Supercritical fl uid extraction from vegetable materials

Rev Chem Eng 27 (2011): 79–156 © 2011 by Walter de Gruyter • Berlin • Boston. DOI 10.1515/REVCE.2011.002

Supercritical fl uid extraction from vegetable materials

Helena Sovov á 1, * and Roumiana P. Stateva 2

1 Institute of Chemical Process Fundamentals of the ASCR, v.v.i., Rozvojova 135, 16502 Prague , Czech Republic , e-mail: [email protected] 2 Institute of Chemical Engineering , Bulgarian Academy of Sciences, 1113 Sofi a , Bulgaria

*Corresponding author

Abstract

In the 21st century, the mission of chemical engineering is to promote innovative technologies that reduce or eliminate the use or generation of hazardous materials in the design and manufacture of chemical products. The sustainable use of renewable resources, complying with consumer health and environmental requirements, motivates the design, optimisa-tion, and application of green benign processes. Supercritical fl uid extraction is a typical example of a novel technology for the ecologically compatible production of natural substances of high industrial potential from renewable resources such as vegetable matrices that fi nds extended industrial application. The present review is devoted to the stage of development of supercritical fl uid extraction from vegetable material in the last 20 years. Without the ambition to be exhaustive, it offers an extended, in comparison with previous reviews, enumera-tion of extracted plant materials, discusses the mathematical modelling of the process, and advocates a choice for the appro-priate model that is based on characteristic times of individual extraction steps. Finally, the attention is focussed on the ele-ments of a thermodynamic modelling framework designed to predict and model robustly and effi ciently the complex phase equilibria of the systems solute + supercritical fl uid.

Keywords: kinetic models; plants and herbs; supercritical fl uid extraction; thermodynamic models.

1. Introduction

A supercritical fl uid (SCF) is a substance above its critical pressure and temperature (Figure 1 ). Its properties range between those of liquid and gas. The most important advan-tages of SCFs applied in extraction are the extreme variabil-ity of their solvent power with pressure and temperature, and their low viscosity, enabling much faster mass transfer than in liquids. No other extraction method can claim such fl ex-ibility. The main drawback of a large-scale SCF application in comparison with conventional methods, namely the high cost of the high-pressure equipment required, can often be

outweighed by superior product properties, lower operating costs, and/or integration of several technological steps into one.

SCF extraction (supercritical extraction, SFE) of natural substances from plants is a relatively new process. The dis-covery of the solvent power of pressurised carbon dioxide was made in the 19th century (Hannay and Hogarth 1879), but its practical application for extraction of vegetable substances was fi rst studied in the 1960s when more sensitive analytical methods indicated trace amounts of residual organic solvents in food samples and initiated concern about their impact on human health. It was realised that dense carbon dioxide in its supercritical or liquid state (the term “ supercritical fl uid extraction ” often covers the extraction with both supercriti-cal and liquid carbon dioxide) is a non-toxic solvent and thus its traces left in extracts are not harmful. Its critical point ( T c = 31.1 ° C, P c = 7.38 MPa) allows application of relatively low operation temperatures so that thermally labile solutes are protected and the extracts better resemble the natural material than the products of steam distillation and conven-tional extraction where the solvent is usually separated from the extract under increased temperature. Carbon dioxide is non-fl ammable, non-explosive, cheap, and easily acces-sible in high purity. To also dissolve more polar substances, supercritical carbon dioxide (SC-CO 2 ) is usually modifi ed by addition of small amounts of polar liquids, such as methanol, ethanol, water, and others.

Initially, the experiments with SC-CO 2 extraction of nat-ural products were conducted in a limited number of labo-ratories, most intensively in Germany (Zosel 1964) and in Russia (Pekhov et al. 1965). Since then, many laboratories in different countries have been equipped with SFE units and extensive research has been done in the extraction of fl a-vours, spices, essential oils, and other substances from herbs and plants. The fi rst pilot and full-scale plants were built for SC-CO 2 extraction of caffeine from coffee beans and tea leaves, the extraction of acids from hops giving taste to bear, and the extraction of taste and fl avour compounds from spice. The number and capacity of industrial units for supercritical extraction and the variety of extracted substances are increas-ing, and today > 200 industrial plants are operating all over the world (Perrut 2007). The two most important commer-cial applications of SFE in the food industry still remain hop extraction and coffee decaffeination (del Valle and Aguilera 1999); however, the production of extracts rich in biologically active substances as antioxidants, lipid-soluble vitamins, and others is fast increasing.

Small-scale SFE for analytical application was developed in the mid-1980s in response to the desire to reduce the use of organic solvents in the laboratory environment (King 1995). Extraction equipment with extractor capacity of several cubic centimetres or less enables a fast and effi cient isolation

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80 H. Sovov á and R.P. Stateva: SFE from vegetable materials

of substances for chromatographic assay from bulk sample matrix. To achieve complete extraction of analytes, high pressures and temperatures are applied and SC-CO 2 is usu-ally modifi ed to increase the solubility of more polar solutes and/or to weaken solute-matrix interaction.

SC-CO 2 and near-critical water (also known as subcritical water, hot pressurised water, HPW) are regarded as the most promising environmentally benign medium not only for the extraction of natural substances but also for various chemi-cal and related processes. The properties of HPW differ from those of water at ambient conditions. Under pressure and high temperature, it becomes an excellent solvent for not only polar compounds but also non-polar substances. Nevertheless, its critical point (22.1 MPa and 374 ° C) is far above the criti-cal point of CO 2 , and even though the operation temperature of subcritical water is usually selected closer to the lower limit of the range 100 – 374 ° C, the process is not appropri-ate for temperature-labile and easily hydrolysable substances. Moreover, HPW is corrosive, in contrast to SC-CO 2 .

Although the focus of the research in SCF applications is moving nowadays to new areas, such as particle design, chemical reactions in supercritical solvents, polymer treat-ment with SCFs, and fractionation of liquid natural products as edible oils in counter-current extraction columns, still the most extended industrial application of SCFs remains the SC-CO 2 extraction from botanic materials. Concerns about the cost and environmental dangers of waste disposal, and the emission of hazardous solvents into the atmosphere moti-vate the design and application of a green technology such as SFE.

Without the ambition to be exhaustive, we have limited the reviewed literature sources almost entirely to original papers. Moreover, during the last few years, several excellent review papers on supercritical extraction from plants have been pub-lished, and there is no benefi t from repetition. However, we believe we can further elaborate several topics and present new information. First, the table of extracted plants, extended in comparison with previous reviews, should help exploit the information contained in the literature. Further, as many papers on mathematical modelling of SFE from plants have been published recently, an attempt is made to review this lit-erature and advocate a classifi cation of the models in relation with characteristic times of individual extraction steps.

Temperature

T

CP

ress

ure

(g)

(sc)

(s)

(l)

Figure 1 Phase diagram with ternary point (T), critical point (C), and solid (s), liquid (l), gaseous (g), and supercritical (sc) state.

We will also focus our attention on the thermodynamic modelling of the complex systems solid solute + SCF. The modelling of systems with an SCF has been comprehen-sively discussed in two books (McHugh and Krukonis 1994, Prausnitz et al. 1999) and several reviews – see, for example, the contributions by Brennecke and Eckert (1989), Johnston et al. (1989), and Ekart et al. (1991), to name just a few. More recent papers and reviews devote particular attention to modelling solid + SCF systems without and with a co-solvent (Ashour et al. 2000, Escobedo-Alvarado et al. 2001, Higashi et al. 2001, Gordillo et al. 2005a) and the main conclusion of the authors can be briefl y summarised as follows: (i) pre-diction of SFE is diffi cult even when experimental data are available to refi ne the models used, (ii) theoretically based models are forced to fi t the data better by the introduction of additional adjusted parameters. Needless to say that this area of research is very competitive and fast moving, and we believe there are still some points that need further attention and elucidation.

2. SFE from plants

2.1. The process and the equipment

The extraction is usually carried out as a semicontinuous process (Figure 2 ). Vegetable material, usually dry and dis-integrated, is charged into an extraction vessel of cylindri-cal shape to obtain a fi xed bed of particles. The supercritical solvent, fed to the extractor continuously by a high-pressure pump at a fi xed fl ow rate, dissolves required substances. The solution fl ows to a separator where the extracted substances precipitate by temperature and/or pressure changes or by applying a mass-separating agent, and the solvent is continu-ously regenerated and recirculated. More separation stages are often used to achieve a partial fractionation of the extract (Brunner 1987, Reverchon 1997).

The typical volume of extractors is from 0.1 to 2 dm 3 on the laboratory scale and from 2 to 5 dm 3 on the pilot scale. Micro-SFE devices are primarily designed for analytical purposes and are frequently connected to an analyser such as gas chro-matograph, gas chromatograph-mass spectrometer, or SCF chromatograph. These instruments use extraction vessels that

Extractor Separator

Con

dens

er

Solution Mixture CO2(g)

CO2(sc) CO2(l)

Figure 2 Simplifi ed scheme of the extraction equipment with CO 2 recycle.


H. Sovov á and R.P. Stateva: SFE from vegetable materials 81

can range from 0.1 cm 3 to several hundred cubic centimetres (Reverchon 1997). In micro- and small-scale extraction, the CO 2 fl ow rate is low and therefore the equipment does not require solvent recycle – CO 2 can be expanded to ambient pressure in the separator and vented.

When the SFE plant is equipped with several separators in series, fractionation of the extracts is possible, operating the separators at different pressures and temperatures. The scope of this operation is to induce the selective precipitation of dif-ferent compound families as a function of their different satu-ration conditions in the solvent. This procedure has often been applied in the SFE of essential oils to separate them from co-extracted cuticular waxes (Reverchon and De Marco 2006).

High capital costs of SFE equipment are usually mentioned among the drawbacks of the process. On the other hand, the operating costs are usually lower than those of conventional extraction. Thus, many large-scale units for the SFE of solid natural materials, mainly for food ingredients and phytophar-maceuticals, are operated worldwide and are economically competitive. Perrut (2000) published a correlation of the investment cost of SFE units delivered on a turn-key basis with the product of total volume of extractors and the design fl ow rate, showing that the cost increases approximately with the square root of the plant capacity. A chapter in a monograph was devoted to the economic evaluation of high-pressure pro-cesses by Lack and Seidlitz (2001). The investment and oper-ating costs were also discussed by Brunner (2005). del Valle et al. (2005a) compiled costs of several production-scale SFE plants of 0.6 – 8 m 3 total extractor capacity and performed a feasibility study of a plant for the extraction of wheat germ oil. They showed how the break-even plant capacity would vary in several countries in Latin America. Simultaneously, Rosa and Meireles (2005a) described the methodology of estimation of the manufacturing costs of SC-CO 2 extracts and used the procedure to estimate the costs of clove bud oil and ginger oleoresin. This methodology was applied also in later publications (Pereira and Meireles 2007, Pereira et al. 2007, Prado et al. 2010, Mezzomo et al. 2011). Fiori (2010) per-formed a study on the possible use of exhausted grape marc for obtaining grape seed oil by means of the SFE based on a thorough analysis of the process, indicating that the proposed industrial application could be economically interesting. Specifi c costs and incomes linked to the supercritical technol-ogy are reported in details for the case study.

Perrut (2000) emphasised the importance of regular main-tenance of the high-pressure equipment, necessary to elimi-nate hazards, and mentions the parts of the equipment that must be inspected fi rst. Cleaning of the equipment was also discussed.

