial was immersed in a cooling bath with ethanol and dry ice. The extractor was connected to the pressure controller and micrometer valve by heated capillaries. The feed was in the range (40-44) g and the flow rate was (1.40-1.45) g/min. In both apparatuses, the rue powder was packed in the extractor vessel between two layers of glass beads separated from rue by thin layers of glass wool. The extractor was pressurized with CO2 and after 15 minutes of static extraction the micrometer valve was opened and the flow rate was adjusted. The extraction pressure and temperature were varied as shown in Table 1. The vials were changed several times in the course of extraction run, their content was weighed before and after removing water with a syringe needle, and they were stored in refrigerator until GC analyses. Extraction pressure and temperature were varied as shown in Table 1. The density of CO2 was obtained from NIST [16]. 2.4. Dynamic measurement of solubility The extractor, a short column of 4 cm3 volume and 8 mm inner diameter, was tightly packed with white powder of xanthotoxin mixed with glass beads, separated by glass wool from layers of glass beads on both ends of the column. The extractor was placed in an air-heated box and connected to the CO2 supply from Isco syringe pump, model 260D (Isco, Inc., USA). The solvent flow was adjusted to 0.1 mL/min in the pump, with the corresponding residence time in the extractor approximately 20 min. The solution from the extractor flowed through a heated micrometer valve to a vial where the extract precipitated. The solubility was determined in the pressure range (12-28) MPa at temperatures (40, 50, and 60) °C. The amount of xanthotoxin extracted with a known amount of CO2, measured in the pump, was determined gravimetrically. As the extract was partially sticking to the inner walls of the valve and to the short capillary, it was not completely collected in the vial. Therefore, we measured the decrease in the mass of the extractor instead of the increase of the mass of the vial. The amount of xanthotoxin extracted with a known amount of CO2, measured in the pump, was determined gravimetrically. As the extract was partially sticking to the inner walls of the valve and to the short capillary, it was not completely collected in the vial. Therefore, we measured the decrease in the mass of the extractor instead of the increase of the mass of the vial. To realize that, when 10 ml CO2 (measured in the pump) had passed through the extractor, the inlet valve was closed and the extractor was depressurized, disconnected from the CO2 line and weighed using an analytical balance. Then it was pressurized again and after 5 min of saturation the CO2 inlet valve was opened, the flow rate was adjusted, and a new measurement started. The measurements were triplicated at each conditions.
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In our preliminary experiments, by varying the flow rate and the amount of CO2 passed through the extractor in one measurement, it was shown that the flow was slow enough to achieve saturation. Furthermore, it was demonstrated that the loss of xanthotoxin dissolved in CO2 flowing out during the depressurization was negligible compared to its amount extracted with 10 mL CO2. The latter can be accounted to the fast decrease in xanthotoxin solubility with decreasing pressure at the beginning of the depressurization process. 2.5. Gas chromatography Quantitative analysis was performed in a Hewlett Packard 6890 gas chromatograph equipped with a flame ionization detector on a fused silica DB-5MS column (30 m × 0.25 mm × 0.25 m) with helium as a carrier gas at flow rate 1 mL/min. The split ratio was typically 1:10. The oven temperature was increased from 50 °C to 290 °C at a rate 3 °C/min. n-Hexadecane was used as internal standard and the quantification of extract components was based on their chromatographic peak areas. The GC-MS unit consisted of Agilent 6890 gas chromatograph equipped with Agilent 5973 mass spectrometer with electron ionization, ionization energy 70 eV, scan mode: 33-400 m/z. The gas chromatographic conditions were identical with those employed for the quantitative analysis. The compounds were identified by comparison of their mass spectra and retention indices with published data [17] and where possible with authentic compounds.
3. Plant composition-dependent model 3.1. Modelling extraction rate The flow pattern in a packed bed column is represented by a series of n ideal mixers. Thus, different degree of axial mixing is simulated, from the lumped parameter model with n = 1 to plug flow with negligible axial mixing at high values of n. The mass balance equations for fluid and solid phases and for the extract are: ,
,
,
,
,
,
,
for j = 1,2,…,n;
′
,
(1)
where wi,j, kg.(kg CO2)-1 is the concentration of i-th extract component in CO2 in the j-th mixer, wsi,j, kg.(kg solid)-1 is the concentration of i-th extract component in the particles in the j-th mixer, t is the extraction time, tr is the residence time in the extractor, q‘, kg.s-1.(kg solid)-1 is the specific flow rate, and = q’tr is the mass ratio of CO2 filling the extraction bed void volume to the plant particles. The extraction yield of i-th component, ei, is given in kg.(kg dry plant)-1. The mass transfer rate over the mass of CO2 in the j-th mixer is ,
,
,
;
(2)
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where w+i,j, kg(kg CO2)-1, is the concentration of i-th component at solid-fluid interface, tf, s, is the fluid phase mass transfer resistance, is the free void of the extraction bed, and kfa0, s-1, is the volumetric fluid phase mass transfer coefficient. The initial and boundary conditions are: 0
,
,
0
,
for j = 1,2,…,n;
,
0 for j = 1
(3)
where wi0 and wsi0 are the initial concentrations of the i-th component in the fluid and solid phase, respectively. The initial concentrations are related to the content of the i-th component in the plant material inserted in the extractor, wui, by mass balance: (4) The model is derived for finely ground plant where the diffusion path in the particles is short and extract is easily accessible. Moreover, some extract components, like cuticular waxes, even occur on the particle surface only. The internal mass transfer resistance is therefore neglected. Next, following Perrut et al. [18], it is assumed that the decrease in the extraction rate observed during a later stage of the extraction indicates the beginning of a solute desorption from the plant matrix after the free solute has been exhausted. Rewritten for a multicomponent model, the equilibrium relationship is: ,
for
,
;
,
,
for
,
(5)
where wsati is the solubility of free i–th component extracted from the mixture of solid phase composition wsi,j, wti is the matrix adsorption capacity for the i-th component, and Ki is the partition coefficient of i-th component, characterizing its adsorption equilibrium. The above equations show that to model the extraction rate, the solubility w+i,j should be known, and particularly the solubility of free substances, wsati,j. That is because, as the initial straight part of experimental extraction curves demonstrates, most of the rue extract was obtained in the first extraction stage, without any effect of solute-matrix interaction on the extraction rate. For the rue extraction, the solubility of furanocoumarins can be read from the initial slopes of the experimental curves. However, and this should be underlined, a very considerable difference between the furanocoumarin solubilities measured for rue samples of different composition was detected. To fully explain and quantify that observation, a suitable and robust instrument, like a TMF, should be available and used. In the subsequent sections, the approaches to modeling the solubility of a single solid solute/solid solute mixture in the scCO2, interwoven in the TMF applied by us, will be briefly presented. 3.2. Solubility modelling To efficiently model and design any extraction process based on supercritical solvents, the solute(s) solubility in scCO2 must be known. However, despite the vital importance of solubility data for the emerging new green technologies, there is still a considerable lack of data because experimental
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determination of the solubilities of various solutes and solid mixtures in supercritical fluids at a range of operating condition is tedious, time-consuming, high-cost and often even not reported in the literature because the scatter of the experimental values is big and unacceptable. Therefore, the interest in developing new and extending the application of the existing models that can accurately correlate and predict the solubilities of pure solid solutes/solid solutes mixtures in supercritical fluids is thriving. This goal is far from trivial as a flexible, robust and efficient modeling tool should be developed, which must comprise methods for estimating the thermophysical properties of pure substances; thermodynamic models for mixture properties; and methods, algorithms and numerical techniques for solving the equilibrium relations [19]. With regard to thermodynamic models, generally theoretical or semi-empirical functional relationships between pressure, volume and temperature, like equations of state (EoSs), are chosen because the interactions are too complex and it is not reasonable to use more fundamentally based equations [20]. The application of EoSs on its own right might be difficult because knowledge of the pure solid solute thermophysical properties including critical and fusion properties, solid molar volume and sublimation pressure, etc. are required. Often, many of those properties are not known and cannot be determined experimentally because the majority of solid solutes of interest to academia and industry are high molar mass, relatively non-volatile and complex substances. Therefore they have to be estimated applying different methods. A completely different approach to modeling solid solubility is the application of empirical models, which are known as density-based models. That approach is favored by many authors as these models do not require pure component properties data and involve equations that contain constants which are adjusted for each compound. The application of density-based models appears to be simple and straightforward as they rely on the knowledge of the thermodynamic behavior of the supercritical solvent only. However, they are mostly capable of correlating, not predicting the solubility [21] as they require availability of sufficient experimental data. Furthermore, as demonstrated by Coelho et al. [22], the determination of density-based models parameters (usually from three to six), is prone to difficulties due to the nonlinear nature of the objective functions usually used. Last but not least, it should be underlined that density-based models cannot be applied to correlate the solubility of multiple solid solutes in scCO2. We will begin by a brief outline of pure solid solubility correlation in scCO2 applying densitybased models. Then, the framework based on application of cubic EoSs as the thermodynamic models, which allows the calculation and prediction of a single solid solute/multiple solid solutes solubility in a system with a supercritical solvent will be given. 3.2.1. Pure solid Density-based model
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To avoid the necessity of providing values for the thermophysical parameters of solids where they are not available, density-based models to correlate the solubility can be employed as a viable alternative. In our case we have chosen the Chrastil equation [23]: (6) This semi-empirical equation correlates the solubility wsat expressed in kg.(kg CO2)-1, CO2 density
f (kg.m-3) and temperature T (K) using three parameters: k is the average number of CO2 molecules associated to a molecule of solute, a is equal to H/R where H is the heat of solvation plus the heat of vaporization of the solute, and b is adjusted to fit the experimental solubility. Thermodynamic modeling framework The TMF designed to model the solubility of a single solid solute and multiple solid-solutes in scCO2 has been discussed in details [11] and in what follows we will present it in a very concise manner. The solubility of a pure solid solute in scCO2 is correlated applying the classical dense gas approach that is based on the equifugacity condition for the solid solute. Thus, provided an EoS is the thermodynamic model for the fluid phase, the expression for the fugacity of the solute in the solid phase f 2solid is:
(7)
s
where P2 is the sublimation (vapor) pressure of the pure solid, 2S is the fugacity coefficient at sublimation pressure and v2solid is the molar volume of the solid, all at temperature T. The fugacity of the solute in the supercritical phase is: (8) Where 2F is the fugacity coefficient, and y2 - the solubility (mole fraction) of the solute in the supercritical phase, and P is the system’s pressure. Introducing certain simplifications, e.g. the solid phase is assumed to be pure and hence the fugacity of the solute in the solid state is equal to the pure solid fugacity, and applying the thermodynamic equilibrium condition, the expression for the mole fraction of the solid component in the fluid phase is:
(9) In the above, the most important variable is the fugacity coefficient of the solid solute in the supercritical fluid phase, 2F , which is calculated by a thermodynamic model.
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The above equations show that the solute solubility is primarily a function of the solid solute pure compound physical properties, the system temperature and pressure, and the fugacity coefficient of the solid solute in the fluid mixture. 3.2.2. Multiple solid solutes For the more complex case of multicomponent solid-SCF (gas) equilibria, Sovova and Stateva (2015), following Prausnitz et al. [24], make the assumption known as Lewis fugacity rule that the fugacity of a component in a mixture is proportional to its mole fraction. Hence, the fugacity of the i-th solute in the solid phase can be calculated according to: (10) where si is the mole fraction of the i-th solute in the system and fi is the fugacity of the pure solute. The fugacity of the i-th solid solute in the mixture is:
exp
(11)
and the fugacity of the i-th solute in the supercritical phase is: (12) The mole fraction of the i-th solid component in the supercritical phase, i.e. its solubility in the SCF at the temperature and pressure of interest, is then:
(13) The solubility of the i-th solute in the supercritical phase, yi, is, as in the case of a binary system, a function of visolid, PiS and iF . 3.2.3. Thermodynamic model In our study we have chosen the Soave-Redlich-Kwong EoS with the one-parameter-per-pair (1PWDW) version of the van der Waals one fluid mixing rule as a representative of the class of cubic EoSs models. As discussed above, its application as a thermodynamic model to calculate the solubilities of either a pure solid solute or a mixture of solids in scCO2 requires information about the compounds critical temperatures, pressures and acentric factors.
3.2.4. Pure component properties The properties required for modeling the solubility of solid solutes in scCO2 are their critical temperature, Tc and critical pressure, pc, melting properties – namely the pure compounds’ solid molar volume, sublimation pressure and enthalpy of fusion. If experimental values for the melting properties are not available they have to be estimated, and details of a possible scenario how to realize that are
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discussed by Coelho et al. [22]. We will just summarize here that the solid molar volumes can be estimated applying the method of Bondi [25], the Clapeyron relation can be used to calculate the sublimation pressures at the temperatures of interest, and the enthalpy of fusion can be estimated applying the method of Jain [26].
4. Application of the model to the SFE of common rue
4.1. Volatiles, coumarins and waxes in common rue The contents of extractable substances in the samples of dry rue were determined by Soxhlet extraction. Approximately 50 compounds were detected by gas chromatography. The major components were 2-undecanone, rutamarin, furanocoumarins psoralen, xanthotoxin and bergapten, and long-chain n-alkanes hentriacontane and tritriacontane in both samples but the percentage of individual substances was different. For the purpose of mathematical modeling, the compounds of similar chemical structure and similar extraction kinetics were regarded as a single pseudo-component. Volatiles. The substances with retention times shorter than the retention time of psoralen were included in the group of volatiles. The major substances in this group were two ketones, 2-nonanone and 2-undecanone, and esters. Thus, the volatiles of sample S1 contained 44.8 % 2-undecanone, 28.6 % undecyl esters, 6.8 % 2-nonanone, and 4.7 % nonyl esters, while the volatiles of sample S2 contained 76.9 % 2-undecanone, 7.6 % undecyl esters, 5.9 % 2-nonanone, and 4.6 % nonyl esters. These results are comparable with the composition of Ruta graveolens essential oil, with 2undecanone (46.8 %) and 2-nonanone (18.8 %) as the main constituents, reported in the study of De Feo et al. [27]. The group of coumarins consists of five furanocoumarins, namely psoralen, xanthotoxin, bergapten, prangenin, as well as oxypeucedanin, and coumarin rutamarin (Table 2). It should be noted that because the solubility of none of the above components in scCO2 has been reported previously in the open literature, we had to choose one of them and measure its solubility. With respect to the commercial availability and affordability of the substances, xanthotoxin was the best choice on the market among them. Hence, the group of coumarins was represented by xanthotoxin. The main components of the group of cuticular waxes were the long-chain alkanes hentriacontane and tritriacontane (Table 3). Supercritical fluid extraction of a mixture of long-chain alkanes, which solubility in scCO2 decreases with increasing length of the carbon chain, was examined previously [11]. We have shown that, if a mixture of such hydrocarbons should be represented by one component in a model for SFE, then the carbon chain of that component should be slightly longer than the average chain length in the mixture. Therefore, n-tritriacontane was selected as the representative of waxes in the model.
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Other detected components not belonging to the volatiles, coumarins, and waxes, like fatty acids, sterols and tocopherols, form the group denoted as “others” in Figure 1. The figure shows considerable difference between the coumarins-to-waxes ratios for rue samples S1 and S2, respectively. It should be noted that the difference in rue composition is very suitable for the purposes of modelling of the dependence of apparent solubility of these pseudo-components on the solid phase composition. The group “others” was not included in the model.
4.2. Shape of extraction curves The volatiles and cuticular waxes are easily accessible to the extraction because of their location. Cuticular waxes cover the surface of leaves, stems, and flowers. Volatiles of Ruta graveolens are stored in secretory cavities [28] which walls became fragile after the treatment with liquid nitrogen and were opened by milling. From the shape of coumarins extraction curve, which does not exhibit any slowdown at the moment when the solution saturated during the static extraction is exhausted, it can be concluded that coumarins also become well accessible by the pretreatment. An example of extraction kinetics is shown in Figure 2, where the yields of volatiles, coumarins and waxes are plotted against the solvent-to-feed ratio. The solvent-to feed value q = = f/(s(1-)) indicates the moment when the solvent filling the bed void volume during the static extraction is just replaced by fresh solvent (if the flow pattern is plug flow). In our experiments, the void fraction was = 0.53 and the particle density determined using pycnometry was s = 1080 kg.m-3. The fastest was the extraction of volatile oil, the kinetics of which can be modeled as washing out of a solute which was completely dissolved in the solvent during the static extraction. The initial condition given by Eq. (4) was reduced to wi0 = wui and Eqs. (1) with ji,j = 0 were solved with the result 1
∑
where
!
,
(14)
By varying the number of mixers we found the best fit of the extraction curve, calculated according to Eq. (24), to the yield of volatiles in the experiment RM6 at n = 2 (Figure 2). Thus, the extraction of volatiles can be modeled as not affected by co-extracted substances, in accordance with the first type of models for multicomponent extraction mentioned in the Introduction. As the interstitial velocity was extremely low (0.4 cm.min-1), the relatively high axial mixing might be caused by natural convection. The extraction of coumarins and waxes was slower than that of volatiles because it was limited by their solubility in scCO2, which we determined from initial slopes of their extraction curves. As the volatiles were washed out in the very beginning of the extraction, and as the shapes of extraction curves of coumarins and waxes were not affected by the presence or absence of volatile oil in the
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extractor, the volatiles were excluded when the multicomponent equilibrium was modeled applying the thermodynamic framework. 4.3. Measurement and correlation of xanthotoxin solubility in scCO2 Xanthotoxin (syn. methoxsalen, 8-methoxypsoralen; 9-methoxy-7H-furo[3,2-g]chromen-7-one) C12H8O4 is a white powder. The results of its solubility measurement in scCO2 are listed in Table 4. The data were obtained as solute-to-solvent mass ratios Sw. Chrastil equation
Preliminary evaluation of xanthotoxin solubility in scCO2 was carried out using Eq. (6) which parameters were optimized to minimize its average absolute relative deviation (AARD) from 69 experimental points (Figure 3). Each point represents one measurement; the experimental error can be estimated from their scatter. The optimized parameters of the Chrastil equation are k = 6.50, a = 5211.7, and b = -27.808. The AARD = 19.7% is relatively high, which is particularly a result of the scatter of experimental points. SRK cubic EoS The application of the SRK cubic EoS to correlate the solubility of xanthotoxin in scCO2 requires knowledge of its fusion and critical properties. The melting temperature of xanthotoxin, as indicated by the supplier, is (148-150) oC and, together with a boiling point value of 414.8 °C at 760 mmHg, are the only properties experimentally measured and available. Hence, all other properties required have to be estimated. The critical temperature and pressure of xanthotoxin were estimated applying the methods suggested in [29,30]. Because the critical parameters of xanthotoxin are hypothetical, and because, to the best of our knowledge, there are no estimations on the properties required published by other authors, there should be an assessment made whether the values reported by us are reasonable. To evaluate the reliability of the critical properties values estimated by us we apply the generalized semi-theoretical expression advocated in [31], which correlates Tc/pc with the van der Waals surface area Qw: Tc/pc = 9.0673 +0.43309(Qw1.3 + Qw1.95)
(15)
where Tc is in Kelvin and pc is in bar. The surface area is a dimensionless parameter and is calculated as the sum of the group area parameters, Qk, according to: ∑
(16)
The ratio of xanthotoxin values estimated by us (given in bold) gives a very good approximation to the theoretically calculated Tc/pc ratio (K.bar-1), namely 26.45 versus 25.65.
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The values of all xanthotoxin thermophysical properties, required for the modelling, either experimentally measured or estimated in this study, are listed in Table 5. To correlate the solubilites of xanthotoxin in scCO2, the unlike-pair interaction parameter, kij was estimated at each temperature of interest to the experiment by minimising the absolute average deviation between our experimental data and the calculated solubility (in mole fractions) applying a standard optimization procedure. The correlations represent quite well the pattern of xanthotoxin solubility behavior with a crossover pressure at about 15.4 MPa (Figure 4). The agreement between the experimentally measured and EoS correlated solubilities of xanthotoxin in scCO2 at the three temperatures of interest to the experiment is shown also in Figure 4. The AARD is 16.8%. 4.4. Solubility of xanthotoxin and n-tritriacontane in the ternary systems with scCO2 As mentioned previously, Chrastil equation was derived for binary systems solute + scCO2, and hence cannot be applied to correlate the solubility of two or more solids in the solvent. Thus, the solubilities of xanthotoxin and n-tritriacontane in ternary mixtures with scCO2 were calculated applying the TMF and following the algorithm outlined in section 3.2.2. The thermophysical properties of n-tritriacontane required for the modeling were estimated and reported previously [11]. They are shown in Table 5. For the ternary system xanthotoxin+n-tririacontane+CO2, in addition to the kij’s for the xanthotoxin+CO2, which, as discussed in the previous section, were estimated from our experimental data, interaction parameters are required also for n-tritiacontane+CO2 and xanthotoxin+n-C33 at the three temperatures of interest to the experiment. With regard to the former, those were determined, as reported by Sovova and Stateva in [11], minimizing the difference between the experimental data of Chandler et al. [32] and calculated solubilities, applying a standard optimization procedure. For the temperatures for which experimental data were not available, the kij parameters were estimated taking into consideration the weak dependence of the binary parameters for n-alkanes+ CO2 on temperature, which assumption, as demonstrated by Sovova and Stateva [11], performs quite well. The kij parameter for xanthotoxin+n-C33 was assumed to be not temperature sensitive and hence a single value for the three temperatures of interest was determined from the best fit to the experimental data corresponding to the initial slopes of the extraction curves. The solubility values for xanthotoxin (wsat1) and n-tritriacontane (wsat2), needed to model the extraction experiments, were calculated for each sample in five points, which represent the compositions of the respective ternary mixtures with CO2. Thus, the first point corresponds to the mixture of coumarins, waxes and CO2 in the extractor at the beginning of extraction, while the other four points were selected in such a way as to simulate the gradual exhaustion of both groups of extracted substances. From the solubility calculations performed for all sets of temperatures and pressures examined, the results for just three instructive examples are chosen and shown in Fig. 5 where the solubilities of the
14
solid mixture constituents are plotted against the decreasing xanthotoxin mass fraction in the mixture, z1, calculated on a solvent-free basis. Figure 5 demonstrates for S1 the influence of temperature on the solubility of the two solid solutes at p = 28 MPa. Thus, the solubility of n-tritriacontane in CO2 (and the solubility of waxes generally) increases with increasing temperature to such extent that the solubility of xanthotoxin, which is less temperature dependent, is suppressed. The influence of samples S1 and S2 composition on the solubility behavior of both solutes in the ternary mixture with CO2 is demonstrated at T = 40 oC. For S1, the solubility of n-tritriacontane in CO2 increases with decreasing z1 in a more pronounced manner than for S2; furthermore the actual solubility values of the model wax are about two times higher than the respective ones for sample S2; the solubility trend of xanthotoxin is the opposite – it decreases more rapidly for S2 than for S1, but the actual solubility is about 1.5 higher for S2 as compared to S1.