2.2. Review papers

Besides the monographs either devoted to the applications of SCFs generally or directly to SFE (e.g., Stahl et al. 1987, King and Bott 1993, Brunner 1994, Rizvi 1994, Koshevoi and Bliagoz 2000), valuable information on the process has been collected and reported in a number of review papers. From those that are not only limited to supercritical extraction from

plants but also examine other SCF applications, we mention here only a few. Thus, the potential applications of SCFs in bioprocessing (as non-aqueous media for enzymatic reac-tions, solvents or anti-solvents in production of micrometre and submicrometre particles, solvents for extraction, rapidly expanding fl uid for disruption of cells) were reviewed by Jarzebski and Malinowski (1995). The exceptional physical properties of SCFs and their exploitation in environmen-tally benign separation and reaction processes, as well as in other new kinds of materials processing are described by Eckert et al. (1996). Hauthal (2001) reviewed the results on SCF fundamentals and their applications. Marr and Gamse (2000) reviewed developments in extraction, fractionation of products, dyeing of fi bres, treatment of contaminated soils, production of powders in micron and submicron range, and reactions in or with SCFs. Perrut (2000) considered the per-spectives of production-scale applications of SCFs also in respect to the economic competitiveness of these processes with conventional ones. Beckman (2004) examined the use of CO 2 to create greener processes and products, with a focus on research and commercialisation efforts since 1995. The lit-erature on chemical and enzymatic reactions and formation of micro- and nanoparticles revealed that careful application of CO 2 technology can result in cleaner and less expensive pro-cesses and products of higher quality. In the recent review of Temelli (2009) on processing of fats and oils using SC-CO 2 , it is shown that SFE of specialty oils has reached commercial scale and that researchers focus on fractionation of complex lipid mixtures, conducting reactions in supercritical fl uid media, and particle formation for the delivery of bioactive lipid components. A bright future is predicted for new inte-grated processes to be developed, targeting ingredients for both food and non-food industrial applications.

High-pressure fl uid phase-equilibria, both experimental methods and systems investigated, were reviewed by Fornari et al. (1990) for data published in the period 1978 – 1987, Dohrn and Brunner (1995) for the period 1988 – 1993, Christov and Dohrn (2002) for the period 1994 – 1999, Dohrn et al. (2010) for the period 2000 – 2004, and Fonseca et al. (2011) for the period 2005 – 2008. The papers also contain solubility data for many substances in supercritical solvents.

The reviews listed below focus directly on SFE.

2.2.1. Extraction for food, drug, and perfume indus-

tries The state of supercritical extraction of natural prod-ucts in the middle of the 1980s was described by Brunner (1987). Palmer and Ting (1995) discussed the actual and potential applications of SCF technology and presented a summary of commercial applications, patented processes, and published research studies on utilisation of SCFs in food processing. Starmans and Nijhuis (1996) compared different methods, including SFE, for extraction of secondary metabo-lites from plant material. Sihvonen et al. (1999) summarised some of the advances and the latest developments in the fi eld of SCF technology focusing on the use of SC-CO 2 in food, nutraceutical, and pharmaceutical applications. Wolski and Ludwiczuk (2001) presented fundamentals of high-pressure extraction and reviewed literature related to supercritical



extraction in different branches of industry. Raventos et al. (2002) focused their review on the applications and potential of SC-CO 2 in the food industry. Rozzi and Singh (2002) dis-cussed the use of SCFs in different processes of food industry and in food analysis. A review including general description of SCFs, their physicochemical properties and particularly the solvent power, effect of solid matrices on the extraction, and application areas of SFE was published by Askin and Otles (2005). Brunner (2005) reviewed the state of SCF applica-tions to food processing. Besides other processes, industrial-scale extraction from solid materials (decaffeination of green coffee beans, production of hops extracts, recovery of aromas and fl avours from herbs and spices, extraction of edible oils, and removal of contaminants) was discussed, including the solvent power of SC-CO 2 , the course of the extraction pro-cess, design of commercial plants and modes of their opera-tion, equipment size, and processing costs. Recent advances in SFE were overviewed by Herrero et al. (2010).

Hierro and Santamaria (1992) reviewed the SFE tech-niques for extraction of vegetable and animal fats and par-ticularly those containing polyunsaturated fatty acids, which have important pharmacological applications. The paper writ-ten by Kerrola (1995) is focused particularly on the extraction of essential oils and fl avour compounds. Another excellent review on SFE and fractionation of essential oils and related products was published by Reverchon (1997). The paper pre-sents experimental techniques for SFE from plants, solubility in SC-CO 2 of different essential oil components, and math-ematical models for the process. Furthermore, the infl uence of operating parameters on extraction rate and extract compo-sition is discussed as well as pre-treatment of raw materials and post-processing of the extracted essential oils. The appli-cations of dense carbon dioxide for the extraction of pharma-ceuticals from various matrices were reviewed by Dean and Khundker (1997). The SFE process parameters required for a preliminary analysis of the manufacturing costs were com-piled from the literature published in 2001 – 2003 by Meireles (2003). Brazilian research on SCFs and their application, including the SFE from vegetable materials, was reviewed by Rosa and Meireles (2005b). Herrero et al. (2006) reviewed the SFE of functional ingredients from plants, food products, algae, and microalgae with special attention to antioxidants, both for SC-CO 2 and subcritical water as solvents. Diaz-Reinoso et al. (2006) published a comprehensive compilation of data on the SFE of antioxidant compounds from vegetal materials and their purifi cation, with particular attention to the substances of a phenolic nature. Wang and Weller (2006) described and compared the conventional Soxhlet extrac-tion with SFE and other alternative methods and summarised potential uses of these methods for the extraction of nutraceu-ticals from plant materials. Reverchon and De Marco (2006) critically analysed the research on supercritical extraction and fractionation in the last decade, including the SFE of essen-tial and seed oils, antioxidants, pharmaceuticals, colouring matters and pesticides, as well as mathematical modelling of SFE. Catchpole et al. (2009) reviewed the extraction and frac-tionation of specialty lipids (high-value seed oils, polyunsatu-rated fatty acid concentrates, carotenoids, and phospholipids)

with near-critical solvents. Pereira and Meireles (2010) pub-lished an extensive review on the SFE of bioactive compounds (essential oils, phenolic compounds, carotenoids, tocopher-ols, and tocotrienols), taking into account extraction yields, solubility, and manufacturing costs, and operation conditions in the extraction and fractionation. Another overview focused on the application of SFE in recovery of bioactive phenolic compounds from natural sources and effects of extraction conditions on the yield, composition, and antioxidant activity of extracts was published by Marostica et al. (2010).

A review of transport properties and solubilities in SCFs, particularly CO 2 , as well as other underlying factors that are responsible for the kinetics and phase equilibrium in SFE pro-cesses, was presented by del Valle and Aguilera (1999). They described the selective CO 2 extraction of essential oils, pun-gent principles, carotenoid pigments, antioxidants, antimicro-bials, and related substances to be used as ingredients for the food, drug, and perfume industries from the point of view of the potential applications of SFE in Latin America. Al-Jabari (2002) considered models for various applications of SFE, showed the importance of modelling the initial static extraction (with no solvent fl ow) preceding the dynamic extraction, and demonstrated the similarity between modelling SFE processes and reversible adsorption/desorption processes. The paper of del Valle et al. (2005a) summarises basic and applied research on phase equilibrium and mass transfer kinetics involved in high-pressure CO 2 extraction from solid substrates and particu-larly the extraction of lipids and essential oils from native Latin American plants. Mass transfer models for SFE of vegetable oils from solid matrix were reviewed by del Valle and de la Fuente (2006). A recent review paper published by Oliveira et al. (2011) includes models for kinetics of SFE from solid par-ticles and for SFE from liquids in counter-current columns.

2.2.2. Extraction for analytical purposes Hawthorne (1990) discussed SFE as a method for extraction of analytes from a bulk sample matrix before their analysis. He consid-ered SFE techniques and hardware and concluded that extrac-tion time is reduced, generation of large volumes of waste solvents is eliminated, and the step of concentration of the extracted analytes is greatly simplifi ed compared with con-ventional liquid solvent extraction techniques. Castioni et al. (1995) focused attention on near-critical extraction of com-pounds of plant origin and its on-line coupling with chro-matographic methods. Modey et al. (1996a) explored the use of SCFs for analytical extraction of natural products and highlighted applications where SFE might be advantageous. Chester et al. (1996) published a review on SCF chromatog-raphy and extraction; 2 years later they continued their review in a new contribution focusing on the most signifi cant arti-cles concerning the topics (Chester et al. 1998). According to the authors, the enhanced performance characteristics of SFE, such as greater selectivity compared with conventional methods, reduced time, greater quantitative yields, lower cost per extraction, and new capabilities, had driven the technol-ogy in the 1990s. The advances in SFE spurred the creation of new extraction techniques known as accelerated solvent extraction, hot (subcritical) water extraction, near-critical



fl uid extraction, enhanced-fl uidity extraction, etc., which are performed below the critical point of the solvent and can be called pressurised fl uid extraction. Smith (1999) reviewed the development in SCF chromatography and SFE of analytes in the last 20 years and showed that there is unity in separation methods and that a continuum exists from gases to liquids. de Castro and Jim é nez-Carmona (2000) emphasised the advan-tages of SFE, such as preconcentration effect, cleaniness and safety, quantitativeness, expeditiousness, and simplicity. They discussed limitations of the method demonstrated when extracting polar analytes, occurrence of matrix-analyte bind-ing that often makes a complete extraction of analyte from natural samples impossible, and mentioned different ways of clean-up of fat-soluble analytes from unwanted matrix com-ponents. Chen and Ling (2000) presented a review on SFE in Chinese herbal medicine. The paper contains lists of applica-tion examples of SFE of useful ingredients from herbs and plants, including the operating parameters, concentrations of modifi ers in CO 2 , extraction yields, and analytical methods. Similar data were given for SFE of pesticide residues from different botanic materials. The authors concluded that SFE had proven to be a practical and powerful method for the extraction of useful ingredients and pesticide residues from natural products and food plants. They regarded as promising the possibility of extracting both types of solutes separately using the same extraction medium at different operating con-ditions, and concluded that a systematic and effective means to reach the optimal extraction conditions were yet to come. Lang and Wai (2001) discussed practical aspects of SFE applications in sample preparation, selection of modifi ers, collection methods, on-line coupling techniques, means for avoiding mechanical problems, and approaches to optimi-sation of SFE conditions. King (2002) reviewed analytical supercritical extraction with carbon dioxide as the extract-ing agent from a wide array of sample types. Zougagh et al. (2004) underlined the great analytical potential of SFE, tried to identify reasons for its rare implementation by routine analytical laboratories, and proposed ways to overcome the shortcomings behind them.

Several papers were focused on particular topics in ana-lytical SFE. Extensive revue on the use of SFE in food analy-sis was published by Anklam et al. (1998). The application of SFE and SCF chromatography in forensic investigations was reviewed by Radcliffe et al. (2000). Turner et al. (2001) reviewed the applications of SFE and chromatography for fat-soluble vitamin analysis, and, in the next review paper, Turner et al. (2002) focused on the modes and optimised con-ditions for the collection of extracted analytes. Smith (2002) published a literature review on extraction with superheated water where the extraction of essential oils, fl avours, and fra-grances from plant materials is mentioned besides other mate-rials. Pourmortazavi and Hajimirsadeghi (2007) discussed the developments, modes, and applications of SFE in the isolation of essential oils from plant matrices; showed how the solubil-ity of the solute in the fl uid, diffusion through the matrix, and collection process affect their extraction yield; and compared the SFE with conventional extraction methods. Mendiola et al. (2007) reviewed the applications of pressurised solvents,

both supercritical and liquid, in sample preparation for food analysis, and concluded that these extraction techniques could be used for routine analysis as fast, reliable, clean, and cheap methods. There is, however, a clear need for their validation before they can be applied as offi cial methods substituting the most laborious, time-consuming, and classical procedures. The application of SC-CO 2 in SFE of lipids and in food pro-cessing generally was reviewed by Sahena et al. (2009).