4.5. Simulation of SFE kinetics The experimental extraction yields are plotted in dependence on extraction time in Figures 6 and 7 together with calculated extraction curves. The solubilities of xanthotoxin and n-tritriacontane in the ternary systems with CO2, calculated applying the TMF for five composition points for each extraction conditions, were interpolated by polynomials of degree 2. The latter were next substituted in eq. (5) of the extraction model where wsat1
and wsat2 were identified with the solubilities of xanthotoxin and n-tritriacontane, respectively, and ws1,j/(ws1,j + ws2,j) was used instead of the xanthotoxin mass fraction in its mixture with ntritriacontane, z1. The mass balance equations were integrated using the Euler’s method. The external mass transfer coefficient was calculated according to Catchpole and King [33]. To be on the safe side, the maximum particle size, 0.6 mm, was inserted in the formula. Still, the kf values were as high as (0.7-2.5).10-5 m.s-1 for xanthotoxin and (0.4-1.7).10-5 m.s-1 for n-tritriacontane, which corresponds to tf values (0.5-2.5) s that are by orders of magnitude less than the residence time. The small mass transfer resistance therefore did not affect the calculated extraction curves. The remaining model parameters were adjusted to minimize the mean absolute deviation between the calculated and experimental extraction yields. The parameters that characterize the adsorption equilibria, namely the adsorbent capacities wti and the partition coefficients Ki for i=1,2, were adjusted to simulate the period of slow extraction (see Table 6). The trend of bond weakening between the solute and the matrix with increasing the power of the solvent is evident: the partition coefficient increases, favoring thus CO2 phase, and the adsorbent capacity mostly decreases. The sharpness of the calculated transition to lower extraction rate increases with increasing number of mixers in the model, n. The values of parameter n adjusted to match the shape of experimental extraction curves are listed in Table 6, too. The large degree of mixing, indicated particularly at the largest residence times, could be related to the extremely low interstitial velocities.
15
The calculated extraction curves represent quite well the pattern of the change of experimental extraction yields vs time as shown in Figures 6 and 7. Quantitatively, the mean absolute deviation between the calculated and experimental extraction yields was related to the asymptotic yield wui in order to obtain the deviation i for each extraction curve: ∆
∑
,
for i=1,2
(17)
where m is the number of experimental points and i indicates the i-th component. The deviation of the yields of coumarins and waxes was similar and ranged from 0.2% for coumarins extracted from sample S2 at 60 °C and 12 MPa to 5.8% for waxes extracted from sample S1 at 40 °C and 28 MPa. The mean value of for the whole set of experiments and both pseudo-components was 2.2%.
5. Conclusions In this study a novel approach to modeling multicomponent supercritical fluid extraction was presented for the first time, and was applied to model the observed different extraction behavior of three groups of rue constituents. Volatile oil, under the extraction conditions examined, was miscible with supercritical CO2 and was thus practically washed out of the extractor in the beginning of the extraction. The behavior of the solid substances, coumarins and waxes, was more complex; their extraction rate was dependent on the composition of rue samples, which prompted us to examine their solubility behavior. One of the targets of the study, therefore, was to model the coumarins (represented by xanthotoxin) and waxes (represented by n-tritriacontane) mixture solubility in CO2 applying a thermodynamic framework (TMF). In addition, the solubility of xanthotoxin in supercritical CO2 was measured and reported in this study. The TMF results obtained were implemented in the model for multicomponent extraction. The good agreement between the extraction curves, calculated applying the model, and the experimental results obtained is an indication of the fact that the interplay between kinetics and phase equilibria should be taken into consideration when a mixture of components of similar concentration but different solubility is extracted. Hence, a rigorous TMF interwoven with an extraction model provide a reliable tool to obtain deeper realistic insight and, presumably, could be used to model extraction of any natural product.
16
Acknowledgements The authors thank Iva Ličková and Markéta Kurčová who performed the extraction experiments and Petra Cuřínová who conducted the GC analysis of extract samples. This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic [grant number 2B06049].
17
References [1] E. Reverchon, R.Taddeo, G. Della Porta, Extraction of sage oil by supercritical CO2: influence of some process parameters, J. Supercritic. Fluids 8 (1995) 302–309. [2] M.D.A. Saldana, R.S. Mohamed, M.G. Baer, P. Mazzafera, Extraction of purine alkaloids from maté (Ilex paraguariensis) using supercritical CO2, J. Agric. Food Chem. 47 (1999) 3804–3808. [3] M.D.A. Saldana, F. Temelli, S.E. Guigard, Apparent solubility of lycopene and beta-carotene in supercritical CO2, CO2 + ethanol and CO2 + canola oil using dynamic extraction of tomatoes, J. Food Eng. 99 (2010) 1–8. [4] H. Sovova, J. Jez, M. Bartlova, J. Stastova, J., Supercritical carbon dioxide extraction of black pepper, J. Supercrit. Fluids 8 (1995) 295–301. [5] L.F. de Franca, M.A.A. Meireles, Modeling the extraction of carotene and lipids from pressed palm oil (Elaesguineensis ) fibers using supercritical CO2, J. Supercrit. Fluids 18 (2000) 35–47. [6] J. Martinez, A.R. Monteiro, P.T.V. Rosa, M.O.M. Marques, M.A.A. Meireles, Multicomponent model to describe extraction of ginger oleoresin with supercritical carbon dioxide, Ind. Eng. Chem. Res. 42 (2003) 1057–1063. [7] S.L. Chia, R. Sulaiman, H.C. Boo, K. Muhammad, F. Umanan, G.H. Chong, Modeling of rice bran oil yield and bioactive compounds obtained using subcritical carbon dioxide Soxhlet extraction (SCDS), Ind. Eng. Chem. Res. 54 (2015) 8546–8553. [8] Z.P. Shen, M.V. Palmer, S.S.T. Ting, R.J. Fairclough, Pilot scale extraction of rice bran oil with dense carbon dioxide, J. Agric. Food Chem. 44 (1996) 3033–3039. [9] F. Gaspar, Extraction of essential oils and cuticular waxes with compressed CO2: effect of extraction pressure and temperature, Ind. Eng. Chem. Res. 41 (2002) 2497–2503. [10] H. Sovova, A.A. Galushko, R.P. Stateva, K. Rochova, M. Sajfrtova, M. Bartlova, Supercritical fluid extraction of minor components of vegetable oils: beta-sitosterol, J. Food Eng. 101 (2010) 201–209. [11] H. Sovova, R. Stateva, A new approach to modelling supercritical CO2 extraction of cuticular waxes: Interplay between solubility and kinetics, Ind. Eng. Chem. Res. 54 (2015) 4861–4870. [12] S. Milesi, B. Massot, E. Gontier, F. Bourgaud, A. Guckert, Ruta graveolens L.: a promising species for the production of furanocoumarins, Plant Sci. 161 (2001) 189–199. [13] F. Conforti, M. Marrelli, F. Menichini, M. Bonesi, G. Statti, E. Provenzano, F. Menichini, Natural and synthetic furanocoumarins as treatment for vitiligo and psoriasis, Current Drug Therapy 4 (2009) 38–58. [14] B. Xu, L. Wang, L. Gonzáles-Molleda, Y. Wang, J. Xu, Y. Yuan, Antiviral activity of (+)rutamarin against Kaposi’s sarcoma-associated herpesvirus by inhibition of the catalytic activity of human topoisomerase II, Antimicrob. Agents Chemoter. 58 (2014) 563–573.
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[15] Y. Zhang, H. Zhang, X.G. Yao, H. Shen, J. Chen, C. Li et al., (+)-Rutamarin as a dual inducer of both GLUT4 translocation and expression efficiently ameliorates glucose homeostasis in insulinresistant mice. PLoS ONE, 7(2) (2012): e31811. [16] National Institute of Standards and Technology U.S., Thermophysical Properties of Fluid Systems. http://webbook.nist.gov/chemistry/fluid, 2011 (accessed 25.05.16). [17] R.P. Adams, Identification of Essential Oil Components by Gas Chromatography Quadrupole Mass Spectroscopy, fourth ed., Allured Publishing Corporation, Illinois, 2007. [18] M. Perrut, J.Y. Clavier, M. Poletto, E. Reverchon, Mathematical modeling of sunflower seed extraction by supercritical CO2, Ind. Eng. Chem. Res. 36 (1997) 430–435. [19] T. Fornari, R.P. Stateva, R.P., Thermophysical properties of pure substances in the context of sustainable high pressure food processes modelling, in: T. Fornari, R.P. Stateva (Eds.), High Pressure Fluid Technology for Green Food Processing, Springer, Cham Heidelberg New York Dordrecht London, 2015, pp. 117–152. [20] H. Sovova, R.P. Stateva, Supercritical fluid extraction from vegetable materials, Rev. Chem. Eng. 27 (3–4) (2011) 79–156. [21] M.A. Khansary, F. Amiri, A. Hosseini, A.H. Sani, H. Shahbeig, Representing solute solubility in supercritical carbon dioxide: A novel empirical model. Chem. Eng. Res. Des. 93 (2015) 355–365. [22] J.A.P. Coelho, R.M. Filipe, G.P. Naydenova, D.S. Yankov, R.P. Stateva, Semi-empirical models and a cubic equation of state for correlation of solids solubility in scCO2: Dyes and calix[4]arenes as illustrative examples. Fluid Phase Equilibria 426 (2016) 37–46. [23] J. Chrastil, Solubility of solids and liquids in supercritical gases. J. Phys. Chem. 86 (1982) 3016– 3021. [24] J.M. Prausnitz, R.N. Lichtenthaler, E.G.D. Azevedo, Molecular Thermodynamics of Fluid-Phase Equilibria, Prentice-Hall, Englewood Cliffs, NJ, 1999. [25] A. Bondi, van der Waals volumes and radii, J. Phys. Chem. 68(3) (1964) 441–451. [26] A. Jain, S.H. Yalkowsky, Estimation of melting points of organic compounds – II, J. Pharm. Sci. 95(12) (2006) 2562–2618. [27] V. De Feo, F. De Simone, F. Senatore, Potential allelochemicals from the essential oil of Ruta graveolens, Phytochemistry 61 (2002) 573–578. [28] A.A. Malik, S.R. Mir, J. Ahmad, J., Ruta graveolens L. essential oil composition under different nutritional treatments, American-Eurasian J. Agric. & Environ. Sci. 13(10) (2013) 1390–1395. [29] W.A. Wakeham, G.St. Cholakov, R.P. Stateva, Liquid density and critical properties of hydrocarbons estimated from molecular structure, J. Chem. Eng. Data 47(3) (2002) 559–570. [30] N. Brauner, R.P. Stateva, G.S. Cholakov, M. Shacham, Structurally “targeted” quantitative structure-property relationship method for property prediction, Ind. Eng. Chem. Res. 45(25) (2006) 8430–8437.
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[31] A. Zbogar, F.V.D. Lopes, G.M. Kontogeorgis, Approach suitable for screening estimation methods for critical properties of heavy compounds, Ind. Eng. Chem. Res. 45(1) (2006) 476–480. [32] K. Chandler, F.L.L. Pouillot, C.A. Eckert, Phase equilibria of alkanes in natural gas systems. 3. Alkanes in carbon dioxide, J. Chem. Eng. Data 41(1) (1996) 6–10. [33] O.J. Catchpole, M.B. King, Measurement and correlation of binary diffusion coefficients in near critical fluids, Ind. Eng. Chem. Res. 33 (1994) 1828–1837.