3. Plants and extracts

A hypothetical list of herbs and other plants subjected to SFE in laboratories is getting longer every week, being extended par-ticularly by the plants growing in Asia and Latin America. Table 1 shows the large range of both plants and extracted substances. To keep its size acceptable, we have excluded the extraction of non-native components as pesticides and herbicides (Lehotay 1997, Motohashi et al. 2000, Aguilera et al. 2005), although the research in this fi eld is promising. Also the extraction with subcritical water (see, e.g., Cacace and Mazza 2006) and with other pressurised solvents than CO 2 was not included. Thus, the references concern the extraction of plant components with dense CO 2 , either pure or modifi ed. Even so, the table could not cover all the papers published on the topic because of their large number. It is based on the data collected in the Institute of Chemical Process Fundamentals, the Czech Republic, for more than two decades and therefore it is not restricted to a certain period of publication or selected literature sources.

The knowledge collected in the literature should certainly not be omitted in further research on SFE.

4. Thermodynamic modelling of systems

vegetable solute + SC-CO 2 + entrainer

The advantages of using SCFs as solvents are numerous and lead to environmental, health and safety, and chemical bene-fi ts. That is why they are referred to as the “ green solvents for the future. ” Furthermore, as discussed previously, the thermo-physical properties of SCFs (high diffusivity, low viscosity, density, and dielectric constant) can be fi ne-tuned by changes of operating pressure and/or temperature, and thus SFE has a great potential as a promising, effi cient, and clean alter-native method compared with the conventional methods of distillation and extraction. Thus, there is a clear-cut need for obtaining detailed knowledge that will allow the design and optimisation of the environmentally benign SFE processes. Thermodynamics of the phase equilibria is a vital part of this knowledge, as the objects of SFE are usually very complex, and can exhibit intricate phase behaviour. To predict correctly and calculate effi ciently the equilibria, a robust and reliable thermodynamic modelling framework (TMF) must be avail-able. The TMF comprises three main elements: a library of thermodynamic parameters pertaining to pure substances and binary interactions; thermodynamic models for mixture pro-perties; and methods, algorithms, and numerical techniques for solving the equilibrium relations.



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atil

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2010

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cera

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Fla

vono

ids

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er e

t al.

2007

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et a

l. 20

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an (

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cum

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Vol

atil

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2004

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va)

germ

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tem

Vol

atil

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Cor

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1994

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1994

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1982

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2003

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Bix

a or

ella

na)

seed

Pig

men

ts, c

arot

enoi

d bi

xin

Cha

o et

al.

1991

, Deg

nan

et a

l. 19

91, A

nder

son

et a

l. 19

97, S

ilva

et a

l. 19

99,

2008

a, N

obre

et a

l. 20

06A

pple

(M

alus

dom

esti

ca)

frui

t, pe

els,

pom

ace

Fla

vour

com

poun

ds, p

olyp

heno

lsB

unds

chuh

et a

l. 19

88, A

dil e

t al.

2007

Apr

icot

(P

runu

s ar

men

iaca

) ke

rnel

s, s

hell

s, b

agas

se,

pom

ace

Oil

, β-c

arot

ene

Nie

wou

dt a

nd B

otha

199

8, D

oker

et a

l. 20

04, S

anal

et a

l. 20

04, 2

005,

Ozk

al e

t al.

2005

, 200

5c

Art

emis

ia h

erba

-alb

a (A

rtem

isia

sie

beri

) he

rbV

olat

ile

oil:

cam

phor

, 1-8

cin

eol

Gha

sem

i et a

l. 20

07A

ssaf

oeti

da (

Fer

ula

assa

-foe

tida

)E

-1-p

rope

nyl s

ec-b

utyl

dis

ulfi d

e,

germ

acre

ne B

Kha

jeh

et a

l. 20

05

Avo

cado

(P

erse

a am

eric

ana)

fru

itO

ilB

otha

and

McC

rind

le 1

999

Bab

chi (

Pso

rale

a co

ryli

toli

a) s

eed

Psor

alen

, iso

psor

alen

Wan

g et

al.

2004

aB

acch

aris

dra

cunc

ulif

olia

leav

esP

heno

lic

com

poun

dsP

iant

ino

et a

l. 20

08B

acur

i (P

lato

nia

insi

gnis

) fr

uit s

hell

sO

leor

esin

Mon

teir

o et

al.

1997

Bai

zi (

Arc

hang

elic

a da

huri

ca)

root

V

olat

ile

oil

Mi e

t al.

2005

Bai

cal s

kull

cap

(Scu

tell

aria

bai

cale

nsis

) ro

otF

lavo

noid

s: b

aica

lin,

bai

cale

in, w

ogon

inL

in e

t al.

1999

, Cha

ng e

t al.

2007

Bar

ley

(Hor

deum

vul

gare

) fr

uit

Vit

amin

E: t

ocop

hero

ls, t

ocot

rien

ols

Col

ombo

et a

l. 19

98B

asil

, sw

eet b

asil

(O

cim

um b

asil

icum

) le

aves

Vol

atil

e oi

l, cu

ticu

lar

wax

es, a

ntio

xida

nts

Haw

thor

ne e

t al.

1989

, Rev

erch

on e

t al.

1993

a, 1

994b

, Rev

erch

on a

nd S

esti

Oss

eo

1994

b, L

acho

wic

z et

al.

1996

, 199

7, E

hler

s et

al.

2001

, Dia

z-M

arot

o et

al.

2002

, G

aina

r et

al.

2002

, Men

aker

et a

l. 20

04, M

azut

ti e

t al.

2006

, Lea

l et a

l. 20

08B

irch

(B

etul

a pe

ndul

a) le

aves

Am

ino

acid

sK

lejd

us e

t al.

2008

Bla

ck c

araw

ay (

Bun

ium

per

sicu

m)

frui

tV

olat

ile

oil,

oil,

anti

oxid

ants

thym

oqui

none

an

d ca

rvac

rol

Pour

mor

taza

vi e

t al.

2005

Bla

ck o

il p

lant

(C

elas

trus

pan

icul

atus

) se

edO

il, s

esqu

iterp

enes

Zha

ng e

t al.

1998

aB

lack

berr

y (R

ubus

fru

tico

sus)

see

dO

ilT

hen

et a

l. 19

98B

lack

seed

(N

igel

la s

ativ

a) f

ruit

Oil

, vol

atil

e oi

l: a

ntio

xida

nts

thym

oqui

none

an

d ca

rvac

rol

Turk

ay e

t al.

1996

, Ful

lana

et a

l. 19

99, M

achm

udah

et a

l. 20

05, R

ao e

t al.

2007

, K

okos

ka e

t al.

2008

Ble

ssed

this

tle

(Cni

cus

bene

dict

us)

leav

es, fl

ow

erin

g to

psSe

squi

terp

ene

lact

one

cnic

inK

ery

et a

l. 19

98



Plan

t par

tE

xtra

ct c

ompo

nent

sR

efer

ence

s

Blu

eber

ry (

Vac

cini

um s

p.)

resi

due

afte

r pr

essi

ngA

ntio

xida

nts

Lar

oze

et a

l. 20

10B

oldo

(P

eum

us b

oldu

s) le

aves

, bar

kV

olat

ile

oil:

ant

ioxi

dant

s; a

lkal

oid

bold

ine

Sarg

enti

and

Lan

cas

1997

b, d

el V

alle

et a

l. 20

04b,

200

5bB

orag

e (B

orag

o of

fi cin

alis

) se

edO

il, γ

-lin

olen

ic a

cid

Ille

s et

al.

1994

, Sen

sido

ni e

t al.

1994

, And

ujar

et a

l. 19

99, D

auks

as e

t al.

2002

b,

Gom

ez a

nd d

e la

Oss

a 20

02, K

otni

k et

al.

2006

, Lu

et a

l. 20

07, S

oto

et a

l. 20

08B

razi

lian

gin

seng

(P

faffi

a p

anic

ulat

a, P

. glo

mer

ata)

ro

otβ-

ecdy

sone

, ant

ioxi

dant

sL

eal e

t al.

2010

Bul

nesi

a sa

rmie

ntoi

woo

dV

olat

ile

oil

Mar

ongi

u et

al.

2007

eB

urit

i (M

auri

tia

fl exu

osa)

fru

itO

il, c

arot

enoi

ds, t

ocop

hero

lsF

ranc

a et

al.

1999

aB

utte

rbur

(P

etas

ites

hyb

ridu

s) r

hizo

mes

Sesq

uite

rpen

es a

s pe

tasi

n, is

opet

asin

, py

rrol

izid

ine

alka

loid

sSt

eine

r et

al.

1998

, Bod

ensi

eck

et a

l. 20

07

Cal

amus

(A

coru

s ca

lam

us, A

. gra

min

ei)

rhiz

omes

Vol

atil

e oi

l: a

coro

ne, i

soac

oron

e, β

-asa

rone

Stah

l and

Kel

ler

1983

, Mar

ongi

u et

al.

2005

c, D

ai e

t al.

2008

Cal

ifor

nia

popp

y (E

schs

chol

tzia

cal

ifor

nica

) ae

rial

pa

rt

Isoq

uino

line

alk

aloi

dsB

ugat

ti e

t al.

1993

Cap

e as

h (E

kebe

rgia

cap

ensi

s) w

ood

Bio

acti

ve c

ompo

unds

Sew

ram

et a

l. 19

98, 2

000

Cap

e go

ld (

Hel

ichr

ysum

spl

endi

dum

) le

aves

Vol

atil

e oi

l: g

erm

acre

ne d

-4-o

l, ge

rma-

cren

e D

, bic

yclo

germ

acre

ne, δ

-cad

inen

eM

aron

giu

et a

l. 20

06c

Cap

e go

oseb

erry

(P

hysa

lis

peru

vian

a)A

ntio

xida

nts

Wu

et a

l. 20

06C

apil

lary

wor

mw

ood

(Art

emis

ia c

apil

lari

s) a

eria

l par

tC

apil

lari

sin

Yan

g et

al.

2007

Car

away

(C

arum

car

vi)

seed

, fru

itV

olat

ile

oil:

lim

onen

e, c

arvo

ne; f

atty

oil

Stah

l and

Ger

ard

1982

a, S

tahl

et a

l. 19

84, K

alli

o et

al.

1994

, Sov

ova

et a

l. 19

94b,

T

hen

et a

l. 19

98, B

aysa

l and

Sta

rman

s 19

99, G

amse

and

Mar

r 20

00,

Ahr

o et

al.

2001

, Cab

izza

et a

l. 20

01, S

edla

kova

et a

l. 20

03a

Car

dam

om (

Ele

ttar

ia c

arda

mom

um)

seed

Vol

atil

e oi

l, pi

gmen

ts, f

atty

aci

ds,

anti

oxid

ants

Pekh

ov a

nd G

onch

aren

ko 1

968,

Nai

k et

al.

1989

, Gop

alak

rish

nan

and

Nar

ayan

an

1991

, Ill

es e

t al.

1998

, Mar

ongi

u et

al.

2004

a, H

amda

n et

al.

2008

Car

quej

a (B

acch

aris

trim

era)

aer

ial p

art

Vol

atil

e oi

lV

arga

s et

al.

2006

, Sil

va e

t al.

2009

Car

rot (

Dau

cus

caro

ta L

.) r

oot,

frui

tO

il, c

arot

enes

, vol

atil

e oi

l, bi

olog

ical

ly

acti

ve s

ubst

ance

sSu

bra

et a

l. 19

94, 1

998,

Bar

th e

t al.

1995

, Veg

a et

al.

1996

, Cha

ndra

and

Nai

r 19

97, R

anal

li e

t al.

2004

, Sun

and

Tem

elli

200

6, G

lisi

c et

al.

2007

a, M

axia

et a

l. 20

09C

ashe

w (

Ana

card

ium

Occ

iden

tale

) pe

rica

rpN

ut s

hell

liqu

id, c

arda

nols

Shob

ha a

nd R

avin

dran

ath

1991

, Sm

ith

et a

l. 20

03, P

atel

et a

l. 20

06C

at’s

cla

w (

Unc

aria

torm

ento

sa)

root

Oxi

ndol

e al

kalo

ids

Lop

ez-A

vila

et a

l. 19

97a

Cat

nip

(Nep

eta

cata

ri, N

. tra

nsca

ucas

ica)

Vol

atil

e oi

l, ne

peto

lact

one,

wax

esD

apke

vici

us e

t al.