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Figure captions Fig 1. The ratios of groups of non-volatile components in common rue samples S1 and S2. Fig. 2. Extraction yields of three groups of compounds extracted with scCO2 at 30 MPa and 40 °C from rue sample S2 (exp. RM6; = 0.95). Model for the yield of volatiles which are initially completely dissolved in scCO2: (______) two mixers, (- - -) three mixers. Fig. 3. The experimental xanthotoxin solubility wsat (kg.(kg CO2)-1) against CO2 density f (kg.m-3) on logarithmic scale. The straight lines represent the Chrastil correlation. Fig. 4. Xanthotoxin solubility in scCO2 (mole fraction). Symbols – experimental points, solid lines – correlations applying the SRK EoS at T = (313.2 323.2, 333.3) K with kij = (0.0847; 0.1066 and 0.1152), respectively. Fig. 5. Solubilities of xanthotoxin (_____) and n-C33 (- - -) in model ternary systems xanthotoxin + nC33 + CO2 for rue samples S1 and S2 in dependence on the xanthotoxin fraction z1 = ws1,j/(ws1,j +
ws2,j) at different pressures and temperatures, calculated applying the TMF. Fig. 6. Experimental (symbols) and calculated (lines) extraction yields from common rue, sample S1. Fig. 7. Experimental (symbols) and calculated (lines) extraction yields from common rue, sample S2.
21
22
23
24
25
26
27
28
Table 1 Extraction conditions Run
T (°C) f (kg/m3) a
P (MPa)
Run
Sample S1
P (MPa)
T (°C) (kg/m3) a
Sample S2
RoI1
28
50
857.1
RM1
12
40
717.8
RoI3
28
40
898.5
RM3
12
60
434.4
RoI4
28
60
814.0
RM6
30
40
909.9
RoI5
20
50
784.3
RM9
30
60
830.3
RoI6
12
50
584.7
a
from NIST [16]
Table 2 Contents of coumarins in dry rue, g.(kg solid)-1 Compound
Sample S1 Sample S2
Rutamarin
1.18
1.41
Psoralen
0.42
0.51
Xanthotoxin
0.48
0.58
Bergapten
0.46
0.55
Prangenin
0.16
0.19
Oxypeucedanin 0.07
0.08
Sum
3.32
2.77
Table 3 Contents of components of cuticular waxes in dry rue, g.(kg solid)-1 Compound
Sample S1 Sample S2
Branched pentacosane 0.05
0.03
n-Heptacosane
0.16
0.17
Hexacosanal
0.15
0.07
n-Nonacosane
0.08
0.19
Hentriacontane
2.13
0.85
n-Tritriacontane
2.13
0.64
Sum
4.70
1.96
29
Table 4 Solubility of xanthotoxin in scCO2 as solute-to-solvent mass ratio, wsat, at T = (313.2-333.2) K 313.2 K P
323.2 K 3
wsat ×10 -1
f
P
333.2 K 3
wsat ×10 -1
f
P
wsat ×103 -1
f
(MPa)
(kg.kg )
(kg.m-3)
(MPa)
(kg.kg )
(kg.m-3)
(MPa)
(kg.kg )
(kg.m-3)
12
0.253
717.8
12
0.156
584.7
12
0.089
434.4
13
0.260
743.0
12
0.131
584.7
12
0.118
434.4
14
0.247
763.3
13
0.350
636.1
12.5
0.140
471.5
14
0.345
763.3
14
0.228
672.2
13
0.260
505.4
15
0.404
780.2
14
0.283
672.2
14
0.324
561.4
16
0.310
794.9
15
0.418
699.8
14
0.184
561.4
20
0.651
839.8
16
0.338
722.1
15
0.418
604.1
20
0.510
839.8
16
0.415
722.1
15
0.379
604.1
23
0.776
865.1
18
0.708
757.1
16
0.426
637.5
23
0.713
865.1
18
0.471
757.1
17
0.687
664.6
25
0.886
879.5
18
0.510
757.1
17
0.491
664.6
28
1.042
898.5
20
0.923
784.3
17
0.792
664.6
20
0.827
784.3
17
0.403
664.6
20
0.857
784.3
17
0.933
664.6
22
0.681
806.6
18
0.530
687.3
23
1.080
816.5
19
0.658
706.7
23
0.835
816.5
20
1.201
723.7
23
0.861
816.5
20
0.657
723.7
23
0.692
816.5
21
0.660
738.8
25
1.237
834.2
21
0.819
738.8
25
1.212
834.2
22
0.979
752.4
25
0.966
834.2
23
0.730
764.7
25
1.175
834.2
23
1.398
764.7
26
0.796
842.3
24
1.152
776.1
26
1.590
842.3
25
1.127
786.6
27
0.868
849.9
25
1.370
786.6
27
1.053
849.9
26
1.244
796.3
28
1.296
857.1
28
1.491
814.0
28
1.335
857.1
30
Table 5 Thermophysical properties Property
Xanthotoxin (C12H8O4) n-Tritriacontane
o
Tm ( C)
148-150
345. ± 3a
pc (bar)
33.9
5.54
Tc (K)
896.8
851
VS (cm3mol-1)
152.7
516.7
H (Jmol )
89300
274200a
Pssubl (bar) at T=313.2 K
1.26810-9
3.2210-13
Pssubl (bar) at T=323.2 K
3.62510-9
8.52410-12
Pssubl (bar) at T=333.2 K
9.82810-9
1.82210-10
s
-1
a
– from NIST [16]
Table 6 Adsorption parameters for coumarins (i=1) and waxes (i=2), number of mixers (n), residence time (tr), and interstitial velocity (u) Exp.
P
T
K1
(MPa) °C (kg.kg-1)
wt1 kg/kg
K2
wt2
n
tr
u
(kg.kg-1) (kg.kg-1) (-) (min) (cm.min-1)
Sample S1 RoI1
28
50
0.037
0.0010
0.070
0.0006
2
13.0
1.27
RoI3
28
40
0.120
0.0010
0.026
0.0014
2
17.2
1.18
RoI4
28
60
0.035
0.0011
0.010
0.0010
1
14.4
1.33
RoI5
20
50
0.026
0.0010
0.015
0.0009
3
13.9
1.38
RoI6
12
50
0.014
0.0013
0.006
0.0019
5
11.2
1.83
RM1
12
40
0.040
0.0012
0.010
0.00125
6
20.8
0.54
RM3
12
60
0.014
0.0032
0.009
0.00186
5
12.5
0.89
RM6
30
40
0.70
0.0005
0.017
0.0012
2
27.1
0.41
RM9
30
60
0.12
0.0006
0.0006
0.020
2
24.6
0.45
Sample S2
31
S0896-8446(16)30295-9 http://dx.doi.org/doi:10.1016/j.supflu.2016.10.008 SUPFLU 3777
To appear in:
J. of Supercritical Fluids
Received date: Revised date: Accepted date:
9-9-2016 13-10-2016 14-10-2016
Please cite this article as: Helena Sovov´a, Marie Sajfrtov´a, Roumiana P.Stateva, A novel model for multicomponent supercritical fluid extraction and its application to Ruta graveolens, The Journal of Supercritical Fluids http://dx.doi.org/10.1016/j.supflu.2016.10.008 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A novel model for multicomponent supercritical fluid extraction and its application to Ruta graveolens Helena Sovováa,* , Marie Sajfrtováa, and Roumiana P. Statevab a
Institute of Chemical Process Fundamentals of the Czech Academy of Sciences, v. v. i., Rozvojová
135, 16502 Prague, Czech Republic b
Institute of Chemical Engineering, Bulgarian Academy of Sciences, Acad. G. Bontchev str., bl.103,
1113 Sofia, Bulgaria *
Corresponding author. E-mail address: [email protected] (H. Sovová).
Graphical abstract
Highlights
Extraction of 2 samples of rue different in contents of coumarins (C) and waxes (W)
Solubility of xanthotoxin (one of common rue furanocoumarins) in CO2 was measured
C+W mixture solubility in CO2 was modeled applying a thermodynamic framework
Extraction curves were calculated using the results of thermodynamic modeling
Abstract In this work, a multicomponent model for understanding the relationship between the chemical compositions of an extract and extracted plant is developed and presented for the first time. Its robustness and efficiency were validated on the example of furanocoumarins and waxes extracted from aerial parts of common rue with supercritical CO2 at pressures and temperatures (12-30) MPa
1
and (313-333) K. For the purpose of modeling, the waxes are represented by n-tritriacontane and furanocoumarins - by xanthotoxin, the solubility of which in CO2 was measured using the dynamic method. A rigorous thermodynamic modeling framework was applied to calculate the compositiondependent solubilities of extracted compounds, which were incorporated in the kinetics model in order to calculate the extraction curves. For individual extraction curves, the average absolute deviation between the calculated and experimental extraction yields, expressed as percentage of the asymptotic extraction yield, was in the range (0.2-5.8)%.
Keywords: supercritical fluid extraction; multicomponent equilibrium; xanthotoxin; waxes; carbon dioxide 1. Introduction Most of the extracts from plants are mixtures of several tens of components and their composition varies in the course of extraction due to the different solubilities of the individual components and/or their different accessibility in the plant matrix. These changes can easily be followed in supercritical fluid extraction (SFE) where semi-continuous set-up allows a separate collection of subsequent extract fractions and their chemical analysis. For example, Reverchon et al. [1] extracted with supercritical carbon dioxide (scCO2) volatile oil from sage and measured different extraction rates of monoterpenes, oxygenated monoterpenes, sesquiterpenes, and oxygenated sesquiterpenes, decreasing in that order in a complete analogy to their decreasing solubility in scCO2. It should be also taken into account that the solubility of a minor component in the solvent can be substantially different from its solubility as a pure substance. Saldana et al. [2], who extracted with scCO2 purine alkaloids caffeine, theobromine and theophylline from herbal mate tea, observed that the solubilities in the binary CO2+purine alkaloid systems were much higher than those obtained during the extraction from plant. In another work, the apparent solubility of carotenoids extracted with scCO2 from freeze-dried tomato skin and pulp was almost one order of magnitude smaller than the solubility of individual carotenoids measured in binary system with scCO2. When co-solvents were used the apparent solubility of carotenoids was increased due to the polarity of co-solvents and perhaps also because of co-solvents’ interaction with the tomato matrix in the multicomponent complex system [3]. Mathematical models for supercritical fluid extraction usually describe the extraction kinetics only globally, regarding the extract as one pseudo-component. Still, several attempts have been made to simulate the evolution of extract composition, distinguishing between volatile oil, cuticular waxes, fatty oil, or other groups of substances in the extract. A simple way to do that is to fit calculated extraction curves separately to each examined substance or group of substances, assuming that extraction is not affected by other co-extracted substances. Such approach was tested for example in
2
the model for scCO2 extraction of volatile oil, lipids, and piperine from black pepper seed [4]. However, the approach was developed predominantly in connection with a logistic model, which was applied by Franca and Meireles in their study on the extraction of free fatty acids, triglycerides, and carotene from palm oil fibres [5], and by Martínez et al. [6] who examined the extraction of ginger rhizome oleoresin composed of monoterpenes, sesquiterpenes, and hydrocarbons and by other authors. Chia et al. [7], who recently investigated the possibility of a separate extraction of groups of compounds, applied the above approach in modeling the scCO2 extraction of tocopherols, tocotrienols, and -oryzanol from rice brain. Another approach to modeling extraction of mixtures from plants takes the multicomponent equilibrium into account. Shen et al. [8], who also extracted rice bran oil with scCO2, evaluated the apparent partition coefficients of triglycerides and oil’s minor components. They compared the composition of the saturated oil solution in CO2, determined from initial slopes of the extraction curves of individual oil components, with the composition of oil in the rice bran determined from its nhexane extract. Gaspar [9] evaluated the selectivity of individual classes of components in the scCO2 extraction of volatile oil from oregano bracts under different extraction conditions. Sovova et al. [10] implemented the separation factor of β-sitosterol to triglycerides into a model for scCO2 extraction of sea buckthorn oil from particle surface, where the dependence of the separation factor on extraction pressure and temperature was calculated using thermodynamic models. The idea of implementing the results obtained from the application of a robust thermodynamic framework, allowing reliable calculation of the solubility of a single solid solute/solid solutes mixture, in the model for supercritical fluid extraction kinetics was further developed by Sovova and Stateva [11] in their recent contribution on the extraction of cuticular waxes. The aims of the present contribution are to: i)
outline the features of a novel model for multicomponent supercritical fluid extraction from plants, which introduces a relation that characterizes in a more realistic manner the influence of the initial plant composition changes on the solubility of the solutes in the scCO2. The new model incorporates elements of the approach developed in [11], and further improves and considerably extends its application;
ii)
validate and demonstrate the robustness and reliability of the novel model on the example of the supercritical extraction of furanocoumarins and waxes from aerial parts of Ruta graveolens.