1996

, B

arth

et a

l. 19

98, C

hotr

atan

adil

ok a

nd C

liff

ord

1998

Ced

ar (

Ced

rus)

woo

dV

olat

ile

oil

Haw

thor

ne e

t al.

1988

Cel

andi

ne (

Che

lido

nium

maj

us)

aeri

al p

art

Alk

aloi

ds c

heli

doni

ne, b

erbe

rine

, cop

tisi

neSa

rkoz

i et a

l. 20

00, T

hen

et a

l. 20

00b

Cel

ery

(Api

um g

rave

olen

s) s

eed,

leaf

, roo

tV

olat

ile

oil,

fatt

y oi

l, fu

rano

coum

arin

s,

fatt

y ac

ids

Moy

ler

1993

, Pep

lons

ki e

t al.

1994

, Cat

chpo

le e

t al.

1996

a, J

arve

npaa

et a

l. 19

97,

Ngu

yen

et a

l. 19

98, D

ella

Por

ta e

t al.

1998

b, P

apam

icha

il e

t al.

2000

, Dau

ksas

et

al. 2

002a

Cer

eals

Toco

pher

ols,

toco

trie

nols

Frat

iann

i et a

l. 20

02C

ham

omil

e (M

atri

cari

a ch

amom

illa

syn

. Cha

mom

illa

re

cuti

ta)

fl ow

ers

Vol

atil

e oi

l, ac

tive

com

pone

nts:

α

-bis

abol

ol, m

atri

cine

, cha

maz

ulen

e;

fl avo

noid

s

Stah

l and

Sch

utz

1978

, Vuo

rela

et a

l. 19

90, R

ever

chon

and

Sen

ator

e 19

94, S

mit

h an

d B

urfo

rd 1

994,

Pek

ic e

t al.

1995

, Tol

ic e

t al.

1996

, Sca

lia

et a

l. 19

99, Z

ekov

ic

2000

, Pov

h et

al.

2001

, Ham

burg

er e

t al.

2004

, Kai

ser

et a

l. 20

04, B

ajer

et a

l. 20

07, K

otni

k et

al.

2007

, Ziz

ovic

et a

l. 20

07a

Che

rry

(Pru

nus

aviu

m)

seed

, pom

ace

Oil

: fre

e fa

tty

acid

s, s

tero

l; p

heno

lic

com

poun

dsB

erna

rdo-

Gil

et a

l. 20

01, A

dil e

t al.

2008

(Tab

le 1

con

tinu

ed)



Plan

t par

tE

xtra

ct c

ompo

nent

sR

efer

ence

s

Che

rvil

(A

nthr

iscu

s ce

refo

lium

) he

rbV

olat

ile

oil,

met

hyl c

havi

col

Sim

andi

et a

l. 19

96C

hine

se m

ahog

any,

ced

rela

, too

n (C

edre

la s

inen

sis

syn.

Too

na s

inen

sis)

woo

d, b

ark

Ced

relo

ne, p

hyto

ster

ols

Mod

ey e

t al.

1996

b

Chi

nese

may

appl

e (D

ysos

ma

plei

anth

a) r

oots

Podo

phyl

loto

xin

Cho

i et a

l. 19

98b

Chi

nese

moo

nsee

d (S

inom

eniu

m a

cutu

m)

vine

ste

mA

lkal

oid

sino

men

ine

Liu

et a

l. 20

05a

Chr

ysan

them

um (

Chr

ysan

them

um c

iner

arii

foli

um,

C. c

oron

ariu

m, C

. seg

etum

, C. fl

osc

ulos

us)

aeri

al p

art

Vol

atil

e oi

l, py

reth

rins

Sena

tore

et a

l. 20

04, M

aron

giu

et a

l. 20

09

Cin

nam

on (

Cin

nam

omum

zey

lani

cum

) an

d ca

ssia

(C

. cas

sia)

bar

kV

olat

ile

oil:

cin

nam

alde

hyde

Stah

l and

Ger

ard

1982

a, H

awth

orne

et a

l. 19

88, M

ille

r et

al.

1995

, Mar

ongi

u et

al.

2007

d

Cit

ruse

s B

erga

mot

(C

itru

s be

rgam

ia)

peel

s, le

aves

, see

dV

olat

ile

oil:

ber

gapt

enPo

iana

et a

l. 19

94, 1

999,

Kon

do e

t al.

2000

Gra

pefr

uit (

Cit

rus

para

disi

) fl a

vedo

, pee

l, se

edV

olat

ile

oil,

fl avo

noid

nar

ingi

n, li

mon

oids

Poia

na e

t al.

1998

, Gia

nnuz

zo e

t al.

2003

, Yu

et a

l. 20

07 L

emon

(C

itru

s li

mon

um)

peel

Vol

atil

e oi

lC

alam

e an

d St

eine

r 19

82, S

ugiy

ama

and

Saito

198

8, H

awth

orne

et a

l. 19

89,

Lan

genf

eld

et a

l. 19

92 L

ime

(Cit

rus

aura

ntif

olia

, C. l

atif

olia

) pe

elV

olat

ile

oil

Haw

thor

ne e

t al.

1989

, Att

i-Sa

ntos

et a

l. 20

05 M

anda

rin

(Cit

rus

reti

cula

ta)

peel

Vol

atil

e oi

l, ca

rote

noid

s, to

coph

erol

sIl

les

et a

l. 19

99b

Ora

nge

(sw

eet o

rang

e) (

Cit

rus

sine

nsis

), b

itte

r or

ange

(C

. aur

anti

um)

peel

Vol

atil

e oi

l, pe

rill

yl a

lcoh

ol, c

arot

enoi

ds,

toco

pher

ols

Haw

thor

ne e

t al.

1988

, Mir

a et

al.

1996

, 199

9, S

arge

nti a

nd L

anca

s 19

98a,

Ill

es

et a

l. 19

99b,

Ber

na e

t al.

2000

, Lee

et a

l. 20

00, 2

001

Sat

sum

a, ta

nger

ine

(Cit

rus

unsh

iu)

pres

s ca

keβ-

Cry

ptox

anth

inL

im e

t al.

2003

Sha

ddoc

k (C

itru

s m

axim

a) p

eel

Cou

mar

ins

impe

rato

rin,

mer

anzi

n,

mer

anzi

n hy

drat

eTe

ng e

t al.

2005

Tai

wan

tang

erin

e (C

itru

s de

pres

sa)

peel

Poly

met

hoxy

fl avo

nes:

nob

ilet

in,

tang

eret

inL

ee a

t al.

2010

Tan

gor

mur

cote

× C

itru

s si

nens

is (

hybr

id)

peel

Vol

atil

e oi

lSa

rgen

ti a

nd L

anca

s 19

98b

Yuz

u (C

itru

s ju

nos)

see

dO

il, β

-sito

ster

ol, s

qual

ene

Uen

o et

al.

2008

Cla

ry s

age

(Sal

via

scla

rea)

her

bV

olat

ile

oil:

scl

areo

lR

onya

i et a

l. 19

99a

Cli

via

(Cli

via

min

iata

) ro

otB

ioac

tive

com

poun

dsSe

wra

m e

t al.

1998

, 200

1C

loud

berr

y (R

ubus

cha

mae

mor

us)

seed

Oil

, β-c

arot

ene,

vol

atil

e oi

l, to

coph

erol

sM

anni

nen

and

Kal

lio

1997

, Man

nine

n et

al.

1997

bC

love

(Sy

zygi

um a

rom

atic

um, E

ugen

ia c

aryo

phyl

lata

) bu

dsV

olat

ile

oil:

eug

enol

, car

yoph

ylle

ne,

euge

nyl a

ceta

teSt

ahl a

nd G

erar

d 19

82a,

Nai

k et

al.

1989

, Gop

alak

rish

nan

et a

l. 19

90, H

usto

n an

d H

ong

1991

, Hau

ptsc

hott

and

Len

tz 1

993,

Moy

ler

1993

, Kol

lman

nsbe

rger

and

Nit

z 19

94, R

ever

chon

and

Mar

rone

199

7, D

ella

Por

ta e

t al.

1998

a, C

liff

ord

et a

l. 19

99,

Rod

rigu

es e

t al.

2002

, Rue

tsch

et a

l. 20

03, G

eng

et a

l. 20

07, G

uan

et a

l. 20

07,

Mar

tine

z et

al.

2007

, Tak

euch

i et a

l. 20

08C

love

bas

il (

Oci

mum

gra

tiss

imum

) le

aves

Vol

atil

e oi

lL

eal e

t al.

2006

Clo

ver,

red

(Tri

foli

um p

rate

nse)

leav

es, r

oot

Isofl

avo

nes,

vol

atil

e oi

lK

lejd

us e

t al.

2005

, Tap

ia e

t al.

2007

Coc

a (E

ryth

roxy

lum

coc

a) le

aves

Coc

aine

Bra

chet

et a

l. 19

99, 2

000

Coc

oa (

The

obro

ma

caca

o) b

eans

/nib

sC

ocoa

but

ter,

theo

brom

ine,

caf

fein

e;

pyra

zine

s fr

om r

oast

ed b

eans

Ros

si e

t al.

1993

, Li a

nd H

artl

and

1996

, San

agi e

t al.

1997

, Sal

dana

et a

l. 20

00b,

c,

2002

, 200

2a, S

kerg

et a

nd K

nez

2001

, M

oham

ed e

t al.

2002

Coc

onut

pal

m (

Coc

os n

ucif

era)

cop

ra, m

eal

Oil

Asi

s et

al.

2006

(Tab

le 1

con

tinu

ed)



Plan

t par

tE

xtra

ct c

ompo

nent

sR

efer

ence

s

Cof

fee

(Cof

fea)

bea

ns

Caf

fein

e, a

rom

a, d

iterp

enes

caf

esto

l and

ka

hweo

l, li

pids

, chl

orog

enic

aci

dsZ

osel

197

8, B

runn

er 1

984,

Sug

iyam

a et

al.

1985

, Pek

er e

t al.

1992

, Roe

the

et a

l. 19

92, P

iets

ch e

t al.

1998

, Ram

os e

t al.

1998

, del

Val

le a

nd A

guil

era

1999

, Oli

veir

a et

al.

1999

, 200

1, S

arra

zin

et a

l. 20

00, A

rauj

o an

d Sa

ndi 2

006,

de

Aze

vedo

et a

l. 20

08a,

200

8b,c

Cor

dia

verb

enac

ea le

aves

Vol

atil

e oi

l: β

-car

yoph

ylle

neQ

uisp

e-C

ondo

ri e

t al.

2008

Cor

iand

er (

Cor

iand

rum

sat

ivum

) fr

uit,

seed

Vol

atil

e oi

l, fa

tty

oil,

anti

oxid

ants

: toc

ophe

-ro

ls, fl

avo

noid

esK

alli

o an

d K

erro

la 1

992,

Ker

rola

and

Kal

lio

1993

, Cat

chpo

le e

t al.

1994

, 199

6a,

1997

, Ani

tesc

u et

al.

1997

, Rib

eiro

et a

l. 19

98, T

hen

et a

l. 19

98a,

Ill

es e

t al.

2000

, Y

epez

et a

l. 20

02, G

ross

o et

al.

2008

C

ork

oak

(Que

rcus

sub

er)

bark

Tri

terp

enes

: fri

edel

in, b

etul

in, β

-sito

ster

ol,

sito

st-4

-en-

3-on

e C

asto

la e

t al.

2005

Cot

ton

(Gos

sypi

um)

seed

Oil

Lis

t et a

l. 19

83, 1

984a

, Sny

der

et a

l. 19

84, K

uk a

nd H

ron

1994

, Tay

lor

et a

l. 19

97,

Bha

ttac

harj

ee e

t al.