The necessary experimental data for testing the model were obtained by supercritical fluid extraction of two samples of Ruta graveolens, also known as common rue, a plant native to the Balkan Peninsula. This plant is rich in furanocoumarins, substances which sensitize skin to light [12]. On the one hand, furanocoumarins can cause dermatitis or blisters when skin is exposed to the sun, but on the other hand they are efficient in phototherapy [13]. Like coumarin and its other derivatives, furanocoumarins are also efficient antifeedants that protect different plants against pests. The major
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coumarin of R. graveolens is rutamarin, which potential as antiviral drug and as a compound efficient against diabetes was revealed recently [14,15]. In our model, the coumarins were represented by the furanocoumarin xanthotoxin, which solubility in scCO2 was, to the best of our knowledge, measured and reported for the first time in this work. Firstly, the experiments will be presented. Then, the new model for multicomponent supercritical fluid extraction, which takes into consideration the influence of plant composition on the extraction, and the corresponding thermodynamic modeling framework (TMF) applied, will be outlined. The performance and viability of the model and the TMF are subsequently demonstrated on the simulation of coumarins and cuticular waxes extraction from rue, where each of the two groups of substances is represented by a single compound. 2. Experimental 2.1. Chemicals and materials Xanthotoxin (>98%) was purchased from Sigma-Aldrich (St Louis, MO, USA). CO2 (>99%) was supplied by Linde (Praha, CR). Common rue was harvested in two successive years. Its aerial parts were dried. Before extraction they were shortly immersed in liquid nitrogen, cut using a mill with rotating knives, and passed through a sieve with 0.6 mm openings. 2.2. Soxhlet extraction 10 g rue and 250 mL n-hexane were placed in a 500 mL flask of Soxhlet extractor and the herb was extracted for 6 h. The solvent was then evaporated in a rotary vacuum evaporator and the dry extract was weighed and stored for chemical analysis. 2.3. Supercritical extraction Different extraction equipment was used for the rue samples S1 and S2 but the extraction procedure was in both cases identical. The extraction of sample S1 was carried out in an apparatus Spe-ed SFE (Applied Separations, USA). The extraction column (volume 32 mL; inner diameter 14 mm) was filled with 12.8-16.0 g of plant particles placed between layers of glass beads serving as solvent flow distributors. The extractor was connected to the equipment with stainless steel capillaries and placed into the air-conditioned box. Carbon dioxide was sucked from a pressure container using a high-pressure pump cooled by water to 5 °C. The solution flowing from the extractor expanded to the ambient pressure in a heated micrometer valve and the extract fractions were collected in an empty glass vial at room temperature. The flow rate was adjusted to (0.87-0.90) g/min. The quantity of CO2 leaving the vial was measured using a gas meter (Pl 0,1, Spectrum Skutec, CR).
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In the case of the sample S2, the extractor of volume 150 ml with an inner diameter 30 mm was equipped with a water heated jacket. The extraction equipment consisted of CO2 compressor with pressure controller, the extractor, a heated micrometer valve with an adapter for air-tight attachment of a vial where the extract was collected, and a gas meter. The vial was immersed in a cooling bath with ethanol and dry ice. The extractor was connected to the pressure controller and micrometer valve by heated capillaries. The feed was in the range (40-44) g and the flow rate was (1.40-1.45) g/min. In both apparatuses, the rue powder was packed in the extractor vessel between two layers of glass beads separated from rue by thin layers of glass wool. The extractor was pressurized with CO2 and after 15 minutes of static extraction the micrometer valve was opened and the flow rate was adjusted. The extraction pressure and temperature were varied as shown in Table 1. The vials were changed several times in the course of extraction run, their content was weighed before and after removing water with a syringe needle, and they were stored in refrigerator until GC analyses. Extraction pressure and temperature were varied as shown in Table 1. The density of CO2 was obtained from NIST [16]. 2.4. Dynamic measurement of solubility The extractor, a short column of 4 cm3 volume and 8 mm inner diameter, was tightly packed with white powder of xanthotoxin mixed with glass beads, separated by glass wool from layers of glass beads on both ends of the column. The extractor was placed in an air-heated box and connected to the CO2 supply from Isco syringe pump, model 260D (Isco, Inc., USA). The solvent flow was adjusted to 0.1 mL/min in the pump, with the corresponding residence time in the extractor approximately 20 min. The solution from the extractor flowed through a heated micrometer valve to a vial where the extract precipitated. The solubility was determined in the pressure range (12-28) MPa at temperatures (40, 50, and 60) °C. The amount of xanthotoxin extracted with a known amount of CO2, measured in the pump, was determined gravimetrically. As the extract was partially sticking to the inner walls of the valve and to the short capillary, it was not completely collected in the vial. Therefore, we measured the decrease in the mass of the extractor instead of the increase of the mass of the vial. The amount of xanthotoxin extracted with a known amount of CO2, measured in the pump, was determined gravimetrically. As the extract was partially sticking to the inner walls of the valve and to the short capillary, it was not completely collected in the vial. Therefore, we measured the decrease in the mass of the extractor instead of the increase of the mass of the vial. To realize that, when 10 ml CO2 (measured in the pump) had passed through the extractor, the inlet valve was closed and the extractor was depressurized, disconnected from the CO2 line and weighed using an analytical balance. Then it was pressurized again and after 5 min of saturation the CO2 inlet valve was opened, the flow rate was adjusted, and a new measurement started. The measurements were triplicated at each conditions.
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In our preliminary experiments, by varying the flow rate and the amount of CO2 passed through the extractor in one measurement, it was shown that the flow was slow enough to achieve saturation. Furthermore, it was demonstrated that the loss of xanthotoxin dissolved in CO2 flowing out during the depressurization was negligible compared to its amount extracted with 10 mL CO2. The latter can be accounted to the fast decrease in xanthotoxin solubility with decreasing pressure at the beginning of the depressurization process. 2.5. Gas chromatography Quantitative analysis was performed in a Hewlett Packard 6890 gas chromatograph equipped with a flame ionization detector on a fused silica DB-5MS column (30 m × 0.25 mm × 0.25 m) with helium as a carrier gas at flow rate 1 mL/min. The split ratio was typically 1:10. The oven temperature was increased from 50 °C to 290 °C at a rate 3 °C/min. n-Hexadecane was used as internal standard and the quantification of extract components was based on their chromatographic peak areas. The GC-MS unit consisted of Agilent 6890 gas chromatograph equipped with Agilent 5973 mass spectrometer with electron ionization, ionization energy 70 eV, scan mode: 33-400 m/z. The gas chromatographic conditions were identical with those employed for the quantitative analysis. The compounds were identified by comparison of their mass spectra and retention indices with published data [17] and where possible with authentic compounds.
3. Plant composition-dependent model 3.1. Modelling extraction rate The flow pattern in a packed bed column is represented by a series of n ideal mixers. Thus, different degree of axial mixing is simulated, from the lumped parameter model with n = 1 to plug flow with negligible axial mixing at high values of n. The mass balance equations for fluid and solid phases and for the extract are: ,
,
,
,
,
,
,
for j = 1,2,…,n;
′
,
(1)
where wi,j, kg.(kg CO2)-1 is the concentration of i-th extract component in CO2 in the j-th mixer, wsi,j, kg.(kg solid)-1 is the concentration of i-th extract component in the particles in the j-th mixer, t is the extraction time, tr is the residence time in the extractor, q‘, kg.s-1.(kg solid)-1 is the specific flow rate, and = q’tr is the mass ratio of CO2 filling the extraction bed void volume to the plant particles. The extraction yield of i-th component, ei, is given in kg.(kg dry plant)-1. The mass transfer rate over the mass of CO2 in the j-th mixer is ,
,
,
;
(2)
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where w+i,j, kg(kg CO2)-1, is the concentration of i-th component at solid-fluid interface, tf, s, is the fluid phase mass transfer resistance, is the free void of the extraction bed, and kfa0, s-1, is the volumetric fluid phase mass transfer coefficient. The initial and boundary conditions are: 0
,
,
0
,
for j = 1,2,…,n;
,
0 for j = 1
(3)
where wi0 and wsi0 are the initial concentrations of the i-th component in the fluid and solid phase, respectively. The initial concentrations are related to the content of the i-th component in the plant material inserted in the extractor, wui, by mass balance: (4) The model is derived for finely ground plant where the diffusion path in the particles is short and extract is easily accessible. Moreover, some extract components, like cuticular waxes, even occur on the particle surface only. The internal mass transfer resistance is therefore neglected. Next, following Perrut et al. [18], it is assumed that the decrease in the extraction rate observed during a later stage of the extraction indicates the beginning of a solute desorption from the plant matrix after the free solute has been exhausted. Rewritten for a multicomponent model, the equilibrium relationship is: ,
for
,
;
,
,
for
,
(5)
where wsati is the solubility of free i–th component extracted from the mixture of solid phase composition wsi,j, wti is the matrix adsorption capacity for the i-th component, and Ki is the partition coefficient of i-th component, characterizing its adsorption equilibrium. The above equations show that to model the extraction rate, the solubility w+i,j should be known, and particularly the solubility of free substances, wsati,j. That is because, as the initial straight part of experimental extraction curves demonstrates, most of the rue extract was obtained in the first extraction stage, without any effect of solute-matrix interaction on the extraction rate. For the rue extraction, the solubility of furanocoumarins can be read from the initial slopes of the experimental curves. However, and this should be underlined, a very considerable difference between the furanocoumarin solubilities measured for rue samples of different composition was detected. To fully explain and quantify that observation, a suitable and robust instrument, like a TMF, should be available and used. In the subsequent sections, the approaches to modeling the solubility of a single solid solute/solid solute mixture in the scCO2, interwoven in the TMF applied by us, will be briefly presented. 3.2. Solubility modelling To efficiently model and design any extraction process based on supercritical solvents, the solute(s) solubility in scCO2 must be known. However, despite the vital importance of solubility data for the emerging new green technologies, there is still a considerable lack of data because experimental
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determination of the solubilities of various solutes and solid mixtures in supercritical fluids at a range of operating condition is tedious, time-consuming, high-cost and often even not reported in the literature because the scatter of the experimental values is big and unacceptable. Therefore, the interest in developing new and extending the application of the existing models that can accurately correlate and predict the solubilities of pure solid solutes/solid solutes mixtures in supercritical fluids is thriving. This goal is far from trivial as a flexible, robust and efficient modeling tool should be developed, which must comprise methods for estimating the thermophysical properties of pure substances; thermodynamic models for mixture properties; and methods, algorithms and numerical techniques for solving the equilibrium relations [19]. With regard to thermodynamic models, generally theoretical or semi-empirical functional relationships between pressure, volume and temperature, like equations of state (EoSs), are chosen because the interactions are too complex and it is not reasonable to use more fundamentally based equations [20]. The application of EoSs on its own right might be difficult because knowledge of the pure solid solute thermophysical properties including critical and fusion properties, solid molar volume and sublimation pressure, etc. are required. Often, many of those properties are not known and cannot be determined experimentally because the majority of solid solutes of interest to academia and industry are high molar mass, relatively non-volatile and complex substances. Therefore they have to be estimated applying different methods. A completely different approach to modeling solid solubility is the application of empirical models, which are known as density-based models. That approach is favored by many authors as these models do not require pure component properties data and involve equations that contain constants which are adjusted for each compound. The application of density-based models appears to be simple and straightforward as they rely on the knowledge of the thermodynamic behavior of the supercritical solvent only. However, they are mostly capable of correlating, not predicting the solubility [21] as they require availability of sufficient experimental data. Furthermore, as demonstrated by Coelho et al. [22], the determination of density-based models parameters (usually from three to six), is prone to difficulties due to the nonlinear nature of the objective functions usually used. Last but not least, it should be underlined that density-based models cannot be applied to correlate the solubility of multiple solid solutes in scCO2. We will begin by a brief outline of pure solid solubility correlation in scCO2 applying densitybased models. Then, the framework based on application of cubic EoSs as the thermodynamic models, which allows the calculation and prediction of a single solid solute/multiple solid solutes solubility in a system with a supercritical solvent will be given. 3.2.1. Pure solid Density-based model
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To avoid the necessity of providing values for the thermophysical parameters of solids where they are not available, density-based models to correlate the solubility can be employed as a viable alternative. In our case we have chosen the Chrastil equation [23]: (6) This semi-empirical equation correlates the solubility wsat expressed in kg.(kg CO2)-1, CO2 density
f (kg.m-3) and temperature T (K) using three parameters: k is the average number of CO2 molecules associated to a molecule of solute, a is equal to H/R where H is the heat of solvation plus the heat of vaporization of the solute, and b is adjusted to fit the experimental solubility. Thermodynamic modeling framework The TMF designed to model the solubility of a single solid solute and multiple solid-solutes in scCO2 has been discussed in details [11] and in what follows we will present it in a very concise manner. The solubility of a pure solid solute in scCO2 is correlated applying the classical dense gas approach that is based on the equifugacity condition for the solid solute. Thus, provided an EoS is the thermodynamic model for the fluid phase, the expression for the fugacity of the solute in the solid phase f 2solid is:
(7)
s
where P2 is the sublimation (vapor) pressure of the pure solid, 2S is the fugacity coefficient at sublimation pressure and v2solid is the molar volume of the solid, all at temperature T. The fugacity of the solute in the supercritical phase is: (8) Where 2F is the fugacity coefficient, and y2 - the solubility (mole fraction) of the solute in the supercritical phase, and P is the system’s pressure. Introducing certain simplifications, e.g. the solid phase is assumed to be pure and hence the fugacity of the solute in the solid state is equal to the pure solid fugacity, and applying the thermodynamic equilibrium condition, the expression for the mole fraction of the solid component in the fluid phase is:
(9) In the above, the most important variable is the fugacity coefficient of the solid solute in the supercritical fluid phase, 2F , which is calculated by a thermodynamic model.
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The above equations show that the solute solubility is primarily a function of the solid solute pure compound physical properties, the system temperature and pressure, and the fugacity coefficient of the solid solute in the fluid mixture. 3.2.2. Multiple solid solutes For the more complex case of multicomponent solid-SCF (gas) equilibria, Sovova and Stateva (2015), following Prausnitz et al. [24], make the assumption known as Lewis fugacity rule that the fugacity of a component in a mixture is proportional to its mole fraction. Hence, the fugacity of the i-th solute in the solid phase can be calculated according to: (10) where si is the mole fraction of the i-th solute in the system and fi is the fugacity of the pure solute. The fugacity of the i-th solid solute in the mixture is:
exp
(11)
and the fugacity of the i-th solute in the supercritical phase is: (12) The mole fraction of the i-th solid component in the supercritical phase, i.e. its solubility in the SCF at the temperature and pressure of interest, is then:
(13) The solubility of the i-th solute in the supercritical phase, yi, is, as in the case of a binary system, a function of visolid, PiS and iF . 3.2.3. Thermodynamic model In our study we have chosen the Soave-Redlich-Kwong EoS with the one-parameter-per-pair (1PWDW) version of the van der Waals one fluid mixing rule as a representative of the class of cubic EoSs models. As discussed above, its application as a thermodynamic model to calculate the solubilities of either a pure solid solute or a mixture of solids in scCO2 requires information about the compounds critical temperatures, pressures and acentric factors.
3.2.4. Pure component properties The properties required for modeling the solubility of solid solutes in scCO2 are their critical temperature, Tc and critical pressure, pc, melting properties – namely the pure compounds’ solid molar volume, sublimation pressure and enthalpy of fusion. If experimental values for the melting properties are not available they have to be estimated, and details of a possible scenario how to realize that are
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discussed by Coelho et al. [22]. We will just summarize here that the solid molar volumes can be estimated applying the method of Bondi [25], the Clapeyron relation can be used to calculate the sublimation pressures at the temperatures of interest, and the enthalpy of fusion can be estimated applying the method of Jain [26].
4. Application of the model to the SFE of common rue
4.1. Volatiles, coumarins and waxes in common rue The contents of extractable substances in the samples of dry rue were determined by Soxhlet extraction. Approximately 50 compounds were detected by gas chromatography. The major components were 2-undecanone, rutamarin, furanocoumarins psoralen, xanthotoxin and bergapten, and long-chain n-alkanes hentriacontane and tritriacontane in both samples but the percentage of individual substances was different. For the purpose of mathematical modeling, the compounds of similar chemical structure and similar extraction kinetics were regarded as a single pseudo-component. Volatiles. The substances with retention times shorter than the retention time of psoralen were included in the group of volatiles. The major substances in this group were two ketones, 2-nonanone and 2-undecanone, and esters. Thus, the volatiles of sample S1 contained 44.8 % 2-undecanone, 28.6 % undecyl esters, 6.8 % 2-nonanone, and 4.7 % nonyl esters, while the volatiles of sample S2 contained 76.9 % 2-undecanone, 7.6 % undecyl esters, 5.9 % 2-nonanone, and 4.6 % nonyl esters. These results are comparable with the composition of Ruta graveolens essential oil, with 2undecanone (46.8 %) and 2-nonanone (18.8 %) as the main constituents, reported in the study of De Feo et al. [27]. The group of coumarins consists of five furanocoumarins, namely psoralen, xanthotoxin, bergapten, prangenin, as well as oxypeucedanin, and coumarin rutamarin (Table 2). It should be noted that because the solubility of none of the above components in scCO2 has been reported previously in the open literature, we had to choose one of them and measure its solubility. With respect to the commercial availability and affordability of the substances, xanthotoxin was the best choice on the market among them. Hence, the group of coumarins was represented by xanthotoxin. The main components of the group of cuticular waxes were the long-chain alkanes hentriacontane and tritriacontane (Table 3). Supercritical fluid extraction of a mixture of long-chain alkanes, which solubility in scCO2 decreases with increasing length of the carbon chain, was examined previously [11]. We have shown that, if a mixture of such hydrocarbons should be represented by one component in a model for SFE, then the carbon chain of that component should be slightly longer than the average chain length in the mixture. Therefore, n-tritriacontane was selected as the representative of waxes in the model.
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Other detected components not belonging to the volatiles, coumarins, and waxes, like fatty acids, sterols and tocopherols, form the group denoted as “others” in Figure 1. The figure shows considerable difference between the coumarins-to-waxes ratios for rue samples S1 and S2, respectively. It should be noted that the difference in rue composition is very suitable for the purposes of modelling of the dependence of apparent solubility of these pseudo-components on the solid phase composition. The group “others” was not included in the model.
4.2. Shape of extraction curves The volatiles and cuticular waxes are easily accessible to the extraction because of their location. Cuticular waxes cover the surface of leaves, stems, and flowers. Volatiles of Ruta graveolens are stored in secretory cavities [28] which walls became fragile after the treatment with liquid nitrogen and were opened by milling. From the shape of coumarins extraction curve, which does not exhibit any slowdown at the moment when the solution saturated during the static extraction is exhausted, it can be concluded that coumarins also become well accessible by the pretreatment. An example of extraction kinetics is shown in Figure 2, where the yields of volatiles, coumarins and waxes are plotted against the solvent-to-feed ratio. The solvent-to feed value q = = f/(s(1-)) indicates the moment when the solvent filling the bed void volume during the static extraction is just replaced by fresh solvent (if the flow pattern is plug flow). In our experiments, the void fraction was = 0.53 and the particle density determined using pycnometry was s = 1080 kg.m-3. The fastest was the extraction of volatile oil, the kinetics of which can be modeled as washing out of a solute which was completely dissolved in the solvent during the static extraction. The initial condition given by Eq. (4) was reduced to wi0 = wui and Eqs. (1) with ji,j = 0 were solved with the result 1
∑
where
!
,
(14)
By varying the number of mixers we found the best fit of the extraction curve, calculated according to Eq. (24), to the yield of volatiles in the experiment RM6 at n = 2 (Figure 2). Thus, the extraction of volatiles can be modeled as not affected by co-extracted substances, in accordance with the first type of models for multicomponent extraction mentioned in the Introduction. As the interstitial velocity was extremely low (0.4 cm.min-1), the relatively high axial mixing might be caused by natural convection. The extraction of coumarins and waxes was slower than that of volatiles because it was limited by their solubility in scCO2, which we determined from initial slopes of their extraction curves. As the volatiles were washed out in the very beginning of the extraction, and as the shapes of extraction curves of coumarins and waxes were not affected by the presence or absence of volatile oil in the
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extractor, the volatiles were excluded when the multicomponent equilibrium was modeled applying the thermodynamic framework. 4.3. Measurement and correlation of xanthotoxin solubility in scCO2 Xanthotoxin (syn. methoxsalen, 8-methoxypsoralen; 9-methoxy-7H-furo[3,2-g]chromen-7-one) C12H8O4 is a white powder. The results of its solubility measurement in scCO2 are listed in Table 4. The data were obtained as solute-to-solvent mass ratios Sw. Chrastil equation
Preliminary evaluation of xanthotoxin solubility in scCO2 was carried out using Eq. (6) which parameters were optimized to minimize its average absolute relative deviation (AARD) from 69 experimental points (Figure 3). Each point represents one measurement; the experimental error can be estimated from their scatter. The optimized parameters of the Chrastil equation are k = 6.50, a = 5211.7, and b = -27.808. The AARD = 19.7% is relatively high, which is particularly a result of the scatter of experimental points. SRK cubic EoS The application of the SRK cubic EoS to correlate the solubility of xanthotoxin in scCO2 requires knowledge of its fusion and critical properties. The melting temperature of xanthotoxin, as indicated by the supplier, is (148-150) oC and, together with a boiling point value of 414.8 °C at 760 mmHg, are the only properties experimentally measured and available. Hence, all other properties required have to be estimated. The critical temperature and pressure of xanthotoxin were estimated applying the methods suggested in [29,30]. Because the critical parameters of xanthotoxin are hypothetical, and because, to the best of our knowledge, there are no estimations on the properties required published by other authors, there should be an assessment made whether the values reported by us are reasonable. To evaluate the reliability of the critical properties values estimated by us we apply the generalized semi-theoretical expression advocated in [31], which correlates Tc/pc with the van der Waals surface area Qw: Tc/pc = 9.0673 +0.43309(Qw1.3 + Qw1.95)
(15)
where Tc is in Kelvin and pc is in bar. The surface area is a dimensionless parameter and is calculated as the sum of the group area parameters, Qk, according to: ∑
(16)
The ratio of xanthotoxin values estimated by us (given in bold) gives a very good approximation to the theoretically calculated Tc/pc ratio (K.bar-1), namely 26.45 versus 25.65.