2007

Cra

toxy

lum

pru

nifo

lium

leav

esV

olat

ile

oil

Cal

ame

and

Stei

ner

1982

, Cao

et a

l. 20

00C

rocu

s, a

utum

n (C

olch

icum

aut

umna

le)

seed

A

lkal

oids

: col

chic

ine,

3-d

imet

hylc

olch

i-ci

ne, c

olch

icos

ide

Ell

ingt

on e

t al.

2003

Cra

nber

ry (

Vac

cini

umk

sp.)

res

idue

aft

er p

ress

ing

Ant

ioxi

dant

sL

aroz

e et

al.

2010

Cre

epin

g sp

ilan

thes

(Sp

ilan

thes

am

eric

ana)

fl ow

ers,

le

aves

, and

ste

ms

Vol

atil

e oi

l: s

esqu

iterp

enes

, hea

vy h

ydro

-ca

rbon

s, a

mid

es, i

nsec

tici

de s

pila

ntho

lSt

ashe

nko

et a

l. 19

96b

Cro

ssbe

rry

(Gre

wia

occ

iden

tali

s) w

ood

Bio

acti

ve c

ompo

unds

Sew

ram

et a

l. 19

98C

roto

n m

atou

rens

is b

ark

Mar

avui

c ac

idSc

hnei

der

et a

l. 19

95C

roto

n ze

hntn

eri l

eave

sV

olat

ile

oil

Sous

a et

al.

2005

Cum

in (

Cum

inum

cym

inum

) se

edV

olat

ile

oil:

cum

inal

dehy

de, c

ymol

Nai

k et

al.

1989

, Eik

ani e

t al.

1999

a, H

eike

s et

al.

2001

Cup

hea

(Cup

hea

visc

osis

sma

×C. l

ance

olat

a) s

eed

Fatt

y oi

lE

ller

et a

l. 20

11C

upua

cu (

The

obro

ma

gran

difl o

rum

) se

edFa

tde

Aze

vedo

et a

l. 20

03C

urra

nt, r

ed a

nd b

lack

(R

ibes

rub

rum

, R. n

igru

m)

seed

Oil

, lin

olen

ic a

cids

The

n et

al.

1998

aC

urry

pla

nt (

imm

orte

lle)

(H

elic

hrys

um it

alic

um)

aeri

al p

art

Vol

atil

e oi

l: n

eryl

ace

tate

, ant

ioxi

dant

s M

aron

giu

et a

l. 20

03b,

Pol

i et a

l. 20

03

Cur

ry tr

ee (

Mur

raya

koe

nigi

i syn

. Cha

lcas

koe

nigi

i)

leav

esV

olat

ile

oil:

bio

cide

sV

asud

evan

et a

l. 19

97

Cyp

ress

, red

(Ta

xodi

um d

isti

chum

) sa

wdu

stV

olat

ile

oil

Fuh

et a

l. 19

96D

ande

lion

(Ta

raxa

cum

offi

cin

ale)

leav

es, r

oots

Ole

ores

in: β

-am

yrin

, β-s

itost

erol

Pepl

onsk

i et a

l. 19

94, G

amse

and

Mar

r 19

99, S

iman

di e

t al.

2002

Dan

shen

(Sa

lvia

mil

tior

rhiz

a) r

oot,

rhiz

omes

Tans

hino

nes

Dea

n et

al.

1998

b, W

ang

et a

l. 20

08a

Der

ris

(Der

ris

elli

ptic

a) r

oot

Inse

ctic

ide

rote

none

D’A

ndre

a et

al.

2007

Di q

ian

(Mar

chan

tia

conv

olut

a) le

aves

Vol

atil

e oi

lC

ao e

t al.

2007

, Xia

o et

al.

2007

Dil

l (A

neth

um g

rave

olen

s) s

eed

Vol

atil

e oi

lG

amse

and

Mar

r 20

00D

iosc

orea

nip

poni

ca tu

ber

Dio

sgen

inL

iu e

t al.

1995

Don

g qu

ai (

Arc

hang

elic

a si

nens

is)

root

Fe

ruli

c ac

idSu

n et

al.

2006

Dor

sten

ia b

ryon

iifo

lia

rhiz

omes

Pim

pine

lin,

isob

erga

pten

, fur

ocou

mar

ins

psor

alen

, ber

gapt

en, i

sopi

mpi

neli

n,

trite

rpen

es

Vil

egas

et a

l. 19

93

Dou

glas

-fi r

(P

seud

otsu

ga m

enzi

esii

) ba

rkW

axM

cDon

ald

et a

l. 19

83D

rago

nhea

d (D

raco

ceph

alum

mol

davi

ca)

herb

Vol

atil

e oi

lH

awth

orne

et a

l. 19

93, K

akas

y et

al.

2006

(Tab

le 1

con

tinu

ed)



Plan

t par

tE

xtra

ct c

ompo

nent

sR

efer

ence

s

Eas

tern

fer

ulag

o (F

erul

ago

nodo

sa L

.)V

olat

ile

oil:

α-p

inen

eR

uber

to e

t al.

1999

Eld

er (

Sam

bucu

s ni

gra)

fru

itO

leor

esin

Pepl

onsk

i et a

l. 19

94E

mbu

rana

(To

rres

ea c

eare

nsis

) se

edC

oum

arin

Rod

rigu

es e

t al.

2008

Eph

edra

(E

phed

ra s

inic

a) a

eria

l par

t E

phed

rine

and

its

deri

vati

ves,

non

acos

an-

10-o

lC

hoi e

t al.

1996

, 199

7, 1

999b

, Kim

and

Yoo

200

0

Esp

inhe

ira

sant

a (M

ayte

nus

aqui

foli

um, M

. ili

cifo

lia)

le

aves

Tri

terp

enes

fri

edel

an-3

-ol,

frie

deli

n; p

hyto

l, sq

uale

ne, l

imon

ene,

toco

pher

ols,

sti

gma-

ster

ol, d

odec

anoi

c ac

id, g

eran

yl a

ceta

te

de V

asco

ncel

os e

t al.

2000

, Mos

si e

t al.

2004

, 201

0

Euc

alyp

tus

(Euc

alyp

tus

glob

ulus

, E. c

amal

dule

nsis

, E

. cit

riod

ora,

E. s

path

ulat

a, E

. mic

roth

eca)

leav

es,

woo

d

Vol

atil

e oi

l: 1

,8-c

ineo

le; l

ipid

s, a

ntio

xida

nts

Haw

thor

ne e

t al.

1989

, Gar

au a

nd P

itta

u 19

98, D

ella

Por

ta e

t al.

1999

, Fad

el e

t al

. 199

9, G

onza

les-

Vil

a et

al.

2000

, Fra

ncis

co e

t al.

2001

, Rod

rigu

es e

t al.

2002

, R

ozzi

et a

l. 20

02a,

El-

Gho

rab

et a

l. 20

03, A

shti

ani e

t al.

2007

Eve

ning

pri

mro

se (

Oen

othe

ra b

ienn

is)

seed

Oil

, γ-l

inol

enic

aci

dFa

vati

et a

l. 19

91, C

atch

pole

et a

l. 19

94, K

ing

et a

l. 19

97, G

awdz

ik e

t al.

1998

, Z

izov

ic e

t al.

1998

, Kot

nik

et a

l. 20

06E

vodi

a (E

vodi

a ru

taec

arpa

) he

rb, fi

bre

Vol

atil

e oi

l, ev

odia

min

e, r

utae

carp

ine

Ma

et a

l. 19

91, L

iu e

t al.

2010

Felt

y ge

rman

der

(Teu

criu

m p

oliu

m)

leav

es, fl

ow

ers

Vol

atil

e oi

lE

ikan

i et a

l. 19

99b

Fenn

el (

Foe

nicu

lum

vul

gare

) se

edV

olat

ile

oil:

ane

thol

, est

rago

l, fe

ncho

ne;

fatt

y oi

l; fl

avon

oids

Nai

k et

al.

1989

, The

n et

al.

1998

a, R

ever

chon

et a

l. 19

99, S

iman

di e

t al.

1999

, Y

amin

i et a

l. 20

02, C

oelh

o et

al.

2003

, Dam

jano

vic

et a

l. 20

05, D

iaz-

Mar

oto

et

al. 2

005,

Mou

ra e

t al.

2005

, Baj

er e

t al.

2007

, Ziz

ovic

et a

l. 20

07a,

Tak

euch

i et a

l. 20

08Fe

verf

ew (

Tana

cetu

m p

arth

eniu

m s

yn.

Chr

ysan

them

um p

arth

eniu

, syn

. Pyr

ethr

um p

arth

e-ni

um)

fl ow

ers,

see

ds

Vol

atil

e oi

l, se

squi

terp

ene

lact

one

part

heno

lide

Smit

h an

d B

urfo

rd 1

992,

199

4, K

ery

et a

l. 19

98, 1

999,

Kap

lan

et a

l. 20

02, C

retn

ik

et a

l. 20

05

Fla

x (L

inum

usi

tati

ssim

um)

seed

, fi b

reO

il; w

ax: n

utra

ceut

ical

oct

acos

anol

The

n et

al.

1998

a, B

arth

et a

nd D

aun

2002

, Boz

an a

nd T

emel

li 2

002,

Mor

riso

n et

al

. 200

6F

rank

ince

nse

(Bos

wel

lia

thur

ifer

a, B

. car

teri

i) r

esin

Vol

atil

e oi

l: i

ncen

sole

ace

tate

, oct

anol

ac

etat

e, in

cens

ole,

phy

lloc

lade

neM

a et

al.

1991

, Mar

ongi

u et

al.

2006

e

Gar

den

ange

lica

(A

ngel

ica

arch

ange

lica

, A. d

ahur

ica,

A

. sin

ensi

s) r

oot,

frui

tV

olat

ile

oil,

fura

noco

umar

ins

Nyk

anen

et a

l. 19

91, K

erro

la a

nd K

alli

o 19

94, K

erro

la e

t al.

1994

b, G

awdz

ik e

t al.

1996

, Don

eanu

and

Ani

tesc

u 19

98, P

arou

l et a

l. 20

02

Gar

lic

(All

ium

sat

ivum

) A

llic

inC

alve

y et

al.

1994

, 199

7, R

ybak

et a

l. 20

04, d

el V

alle

et a

l. 20

08G

eran

ium

(P

elar

goni

um g

rave

olen

s) fl

ower

s, le

aves

, st

ems,

sta

lkV

olat

ile

oil

Rei

s M

acha

do e

t al.

1993

, Pet

erso

n et

al.

2006

, Gom

es e

t al.

2007

Gia

nt f

enne

l (F

erul

a co

mm

unis

) fl o

wer

head

sV

olat

ile

oil:

gur

june

nes,

sel

inen

esM

aron

giu

et a

l. 20

05a

Gin

ger

(Zin

gibe

r of

fi cin

alis

) R

hizo

mes

Vol

atil

e oi

l, gi

nger

ols,

ole

ores

in, a

ntio

xi-

dant

s, a

ntic

ance

r su

bsta

nces

Pekh

ov a

nd G

onch

aren

ko 1

968,

Kru

koni

s 19

85, C

hen

et a

l. 19

86, N

aik

et a

l. 19

89,

Kan

diah

and

Spi

ro 1

990,

Moy

ler

1993

, Bar

tley

and

Fol

ey 1

994,

Bar

tley

199

5,

Yon

ei e

t al.

1995

a, R

oy e

t al.

1996

a, B

adal

yan

et a

l. 19

98, M

onte

iro

et a

l. 19

98,

Ngu

yen

et a

l. 19

98, B

artl

ey a

nd J

acob

s 20

00, R

odri

gues

et a

l. 20

02, Z

anca

n et

al

. 200

2, C

atch

pole

et a

l. 20

03, L

eal e

t al.

2003

, Mar

tine

z et

al.

2003

, Liu

et a

l. 20

05a,

Bal

acha

ndra

n et

al.