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The values of all xanthotoxin thermophysical properties, required for the modelling, either experimentally measured or estimated in this study, are listed in Table 5. To correlate the solubilites of xanthotoxin in scCO2, the unlike-pair interaction parameter, kij was estimated at each temperature of interest to the experiment by minimising the absolute average deviation between our experimental data and the calculated solubility (in mole fractions) applying a standard optimization procedure. The correlations represent quite well the pattern of xanthotoxin solubility behavior with a crossover pressure at about 15.4 MPa (Figure 4). The agreement between the experimentally measured and EoS correlated solubilities of xanthotoxin in scCO2 at the three temperatures of interest to the experiment is shown also in Figure 4. The AARD is 16.8%. 4.4. Solubility of xanthotoxin and n-tritriacontane in the ternary systems with scCO2 As mentioned previously, Chrastil equation was derived for binary systems solute + scCO2, and hence cannot be applied to correlate the solubility of two or more solids in the solvent. Thus, the solubilities of xanthotoxin and n-tritriacontane in ternary mixtures with scCO2 were calculated applying the TMF and following the algorithm outlined in section 3.2.2. The thermophysical properties of n-tritriacontane required for the modeling were estimated and reported previously [11]. They are shown in Table 5. For the ternary system xanthotoxin+n-tririacontane+CO2, in addition to the kij’s for the xanthotoxin+CO2, which, as discussed in the previous section, were estimated from our experimental data, interaction parameters are required also for n-tritiacontane+CO2 and xanthotoxin+n-C33 at the three temperatures of interest to the experiment. With regard to the former, those were determined, as reported by Sovova and Stateva in [11], minimizing the difference between the experimental data of Chandler et al. [32] and calculated solubilities, applying a standard optimization procedure. For the temperatures for which experimental data were not available, the kij parameters were estimated taking into consideration the weak dependence of the binary parameters for n-alkanes+ CO2 on temperature, which assumption, as demonstrated by Sovova and Stateva [11], performs quite well. The kij parameter for xanthotoxin+n-C33 was assumed to be not temperature sensitive and hence a single value for the three temperatures of interest was determined from the best fit to the experimental data corresponding to the initial slopes of the extraction curves. The solubility values for xanthotoxin (wsat1) and n-tritriacontane (wsat2), needed to model the extraction experiments, were calculated for each sample in five points, which represent the compositions of the respective ternary mixtures with CO2. Thus, the first point corresponds to the mixture of coumarins, waxes and CO2 in the extractor at the beginning of extraction, while the other four points were selected in such a way as to simulate the gradual exhaustion of both groups of extracted substances. From the solubility calculations performed for all sets of temperatures and pressures examined, the results for just three instructive examples are chosen and shown in Fig. 5 where the solubilities of the
14
solid mixture constituents are plotted against the decreasing xanthotoxin mass fraction in the mixture, z1, calculated on a solvent-free basis. Figure 5 demonstrates for S1 the influence of temperature on the solubility of the two solid solutes at p = 28 MPa. Thus, the solubility of n-tritriacontane in CO2 (and the solubility of waxes generally) increases with increasing temperature to such extent that the solubility of xanthotoxin, which is less temperature dependent, is suppressed. The influence of samples S1 and S2 composition on the solubility behavior of both solutes in the ternary mixture with CO2 is demonstrated at T = 40 oC. For S1, the solubility of n-tritriacontane in CO2 increases with decreasing z1 in a more pronounced manner than for S2; furthermore the actual solubility values of the model wax are about two times higher than the respective ones for sample S2; the solubility trend of xanthotoxin is the opposite – it decreases more rapidly for S2 than for S1, but the actual solubility is about 1.5 higher for S2 as compared to S1.
4.5. Simulation of SFE kinetics The experimental extraction yields are plotted in dependence on extraction time in Figures 6 and 7 together with calculated extraction curves. The solubilities of xanthotoxin and n-tritriacontane in the ternary systems with CO2, calculated applying the TMF for five composition points for each extraction conditions, were interpolated by polynomials of degree 2. The latter were next substituted in eq. (5) of the extraction model where wsat1
and wsat2 were identified with the solubilities of xanthotoxin and n-tritriacontane, respectively, and ws1,j/(ws1,j + ws2,j) was used instead of the xanthotoxin mass fraction in its mixture with ntritriacontane, z1. The mass balance equations were integrated using the Euler’s method. The external mass transfer coefficient was calculated according to Catchpole and King [33]. To be on the safe side, the maximum particle size, 0.6 mm, was inserted in the formula. Still, the kf values were as high as (0.7-2.5).10-5 m.s-1 for xanthotoxin and (0.4-1.7).10-5 m.s-1 for n-tritriacontane, which corresponds to tf values (0.5-2.5) s that are by orders of magnitude less than the residence time. The small mass transfer resistance therefore did not affect the calculated extraction curves. The remaining model parameters were adjusted to minimize the mean absolute deviation between the calculated and experimental extraction yields. The parameters that characterize the adsorption equilibria, namely the adsorbent capacities wti and the partition coefficients Ki for i=1,2, were adjusted to simulate the period of slow extraction (see Table 6). The trend of bond weakening between the solute and the matrix with increasing the power of the solvent is evident: the partition coefficient increases, favoring thus CO2 phase, and the adsorbent capacity mostly decreases. The sharpness of the calculated transition to lower extraction rate increases with increasing number of mixers in the model, n. The values of parameter n adjusted to match the shape of experimental extraction curves are listed in Table 6, too. The large degree of mixing, indicated particularly at the largest residence times, could be related to the extremely low interstitial velocities.
15
The calculated extraction curves represent quite well the pattern of the change of experimental extraction yields vs time as shown in Figures 6 and 7. Quantitatively, the mean absolute deviation between the calculated and experimental extraction yields was related to the asymptotic yield wui in order to obtain the deviation i for each extraction curve: ∆
∑
,
for i=1,2
(17)
where m is the number of experimental points and i indicates the i-th component. The deviation of the yields of coumarins and waxes was similar and ranged from 0.2% for coumarins extracted from sample S2 at 60 °C and 12 MPa to 5.8% for waxes extracted from sample S1 at 40 °C and 28 MPa. The mean value of for the whole set of experiments and both pseudo-components was 2.2%.
5. Conclusions In this study a novel approach to modeling multicomponent supercritical fluid extraction was presented for the first time, and was applied to model the observed different extraction behavior of three groups of rue constituents. Volatile oil, under the extraction conditions examined, was miscible with supercritical CO2 and was thus practically washed out of the extractor in the beginning of the extraction. The behavior of the solid substances, coumarins and waxes, was more complex; their extraction rate was dependent on the composition of rue samples, which prompted us to examine their solubility behavior. One of the targets of the study, therefore, was to model the coumarins (represented by xanthotoxin) and waxes (represented by n-tritriacontane) mixture solubility in CO2 applying a thermodynamic framework (TMF). In addition, the solubility of xanthotoxin in supercritical CO2 was measured and reported in this study. The TMF results obtained were implemented in the model for multicomponent extraction. The good agreement between the extraction curves, calculated applying the model, and the experimental results obtained is an indication of the fact that the interplay between kinetics and phase equilibria should be taken into consideration when a mixture of components of similar concentration but different solubility is extracted. Hence, a rigorous TMF interwoven with an extraction model provide a reliable tool to obtain deeper realistic insight and, presumably, could be used to model extraction of any natural product.
16
Acknowledgements The authors thank Iva Ličková and Markéta Kurčová who performed the extraction experiments and Petra Cuřínová who conducted the GC analysis of extract samples. This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic [grant number 2B06049].
17
References [1] E. Reverchon, R.Taddeo, G. Della Porta, Extraction of sage oil by supercritical CO2: influence of some process parameters, J. Supercritic. Fluids 8 (1995) 302–309. [2] M.D.A. Saldana, R.S. Mohamed, M.G. Baer, P. Mazzafera, Extraction of purine alkaloids from maté (Ilex paraguariensis) using supercritical CO2, J. Agric. Food Chem. 47 (1999) 3804–3808. [3] M.D.A. Saldana, F. Temelli, S.E. Guigard, Apparent solubility of lycopene and beta-carotene in supercritical CO2, CO2 + ethanol and CO2 + canola oil using dynamic extraction of tomatoes, J. Food Eng. 99 (2010) 1–8. [4] H. Sovova, J. Jez, M. Bartlova, J. Stastova, J., Supercritical carbon dioxide extraction of black pepper, J. Supercrit. Fluids 8 (1995) 295–301. [5] L.F. de Franca, M.A.A. Meireles, Modeling the extraction of carotene and lipids from pressed palm oil (Elaesguineensis ) fibers using supercritical CO2, J. Supercrit. Fluids 18 (2000) 35–47. [6] J. Martinez, A.R. Monteiro, P.T.V. Rosa, M.O.M. Marques, M.A.A. Meireles, Multicomponent model to describe extraction of ginger oleoresin with supercritical carbon dioxide, Ind. Eng. Chem. Res. 42 (2003) 1057–1063. [7] S.L. Chia, R. Sulaiman, H.C. Boo, K. Muhammad, F. Umanan, G.H. Chong, Modeling of rice bran oil yield and bioactive compounds obtained using subcritical carbon dioxide Soxhlet extraction (SCDS), Ind. Eng. Chem. Res. 54 (2015) 8546–8553. [8] Z.P. Shen, M.V. Palmer, S.S.T. Ting, R.J. Fairclough, Pilot scale extraction of rice bran oil with dense carbon dioxide, J. Agric. Food Chem. 44 (1996) 3033–3039. [9] F. Gaspar, Extraction of essential oils and cuticular waxes with compressed CO2: effect of extraction pressure and temperature, Ind. Eng. Chem. Res. 41 (2002) 2497–2503. [10] H. Sovova, A.A. Galushko, R.P. Stateva, K. Rochova, M. Sajfrtova, M. Bartlova, Supercritical fluid extraction of minor components of vegetable oils: beta-sitosterol, J. Food Eng. 101 (2010) 201–209. [11] H. Sovova, R. Stateva, A new approach to modelling supercritical CO2 extraction of cuticular waxes: Interplay between solubility and kinetics, Ind. Eng. Chem. Res. 54 (2015) 4861–4870. [12] S. Milesi, B. Massot, E. Gontier, F. Bourgaud, A. Guckert, Ruta graveolens L.: a promising species for the production of furanocoumarins, Plant Sci. 161 (2001) 189–199. [13] F. Conforti, M. Marrelli, F. Menichini, M. Bonesi, G. Statti, E. Provenzano, F. Menichini, Natural and synthetic furanocoumarins as treatment for vitiligo and psoriasis, Current Drug Therapy 4 (2009) 38–58. [14] B. Xu, L. Wang, L. Gonzáles-Molleda, Y. Wang, J. Xu, Y. Yuan, Antiviral activity of (+)rutamarin against Kaposi’s sarcoma-associated herpesvirus by inhibition of the catalytic activity of human topoisomerase II, Antimicrob. Agents Chemoter. 58 (2014) 563–573.
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[15] Y. Zhang, H. Zhang, X.G. Yao, H. Shen, J. Chen, C. Li et al., (+)-Rutamarin as a dual inducer of both GLUT4 translocation and expression efficiently ameliorates glucose homeostasis in insulinresistant mice. PLoS ONE, 7(2) (2012): e31811. [16] National Institute of Standards and Technology U.S., Thermophysical Properties of Fluid Systems. http://webbook.nist.gov/chemistry/fluid, 2011 (accessed 25.05.16). [17] R.P. Adams, Identification of Essential Oil Components by Gas Chromatography Quadrupole Mass Spectroscopy, fourth ed., Allured Publishing Corporation, Illinois, 2007. [18] M. Perrut, J.Y. Clavier, M. Poletto, E. Reverchon, Mathematical modeling of sunflower seed extraction by supercritical CO2, Ind. Eng. Chem. Res. 36 (1997) 430–435. [19] T. Fornari, R.P. Stateva, R.P., Thermophysical properties of pure substances in the context of sustainable high pressure food processes modelling, in: T. Fornari, R.P. Stateva (Eds.), High Pressure Fluid Technology for Green Food Processing, Springer, Cham Heidelberg New York Dordrecht London, 2015, pp. 117–152. [20] H. Sovova, R.P. Stateva, Supercritical fluid extraction from vegetable materials, Rev. Chem. Eng. 27 (3–4) (2011) 79–156. [21] M.A. Khansary, F. Amiri, A. Hosseini, A.H. Sani, H. Shahbeig, Representing solute solubility in supercritical carbon dioxide: A novel empirical model. Chem. Eng. Res. Des. 93 (2015) 355–365. [22] J.A.P. Coelho, R.M. Filipe, G.P. Naydenova, D.S. Yankov, R.P. Stateva, Semi-empirical models and a cubic equation of state for correlation of solids solubility in scCO2: Dyes and calix[4]arenes as illustrative examples. Fluid Phase Equilibria 426 (2016) 37–46. [23] J. Chrastil, Solubility of solids and liquids in supercritical gases. J. Phys. Chem. 86 (1982) 3016– 3021. [24] J.M. Prausnitz, R.N. Lichtenthaler, E.G.D. Azevedo, Molecular Thermodynamics of Fluid-Phase Equilibria, Prentice-Hall, Englewood Cliffs, NJ, 1999. [25] A. Bondi, van der Waals volumes and radii, J. Phys. Chem. 68(3) (1964) 441–451. [26] A. Jain, S.H. Yalkowsky, Estimation of melting points of organic compounds – II, J. Pharm. Sci. 95(12) (2006) 2562–2618. [27] V. De Feo, F. De Simone, F. Senatore, Potential allelochemicals from the essential oil of Ruta graveolens, Phytochemistry 61 (2002) 573–578. [28] A.A. Malik, S.R. Mir, J. Ahmad, J., Ruta graveolens L. essential oil composition under different nutritional treatments, American-Eurasian J. Agric. & Environ. Sci. 13(10) (2013) 1390–1395. [29] W.A. Wakeham, G.St. Cholakov, R.P. Stateva, Liquid density and critical properties of hydrocarbons estimated from molecular structure, J. Chem. Eng. Data 47(3) (2002) 559–570. [30] N. Brauner, R.P. Stateva, G.S. Cholakov, M. Shacham, Structurally “targeted” quantitative structure-property relationship method for property prediction, Ind. Eng. Chem. Res. 45(25) (2006) 8430–8437.
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[31] A. Zbogar, F.V.D. Lopes, G.M. Kontogeorgis, Approach suitable for screening estimation methods for critical properties of heavy compounds, Ind. Eng. Chem. Res. 45(1) (2006) 476–480. [32] K. Chandler, F.L.L. Pouillot, C.A. Eckert, Phase equilibria of alkanes in natural gas systems. 3. Alkanes in carbon dioxide, J. Chem. Eng. Data 41(1) (1996) 6–10. [33] O.J. Catchpole, M.B. King, Measurement and correlation of binary diffusion coefficients in near critical fluids, Ind. Eng. Chem. Res. 33 (1994) 1828–1837.
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Figure captions Fig 1. The ratios of groups of non-volatile components in common rue samples S1 and S2. Fig. 2. Extraction yields of three groups of compounds extracted with scCO2 at 30 MPa and 40 °C from rue sample S2 (exp. RM6; = 0.95). Model for the yield of volatiles which are initially completely dissolved in scCO2: (______) two mixers, (- - -) three mixers. Fig. 3. The experimental xanthotoxin solubility wsat (kg.(kg CO2)-1) against CO2 density f (kg.m-3) on logarithmic scale. The straight lines represent the Chrastil correlation. Fig. 4. Xanthotoxin solubility in scCO2 (mole fraction). Symbols – experimental points, solid lines – correlations applying the SRK EoS at T = (313.2 323.2, 333.3) K with kij = (0.0847; 0.1066 and 0.1152), respectively. Fig. 5. Solubilities of xanthotoxin (_____) and n-C33 (- - -) in model ternary systems xanthotoxin + nC33 + CO2 for rue samples S1 and S2 in dependence on the xanthotoxin fraction z1 = ws1,j/(ws1,j +
ws2,j) at different pressures and temperatures, calculated applying the TMF. Fig. 6. Experimental (symbols) and calculated (lines) extraction yields from common rue, sample S1. Fig. 7. Experimental (symbols) and calculated (lines) extraction yields from common rue, sample S2.
21
22
23
24
25
26
27
28
Table 1 Extraction conditions Run
T (°C) f (kg/m3) a
P (MPa)
Run
Sample S1
P (MPa)
T (°C) (kg/m3) a
Sample S2
RoI1
28
50
857.1
RM1
12
40
717.8
RoI3
28
40
898.5
RM3
12
60
434.4
RoI4
28
60
814.0
RM6
30
40
909.9
RoI5
20
50
784.3
RM9
30
60
830.3
RoI6
12
50
584.7
a
from NIST [16]
Table 2 Contents of coumarins in dry rue, g.(kg solid)-1 Compound
Sample S1 Sample S2
Rutamarin
1.18
1.41
Psoralen
0.42
0.51
Xanthotoxin
0.48
0.58
Bergapten
0.46
0.55
Prangenin
0.16
0.19
Oxypeucedanin 0.07
0.08
Sum
3.32
2.77
Table 3 Contents of components of cuticular waxes in dry rue, g.(kg solid)-1 Compound
Sample S1 Sample S2
Branched pentacosane 0.05
0.03
n-Heptacosane
0.16
0.17
Hexacosanal
0.15
0.07
n-Nonacosane
0.08
0.19
Hentriacontane
2.13
0.85
n-Tritriacontane
2.13
0.64
Sum
4.70
1.96
29
Table 4 Solubility of xanthotoxin in scCO2 as solute-to-solvent mass ratio, wsat, at T = (313.2-333.2) K 313.2 K P
323.2 K 3
wsat ×10 -1
f
P
333.2 K 3
wsat ×10 -1
f
P
wsat ×103 -1
f
(MPa)
(kg.kg )
(kg.m-3)
(MPa)
(kg.kg )
(kg.m-3)
(MPa)
(kg.kg )
(kg.m-3)
12
0.253
717.8
12
0.156
584.7
12
0.089
434.4
13
0.260
743.0
12
0.131
584.7
12
0.118
434.4
14
0.247
763.3
13
0.350
636.1
12.5
0.140
471.5
14
0.345
763.3
14
0.228
672.2
13
0.260
505.4
15
0.404
780.2
14
0.283
672.2
14
0.324
561.4
16
0.310
794.9
15
0.418
699.8
14
0.184
561.4
20
0.651
839.8
16
0.338
722.1
15
0.418
604.1
20
0.510
839.8
16
0.415
722.1
15
0.379
604.1
23
0.776
865.1
18
0.708
757.1
16
0.426
637.5
23
0.713
865.1
18
0.471
757.1
17
0.687
664.6
25
0.886
879.5
18
0.510
757.1
17
0.491
664.6
28
1.042
898.5
20
0.923
784.3
17
0.792
664.6
20
0.827
784.3
17
0.403
664.6
20
0.857
784.3
17
0.933
664.6
22
0.681
806.6
18
0.530
687.3
23
1.080
816.5
19
0.658
706.7
23
0.835
816.5
20
1.201
723.7
23
0.861
816.5
20
0.657
723.7
23
0.692
816.5
21
0.660
738.8
25
1.237
834.2
21
0.819
738.8
25
1.212
834.2
22
0.979
752.4
25
0.966
834.2
23
0.730
764.7
25
1.175
834.2
23
1.398
764.7
26
0.796
842.3
24
1.152
776.1
26
1.590
842.3
25
1.127
786.6
27
0.868
849.9
25
1.370
786.6
27
1.053
849.9
26
1.244
796.3
28
1.296
857.1
28
1.491
814.0
28
1.335
857.1
30
Table 5 Thermophysical properties Property
Xanthotoxin (C12H8O4) n-Tritriacontane
o
Tm ( C)
148-150
345. ± 3a
pc (bar)
33.9
5.54
Tc (K)
896.8
851
VS (cm3mol-1)
152.7
516.7
H (Jmol )
89300
274200a
Pssubl (bar) at T=313.2 K
1.26810-9
3.2210-13
Pssubl (bar) at T=323.2 K
3.62510-9
8.52410-12
Pssubl (bar) at T=333.2 K
9.82810-9
1.82210-10
s
-1
a
– from NIST [16]
Table 6 Adsorption parameters for coumarins (i=1) and waxes (i=2), number of mixers (n), residence time (tr), and interstitial velocity (u) Exp.
P
T
K1
(MPa) °C (kg.kg-1)
wt1 kg/kg
K2
wt2
n
tr
u
(kg.kg-1) (kg.kg-1) (-) (min) (cm.min-1)
Sample S1 RoI1
28
50
0.037
0.0010
0.070
0.0006
2
13.0
1.27
RoI3
28
40
0.120
0.0010
0.026
0.0014
2
17.2
1.18
RoI4
28
60
0.035
0.0011
0.010
0.0010
1
14.4
1.33
RoI5
20
50
0.026
0.0010
0.015
0.0009
3
13.9
1.38
RoI6
12
50
0.014
0.0013
0.006
0.0019
5
11.2
1.83
RM1
12
40
0.040
0.0012
0.010
0.00125
6
20.8
0.54
RM3
12
60
0.014
0.0032
0.009
0.00186
5
12.5
0.89
RM6
30
40
0.70
0.0005
0.017
0.0012
2
27.1
0.41
RM9
30
60
0.12
0.0006
0.0006
0.020
2
24.6
0.45
Sample S2
31