2006

, 200

7G

inkg

o, m

aide

nhai

r tr

ee (

Gin

kgo

bilo

ba)

leav

esTe

rpen

e tr

ilac

tone

s gi

nkgo

lide

s, b

ilob

alid

e;

fl avo

noid

sC

hoi e

t al.

2002

c, C

hiu

et a

l. 20

02, Y

ang

et a

l. 20

02, M

anni

la e

t al.

2003

Gin

seng

(P

anax

gin

seng

) ro

ot h

air,

leav

es, s

eed

Oil

, gin

seno

side

s; s

apon

ins

Wan

g et

al.

2001

, Liu

et a

l. 20

05a,

Woo

d et

al.

2006

, Zha

ng e

t al.

2006

a,

Luo

et a

l. 20

07

(Tab

le 1

con

tinu

ed)



Plan

t par

tE

xtra

ct c

ompo

nent

sR

efer

ence

s

Gra

pe (

Vit

is v

inif

era)

see

d, p

ulp,

ski

nFa

tty

oil,

lino

leic

aci

d, to

coph

erol

s, to

cot-

rien

ols,

tann

ins,

gly

cosi

des,

pol

yphe

nols

: (+

)-ca

tech

in, (

-)-e

pica

tech

in, r

utin

, que

rce-

tin,

res

vera

trol

– a

ntio

xida

nts

Sovo

va e

t al.

1994

a, G

omez

et a

l. 19

96, M

urga

et a

l. 19

98, 2

000,

Pal

ma

and

Tayl

or 1

999,

Pal

ma

et a

l. 19

99, 2

000,

Arc

e et

al.

2001

, Pas

cual

-Mar

ti e

t al.

2001

, Pa

lenz

uela

et a

l. 20

02, 2

004,

Cao

and

Ito

200

3, A

shra

f-K

hora

ssan

i and

Tay

lor

2004

, Lou

li e

t al.

2004

b, B

ever

idge

et a

l. 20

05, C

hafe

r et

al.

2005

, Bra

vi e

t al.

2007

, Fio

ri 2

007,

Cam

pos

et a

l. 20

08, d

a Si

lva

et a

l. 20

08a,

Fio

ri e

t al.

2008

, Fr

eita

s et

al.

2008

a, 2

008b

Gre

ater

duc

kwee

d (S

piro

dela

pol

yrhi

za)

enti

re p

lant

Squa

lene

, sti

gmas

tero

lC

hoi e

t al.

1997

Gre

cian

fox

glov

e (D

igit

alis

lana

ta)

leav

esD

igox

inM

oore

and

Tay

lor

1995

, 199

6, 1

997

Gre

ek s

age

(Sal

via

tril

oba,

S. f

ruti

cosa

)V

olat

ile

oil

Ron

yai e

t al.

1999

bG

uaco

(M

ikan

ia g

lom

erat

a) le

aves

Cou

mar

in, k

aure

noic

aci

d, lu

peol

kip

eol

acet

ate

Vil

egas

et a

l. 19

97, C

eleg

hini

et a

l. 20

01

Gua

raná

(P

auli

nia

cupa

na)

seed

Caf

fein

e, m

ethy

lxan

thin

esM

ehr

et a

l. 19

96, S

alda

na e

t al.

2000

b,c,

200

2b,c

Gua

va (

Psi

dium

gua

java

) le

aves

Vol

atil

e oi

lSa

grer

o-N

ieve

s et

al.

1994

aG

uine

a pe

pper

(A

fram

omum

mel

egue

ta)

seed

Ole

ores

inFe

rnan

dez

et a

l. 20

06G

utta

-per

cha

tree

(ha

rdy

rubb

er tr

ee)

(Euc

omm

ia

ulm

oide

s) s

eed

Auc

ubin

Li e

t al.

2009

Haw

thor

n (C

rata

egus

sp.

)L

ipop

hili

c co

mpo

unds

Ham

burg

er e

t al.

2004

Haz

el (

Cor

ylus

ave

llan

a) n

utO

il, s

tero

ls, t

ocop

hero

lsB

erna

rdo-

Gil

et a

l. 20

02, O

zkal

et a

l. 20

05b,

c, B

erna

rdo-

Gil

and

Cas

quil

ho 2

007

Hib

iscu

s (H

ibis

cus

escu

lent

us, H

. dif

fere

nt s

sp.)

see

dO

il, a

ntio

xida

nts

Hol

ser

and

Bos

t 200

4, C

han

and

Ism

ail 2

009

Hol

y ba

sil,

tuls

i (O

cim

um s

anct

um)

leav

esV

olat

ile

oil,

bioc

ides

Vas

udev

an e

t al.

1997

Hop

(H

umul

us lu

pulu

s) fl

ower

sV

olat

ile

oil,

resi

ns, b

itte

r ac

ids,

wax

es, a

nd

lipi

dsPe

khov

and

Gon

char

enko

196

8, H

uber

t and

Vit

zthu

m 1

978,

Law

s 19

79, S

harp

e an

d C

rabb

198

0, S

harp

e et

al.

1980

, Gar

dner

198

2, V

ollb

rech

t 198

2, L

ange

zaal

et

al. 1

990,

Dao

ud a

nd K

usin

ski 1

992,

Ver

schu

ere

et a

l. 19

92, M

oyle

r 19

93, I

mbe

rt

et a

l. 19

98, d

el V

alle

and

Agu

iler

a 19

99, d

el V

alle

et a

l. 20

03b,

Zek

ovic

et a

l. 20

07, R

oj a

nd S

kow

rons

ki 2

006

Hor

seta

il (

Equ

iset

um g

igan

teum

)O

leor

esin

Mic

hiel

in e

t al.

2005

Hu

zhan

g (P

olyg

onum

cus

pida

tum

) he

rb, r

oot

Res

vera

trol

, pic

eid,

em

odin

, phy

scio

nW

enli

et a

l. 20

05, Y

u et

al.

2005

, Lu

et a

l. 20

06, M

achm

udah

et a

l. 20

09b

Hys

sop

(Hys

sopu

s of

fi cin

alis

)V

olat

ile

oil,

anti

oxid

ants

Ker

rola

et a

l. 19

94a,

Dap

kevi

cius

et a

l. 19

96, L

anga

et a

l. 20

09, K

azaz

i et a

l. 20

07, B

abov

i et a

l. 20

10In

ula

(Inu

la v

isco

sa, I

. gra

veol

ens)

leav

esV

olat

ile

oil

Mar

ongi

u et

al.

2003

cIr

ania

n sp

urge

(E

upho

rbia

mac

rocl

ada)

leav

es a

nd

stal

ks (

as p

etro

-cro

ps)

Hyd

roca

rbon

sO

zcan

and

Ozc

an 2

004

Iron

wee

d (V

erno

nia

gala

men

sis)

see

d O

il, v

erno

lic

acid

Kin

g et

al.

2001

Japa

nese

pep

per,

Sich

uan

pepp

er (

Xan

thox

ylum

pi

peri

tum

)Sa

nsho

ol c

ompo

unds

Mac

hmud

ah e

t al.

2009

a

Japa

nese

per

sim

mon

(D

iosp

yros

kak

i) p

eels

Car

oten

oids

Taka

hash

i et a

l. 20

06Ja

smin

e (J

asm

inum

offi

cin

alis

, J. g

rand

ifl o

rum

) fl o

wer

sV

olat

ile

oil

Rag

hura

m R

ao e

t al.

1992

, Sas

try

and

Muk

hopa

dhya

y 19

94

Jojo

ba (

Sim

mon

dsia

cal

ifor

nica

, S. c

hine

nsis

) se

edO

ilF

ried

rich

et a

l. 19

84, F

ried

rich

198

8, S

algi

n et

al.

2004

, 200

7Ju

nipe

r (J

unip

erus

com

mun

is, J

. rig

ida,

J. o

xyce

drus

, J.

pho

enic

a) f

ruit

, lea

ves,

woo

dV

olat

ile

oil,

bioa

ctiv

e co

mpo

unds

, an

tim

icro

bial

sM

oyle

r 19

93, C

hatz

opou

lou

2002

, Dam

jano

vic

et a

l. 20

03, 2

006,

Mar

ongi

u et

al.

2003

a, 2

004c

, 200

6c, P

ark

et a

l. 20

04, P

ourm

orta

zavi

et a

l. 20

04,

Bar

jakt

arov

ic e

t al.

2005

, Gli

sic

et a

l. 20

07b,

Med

ini e

t al.

2008

(Tab

le 1

con

tinu

ed)



Plan

t par

tE

xtra

ct c

ompo

nent

sR

efer

ence

s

Kav

a (P

iper

met

hyst

icum

) he

rb, s

tem

s, r

oot

Ole

ores

in, k

ava

lact

ones

Lop

ez-A

vila

and

Ben

edic

to 1

997,

Ash

raf-

Kho

rass

ani e

t al.

1999

, Cat

chpo

le e

t al.

2000

, 200

2K

ola

tree

(C

ola)

nut

sC

affe

ine

Ndi

omu

and

Sim

pson

198

8K

udzu

(P

uera

ria

loba

ta)

root

F

lavo

noid

sW

ang

et a

l. 20

08b

Lau

rel,

daph

ne (

Lau

rus

nobi

lis)

leav

es, s

eed

Vol

atil

e oi

l, to

coph

erol

s, o

ilO

zek

et a

l. 19

98, C

ared

da e

t al.

2002

, Gom

ez-C

oron

ado

et a

l. 20

04, B

eis

and

Dun

ford

200

6, S

anto

yo e

t al.

2006

a, M

arzo

uki e

t al.

2008

Lav

ende

r (L

avan

dula

inte

rmed

ia, L

. sto

echa

s,

L. a

ugus

tifo

lia)

fl ow

ers

Vol

atil

e oi

l, pa

sty

prod

ucts

, ant

ioxi

dant

s,

anti

mic

robi

als

Sim

andi

et a

l. 19

93, A

daso

glu

et a

l. 19

94, W

alke

r et

al.

1994

b, R

ever

chon

et a

l. 19

95c,

Dap

kevi

cius

et a

l. 19

96, F

eket

e et

al.

1996

, Osz

agya

n et

al.

1996

, Akg

un e

t al

. 200

0, 2

001,

Flo

res

et a

l. 20

05, Z

orca

et a

l. 20

06L

emon

bal

m (

Mel

issa

offi

cin

alis

)V

olat

ile

oil,

anti

oxid

ants

Rib

eiro

et a

l. 20

01, R

ozzi

et a

l. 20

02a,

Zia

kova

et a

l. 20

02, M

aron

giu

et a

l. 20

04d

Lem

on b

eeba

lm (

Mon

ardi

a ci

trio

dora

)V

olat

ile

oil

Roz

zi e

t al.

2002

aL

emon

ver

bena

(A

loys

ia tr

iphy

lla)

leav

esV

olat

ile

oil

Cra

bas

et a

l. 20

03, P

erei

ra a

nd M

eire

les

2007

Lem

ongr

ass

(Cym

bopo

gon

citr

atus

) le

aves

, ste

ms

Vol

atil

e oi

lN

diom

u an

d Si

mps

on 1

988,

Sar

gent

i and

Lan

cas

1997

a, C

arls

on e

t al.

2001

, Roz

zi

et a

l. 20

02a,

Mar

ongi

u et

al.

2006

a, H

a et

al.

2008

Lic

oric

e (G

lycy

rrhi

za g

labr

a)G

lycy

rrhi

zin

Kim

et a

l. 20

04, 2

005

Lil

ac (

Syri

nga)

fl ow

ers

Vol

atil

e oi

l, w

axC

alam

e an

d St

eine

r 19

82L

inde

ra s

tryc

hnif

olia

Sesq

uite

rpen

oids

Li e

t al.

2002

Loq

uat (

Eri

obot

rya

japo

nica

) se

edO

il, a

myg

dali

n, β

-sito

ster

olK

awah

ito e

t al.

2008

, Mac

hmud

ah e

t al.

2008

bL

ovag

e (L

evis

ticu

m o

ffi c

inal

e) s

eed,

leav

es, a

nd r

oots

Vol

atil

e oi

l: li

gust

ilid

eD

auks

as e

t al.

1998

, 199

9, 2

002a

, Men

aker

et a

l. 20

04L

ove-

in-a

-mis

t (N

igel

la d

amas

cena

) se

edO

il, v

olat

ile

oil

Dau

ksas

et a

l. 20

02c

Luo

han

guo

(Sir

aiti

a gr

osve

nori

i) f

ruit

Swee

tene

rs: m

ogro

side

sX

ia e

t al.

2008

Lup

ine

(Lup

inus

) O

il, a

lkal

oids

Stah

l et a

l. 19

81, N

ossa

ck e

t al.

2000

Mac

adam

ia (

Mac

adam

ia in

tegr

ifol

ia)

nuts

Oil

Silv

a et

al.

2008

aM

adag

asca

r pe

riw

inkl

e (C

atha

rant

hus

rose

us)

Indo

le a

lkal

oids

vin

doli

ne, v

inbl

asti

neSo

ng e

t al.

1992

, Cho

i et a

l. 20

02a

Mag

noli

a (M

agno

lia

gran

difl o

ra, M

. vir

gini

ana,

M

. offi

cin

alis

) ba

r, ro

otSe

squi

terp

ene

lact

ones

pat

heno

lide

, cos

-tu

noli

de, s

esqu

itepr

ene

cycl

ocol

oren

one,

an

tioxi

dant

s, n

eoli

gnan

s ho

noki

ol, m

agno

lol

Cas

tane

da-A

cost

a et

al.

1995

, Cha

ndra

and

Nai

r 19

95, S

uto

et a

l. 19

97, D

ean

et a

l. 19

98a,

Pal

too

et a

l. 19

99, C

heah

et a

l. 20

10

Mai

ze (

corn

) (Z

ea m

ays)

bra

n, g

erm

Oil

, ste

rols

, fer

ulat

e-ph

ytos

tero

l est

ers,

ph

osph

olip

ids,

bea

uver

icin

Chr

isti

anso

n et

al.

1984

, Lis

t et a

l. 19

84b,

Wil

p an

d E

gger

s 19

91, T

aylo

r et

al.

1993

, Fon

tan

et a

l. 19

94, R

onya

i et a

l. 19

98a,

Tay

lor

and

Kin

g 20

00, 2

002,

A

mbr

osin

o et

al.

2004

, Nag

y et

al.

2008

Mam

a ca

dela

(sw

eet c

otto

n pl

ant)

(B

rosi

mum

gau

d-ic

haud

ii)

bark

, roo

tsTe

rpen

oids

, fur

ocou

mar

ins

psor

alen

, be

rgap

ten

Vil

egas

et a

l. 19

93

Man

go (

Man

gife

ra in

dica

) le

aves

Ole

ores

inPe

reir

a an

d M

eire

les

2007

Mar

al r

oot (

Leu

zea

cart

ham

oide

s sy

n. R

hapo

ntic

um

cart

ham

oide

s) r

oot a

nd le

aves

Ecd

yste

rone

, cyn

arop

icri

nSo

vova

et a

l. 20

08

Mar

ies

fi r

(Abi

es m

arie

sii)

leav

esM

alto

l (an

tifu

ngal

act

ivit

y)O

hira

and

Yat

agai

199

3M

arig

old

(Cal

endu

la o

ffi c

inal

is)

fl ow

ers

Ole

ores

in, v

olat

ile

oil,

trite

rpen

oids

: fa

radi

ol m

onoe

ster

s, m

onoo

l tar

axas

tero

l, lu

peol

, β-a

myr

in; l

utei

n

Ron

yai e

t al.

1998

b, C

raba

s et

al.

2003

, Bau

man

n et

al.

2004

, Ham

burg

er e

t al.

2004

, Cam

pos

et a

l. 20

05, D

anie

lski

et a

l. 20

07, P

etro

vic

et a

l. 20

07, Z

izov

ic e

t al.

2007

a, N

agy

et a

l. 20

08M

arjo

ram

(M

ajor

ana

hort

ensi

s sy

n. O

riga

num

maj

o-ra

na L

.) le

aves

Vol

atil

e oi

l, cu

ticu

lar

wax

es, p

igm

ents

, an

tim

icro

bial

s, a

ntio

xida

nts:

urs

olic

aci

d,

carn

osic

aci

d, c

arno

sol

Rev

erch

on 1

992,

Rev

erch

on e

t al.

1993

, Rev

erch

on a

nd S

esti

Oss

eo 1

994b

, D

apke

vici

us e

t al.

1996

, Vag

i et a

l. 20

02, 2

005a

,b, R

odri

gues

et a

l. 20

03a,

E

l-G

hora

b et

al.

2004

(Tab

le 1

con

tinu

ed)



Plan

t par

tE

xtra

ct c

ompo

nent

sR

efer

ence

s

Mas

tic

(Pis

taci

a le

ntis

cus)

leav

es, b

erri

esV

olat

ile

oil,

wax

esC

ongi

u et

al.

2002

Med

lar

(Mes

pilu

s ge

rman

ica)

see

dV

olat

ile

oil

Pour

mor

taza

vi e

t al.

2005

Mex

ican

sun

fl ow

er (

Tit

honi

a di

vers

ifol

ia)

aeri

al p

art

Sesq

uite

rpen

e la

cton

e ta

giti

nin

CZ

iem

ons

et a

l. 20

05, 2

007

Mil

kwee

d (A

scle

pias

fru

tico

sa)

root

, see

dB

ioac

tive

com

poun

ds; f

atty

oil

, cis

-vac

ce-

nic

acid

Sew

ram

et a

l. 19

98, T

urne

r an

d M

cKeo

n 20

02

Min

t (M

enth

a pi

peri

ta, M

. spi

cata

, M. p

uleg

ium

, R

oman

ian

min

t hyb

rid)

leav

es, fl

ow

ers

Vol

atil

e oi

l, cu

ticu

lar

wax

es, s

qual

ene,

ca

rote

noid

sSe

nich

et a

l. 19

74, B

arto

n et

al.

1992

, Got

o et

al.

1993

, Haw

thor

ne e

t al.

1993

, Si

man

di e

t al.

1993

, Rev

erch

on e

t al.

1994

a, R

oy e

t al.

1996

c, B

arth

et a

l. 19

98,

Ale

ksov

ski e

t al.

1999

, Am

man

n et

al.

1999

, Pin

o et

al.

1999

, Rei

s-V

asco

et a

l. 19

99, 2

000,

Kim

and

Hon

g 20

00, Q

afi s

heh

and

Bar

th 2

000,

Kub

atov

a et

al.

2001

, M

aron

giu

et a

l. 20

01, P

op a

nd B

arth

200

1, D

iaz-

Mar

oto

et a

l. 20

02, A

ghel

et a

l. 20

04, Z

izov

ic e

t al.

2005

, A

l-M

arzo

uqi e

t al.

2007

, Gom

ez-P

riet

o et

al.

2007

, Z

ekov

ic e

t al.

2009

Mos

o-ba

mbo

o (P

hyll

osta

chys

het

eroc

ycla

) H

ydro

carb

ons,

ant

imic

robi

als,

ant

ioxi

dant

s an

d fu

ngic

ides

Qui

tain

et a

l. 20

04

Mou

tan

(Pae

onia

suf

frut

icos

a) c

orte

xPa

eono

lD

ean

and

Liu

200

0M

ulbe

rry

tree

(M

orus

alb

a) b

ark,

leav

es, r

oot b

ark

Tri

terp

ene

α-a

myr

in a

ceta

te, a

ntio

xida

nts

β-ca

rote

ne, α

-toc

ophe

rol

Joo

et a

l. 19

94, C

hoi e

t al.

1997

Mus

hroo

ms

and

fung

i O

leor

esin

, oil

, erg

oste

rol,

carb

oxyl

ic a

nd

fatt

y ac

ids,

ant

ioxi

dant

s, s

ubst

ance

s of

an

tim

icro

bial

act

ivit

y, p

olys

acch

arid

es

del V

alle

and

Agu

iler

a 19

89, S

akak

i et a

l. 19

90, Y

oung

and

Gam

es 1

993,

Abd

ulah

et

al.

1994

, Wal

ker

et a

l. 19

99, Z

hang

et a

l. 20

06a,

Kit

zber

ger

et a

l. 20

07, 2

009

Mus

tard

(B

rass

ica

sp.)

see

dO

ilB

arth

et a

nd D

aun

2002

Myr

rh h

erb

(Com

mip

hora

mol

mol

, C. m

yrrh

a)

Vol

atil

e oi

lM

a et

al.

1991

, Mar

ongi

u et

al.

2005

cM

yrtl

e (M

yrtu

s co

mm

unis

) le

aves

Vol

atil

e oi

lG

arau

and

Pit

tau

1998

Nar

row

-lea

f pu

rple

con

efl o

wer

(E

chin

acea

an

gust

ifol

ia)

aeri

al p

art

Alk

ylam

ides

Sun

et a

l. 20

02

Nee

m tr

ee (

Aza

dira

chta

indi

ca)

seed

, ker

nel

Inse

ctic

ides

, pha

rmac

euti

cals

: aza

dira

chti

n A

, nim

bin,

sal

anni

n, c

utic

ular

wax

esC

erni

a et

al.

1994

, Joh

nson

and

Mor

gan

1997

, Am

bros

ino

et a

l. 19

99,

Tont

hubt

him

thon

g et

al.

2001

, 200

4, M

ongk

holk

hajo

rnsi

lp e

t al.

2005

Nit

rari

a ta

ngut

orum

see

dO

il: u

nsat

urat

ed f

atty

aci

dsW

ang

et a

l. 20

07, S

uo a

nd W

ang

2010

Nut

meg

(M

yris

tica

fra

gran

s) n

utm

eg, m

ace

Vol

atil

e oi

l, nu

tmeg

but

ter

Pekh

ov a

nd G

onch

aren

ko 1

968,

Hub

ert a

nd V

itzt

hum

197

8, M

oyle

r 19

93, N

guye

n et

al.

1998

, Spr

icig

o et

al.

1999

, 200

1, M

achm

udah

et a

l. 20

06O

ak (

Que

rcus

rot

undi

foli

a, Q

. sub

er)

frui

tA

corn

oil

, ste

rols

, toc

ophe

rols

, wax

esL

opes

et a

l. 19

98, L

opes

and

Ber

nard

o-G

il 2

005,

Ber

nard

o-G

il e

t al.

2007

Oil

pal

m tr

ee (

Ela

eis

guin

eens

is)

kern

el, l

eave

s,

mes

ocar

p fi b

res

Oil

, fat

ty a

cids

, α-t

ocop

hero

l, α

- an

d β-

caro

tene

, squ

alen

e, s

tero

lsB

irti

gh e

t al.

1995

, Fra

nca

and

Mei

rele

s 20

00, H

assa

n et

al.

2000

, Rah

man

et a

l. 20

01, N

orul

aini

et a

l. 20

04a,

b, 2

008,

Lau

et a

l. 20

06a,

b, 2

007,

200

8, Z

aidu

l et a

l. 20

06a,

b, 2

007a

,bO

kra

(Abe

lmos

chus

esc

ulen

tes

syn.

Hib

iscu

s es

cu-

lent

es)

seed

Oil

, β-s

itost

erol

, toc

ophe

rols

And

ras

et a

l. 20

05

Oli

ve tr

ee (

Ole

a eu

ropa

ea)

leav

es, h

usk,

pom

ace

Oil

, toc

ophe

rols

, phe

nols

, squ

alen

eE

squi

vel a

nd B

erna

rdo-

Gil

199

3, d

e L

ucas

et a

l. 19

98, 2

002a

,b, 2

003,

Le

Flo

ch

et a

l. 19

98, E

squi

vel e

t al.

1999

b, I

bane

z et

al.

2000

a, S

tavr

ouli

as a

nd P

anay

iout

ou

2005

, del

Val

le e

t al.

2006

Oni

on (

All

ium

cep

a) b

ulb,

ski

nO

leor

esin

, fl a

vour

, sul

phur

, que

rcet

inC

alve

y et

al.

1994

, 199

7, G

uyer

and

Sin

ha 1

995,

Dro

n et

al.

1997

, Sas

s-K

iss

et a

l. 19

98, S

iman

di e

t al.

2000

, Mar

tino

and

Guy

er 2

004

Ora

nge

jasm

ine

(M

urra

ya p

anic

ulat

a) fl

ower

sV

olat

ile

oil

Mar

quin

a-C

hids

ey e

t al.

2000

(Tab

le 1

con

tinu

ed)



Plan

t par

tE

xtra

ct c

ompo

nent

sR

efer

ence

s

Ore

gano

, wil

d m

arjo

ram

(O

riga

num

vul

gare

, O.

vire

ns)

leav

es, b

ract

sV

olat

ile

oil,

cuti

cula

r w

axes

, res

inoi

d co

m-

poun

ds, a

ntio

xida

nts

Ond

arza

and

San

chez

199

0, D

apke

vici

us e

t al.

1996

, Gas

par

et a

l. 19

98, 2

000,

20

01, 2

003,

Sim

andi

et a

l. 19

98, D

iaz-

Mar

oto

et a

l. 20

02, G

aspa

r 20

02, L

eeke

et

al. 2

002,

Men

aker

et a

l. 20

04, R

odri

gues

et a

l. 20

04, L

u et

al.

2005

, Cav

ero

et a

l. 20

06, S

anto

yo e

t al.

2006

aO

sage

ora

nge

tree

(M

aclu

ra p

omif

era)

roo

t bar

k, f

ruit

Xan

thon

es, fl

ava

none

s, is

ofl a

vono

ids:

os

ajin

, pom

ifer

in, l

upeo

l, an

d bu

tyro

sper

-m

ol e

ster

s

Dja

rmat

i et a

l. 19

98, d

a C

osta

et a

l. 19

99

Ox

knee

(A

chyr

anth

es b

iden

tata

) ro

otE

cdys

tero

neZ

heng

et a

l. 20

08Pa

ndan

(P

anda

nus

amar

ylli

foli

us)

leav

es2-

Ace

tyl-1

-pyr

roli

ne, v

olat

ile

oil

Lao

haku

njit

and

Noo

mho

rm 2

004,

Bha

ttac

harj

ee e

t al.

2005

Papr

ika,

red

pep

per

(Cap

sicu

m a

nnuu

m),

and

chi

llie

s (C

apsi

cum

fru

tesc

ens)

fru

itO

il, t

ocop

hero

ls, c

apsa

icin

alk

aloi

ds,

caro

teno

ids

Hub

ert a

nd V

itzt

hum

197

8, C

oene

n 19

83, C

oene

n an

d K

rieg

el 1

984,

Yao

et a

l. 19

94, P

eusc

h et

al.

1997

, Ngu

yen

et a

l. 19

98, S

kerg

et e

t al.

1998

, Ill

es e

t al.

1999

a,

Jare

n-G

alan

et a

l. 19

99, S

ato

et a

l. 19

99, W

eath

ers

et a

l. 19

99, G

nayf

eed

et a

l. 20

01, S

kerg

et a

nd K

nez

2001

, Am

brog

i et a

l. 20

02, D

aood

et a

l. 20

02, C

atch

pole

et

al.

2003

, del

Val

le e

t al.

2003

a, 2

003c

, Dua

rte

et a

l. 20

04, P

erva

-Uzu

nali

c et

al.

2004

, Uqu

iche

et a

l. 20

04, 2

005,

Fer

nand

ez-T

ruji

llo

2008

, Nag

y et

al.

2008

, Nag

y an

d Si

man

di 2

008,

Tep

ic e

t al.

2009

, Ric

hins

et a

l. 20

10, L

i et a

l. 20

11Pa

rsle

y (P

etro

seli

num

cri

spum

, Api

um p

etro

seli

num

) se

ed, l

eave

sV

olat

ile

oil:

est

rago

leN

aik

et a

l. 19

89, D

ella

Por

ta e

t al.

1998

b, T

hen

et a

l. 19

98a,

Lou

li e

t al.

2004

a

Pass

ion

(Pas

sifl o

ra e

duli

s) f

ruit

, lea

ves

Gly

cosy

late

d fl a

vono

ids

Mor

aes

et a

l. 19

97Pe

ach

(Pru

nus

pers

ica)

pom

ace

Poly

phen

ols

Adi

l et a

l. 20

07Pe

anut

(A

rach

is h

ypro

gaea

)O

ilSn

yder

et a

l. 19

84, G

oodr

um a

nd K

ilgo

198

7, K

ing

and

Cat

chpo

le 1

993,

Lan

cas

et

al. 1

994,

San

terr

e et

al.

1994

, Goo

drum

et a

l. 19

96Pe

can

(Car

ya il

lino

ensi

s) k

erne

ls, h

alve

sO

ilM

anes

s et

al.

1995

, Zha

ng e

t al.

1995

a, A

lexa

nder

et a

l. 19

97, L

i et a

l. 19

99Pe

pper

, bla

ck (

Pip

er n

igru

m)

frui

tO

leor

esin

: vol

atil

e oi

l, pi

peri

neH

uber

t and

Vit

zthu

m 1

978,

Cal

ame

and

Stei

ner

1982

, Vid

al a

nd R

icha

rd 1

987,

Fe

rrei

ra e

t al.

1993

, 199

9, S

ovov

a et

al.

1995

, Ngu

yen

et a

l. 19

98, S

kerg

et a

nd

Kne

z 20

01, F

erre

ira

and

Mei

rele

s 20

02, C

atch

pole

et a

l. 20

03, P

erak

is e

t al.

2005

, Iz

adif

ar a

nd A

bdol

ahi 2

006,

Li e

t al.

2006

Phy

sic

nut (

Jatr

opha

cur

cas)

see

dO

ilM

achm

udah

et a

l. 20

08b

Pepp

er tr

ee (

Schi

nus

mol

le)

Vol

atil

e oi

l: p

hell

andr

enes

, lim

onen

e,

elem

ol, α

-eud

esm

olM

aron

giu

et a

l. 20

04b

Pim

ento

, all

spic

e, J

amai

ca p

eppe

r (P

imen

ta d

ioic

a)

berr

ies,

leav

esV

olat

ile

oil:

eug

enol

Kru

koni

s 19

85, P

ino

et a

l. 19

97, M

aron

giu

et a

l. 20

05b

Pin

e (P

inus

pal

ustr

is, P

. syl

vest

ris,

P. p

inas

ter,

P

. nig

ra)

woo

d, n

eedl

es, b

ark

Vol

atil

e oi

l, re

sin,

fat

ty a

cids

; man

oyl

oxid

e; p

heno

lic

anti

oxid

ants

McD

onal

d et

al.

1983

, Ora

v et

al.

1998

, Rui

vo e

t al.

2000

, Duq

uesn

oy e

t al.

2007

, B

raga

et a

l. 20

08P

inec

one

ging

er (

Zin

gibe

r ze

rum

bet)

O

leor

esin

Ahm

ad e

t al.

1994

Pin

k tr

umpe

t tre

e (T

abeb

uia

avel

lane

dae)

woo

dL

apac

hol,

lapa

chon

esV

iana

et a

l. 20

03P

ista

cia

(Pis

taci

a ve

ra, P

. len

tisc

us)

nuts

, hul

lL

ipid

s, a

ntio

xida

nts,

vol

atil

e oi

lB

alab

an e

t al.

1998

, Pal

azog

lu a

nd B

alab

an 1

998,

Gol

i et a

l. 20

05P

itan

ga (

Eug

enia

uni

fl ora

) fr

uit p

ulp

Car

oten

oids

lyco

pene

, rub

ixan

thin

Filh

o et

al.

2008

Pol

ygal

a cy

pari

ssia

s ro

ot, s

tem

s, le

aves

Tri

terp

enes

, phy

tost

erol

s, m

ethy

l sal

icyl

ate

Wei

nhol

d et

al.

2008

Pom

egra

nate

(P

unic

a gr

anat

um)

seed

Vol

atil

e oi

l, fa

tty

oil,

phen

olic

com

poun

dsA

bbas

i et a

l. 20

08a,

bPo

ppy

(Pap

aver

bra

ctea

tum

) se

ed, s

traw

Oil

, toc

ol, o

pium

alk

aloi

ds th

ebai

ne,

code

ine,

mor

phin

eSt

ahl a

nd W

illi

ng 1

980,

Ndi

omu

and

Sim

pson

198

8, J

anic

ot e

t al.

1990

, The

n et

al

. 200

0, B

ozan

and

Tem

elli

200

3

(Tab

le 1

con

tinu

ed)



Plan

t par

tE

xtra

ct c

ompo

nent

sR

efer

ence

s

Pro

so m

ille

t (P

anic

um m

ilia

ceum

) br

anO

ilD

evit

tori

et a

l. 20

00P

umpk

in (

Cuc

urbi

ta fi

cifo

lia,

C. m

osch

ata)

fl es

h,

seed

Oil

, car

oten

oids

Ber

nard

o-G

il a

nd L

opes

200

4, Y

u et

al.

2004

, Seo

et a

l. 20

05, N

agy

et a

l. 20

08

Pup

unha

(G

uili

elm

a sp

ecio

sa)

frui

tO

ilA

rauj

o et

al.

2000

Pur

ple

cone

fl ow

er (

Ech

inac

ea p

urpu

rea)

aer

ial p

art

Alk

ylam

ides

Cat

chpo

le e

t al.

2000

, 200

2P

yret

hrum

(C

hrys

anth

emum

cin

erar

iaef

oliu

m)

fl ow

ers

Inse

ctic

ides

pyr

ethr

ins

Stah

l and

Sch

utz

1980

b, B

unze

nber

ger

et a

l. 19

83, P

an e

t al.

1995

, Ott

erba

ch a

nd

Wen

claw

iak

1999

, Kir

iam

iti e

t al.

2003

a,b,

O’M

ahon

y et

al.

2003

Rag

wor

t (Se

neci

o in

aequ

iden

s, S

. cor

datu

s)P

yrro

lizi

dine

alk

aloi

ds: s

enec

ioni

ne,

sene

ciph

ylli

neB

icch

i et a

l. 19

91

Rai

n da

isy

(Dim

orph

othe

ca p

luvi

alis

) se

ed

Oil

, toc

ophe

rols

, dim

orph

ecol

ic a

cid,

tr

i- a

nd d

i-di

mor

phec

olin

Muu

se e

t al.

1994

, Cup

erus

et a

l. 19

96

Rap

e, c

anol

a (B

rasi

ca n

apus

, B. c

ampe

stri

s) s

eed

Oil

, pol

yuns

atur

ated

fat

ty a

cids

, pho

spho

li-

pids

, phe

noli

c ac

ids

Stah

l et a

l. 19

80, B

unze

nber

ger

et a

l. 19

83, B

runn

er 1

984,

Bul

ley

et a

l. 19

84,

Egg

ers

et a

l. 19

85, L

ee e

t al.

1986

, Kin

g et

al.

1987

, Fat

tori

et a

l. 19

88, T

emel

li

1992

, Tay

lor

et a

l. 19

93, 1

997,

Wal

ker

et a

l. 19

94a,

Dun

ford

and

Tem

elli

199

5,

1997

, Goo

drum

et a

l. 19

96, M

onta

nari

et a

l. 19

96, B

ruhl

and

Mat

thau

s 19

99,

Mat

thau

s an

d B

ruhl

199

9, 2

001,

Bar

thet

and

Dau

n 20

02, L

uque

-Gar

cia

and

de

Cas

tro

2004

, Ger

mai

n et

al.

2005

, del

Val

le e

t al.

2006

, Jen

ab e

t al.

2006

, Don

g an

d W

alke

r 20

08, S

un e

t al.

2008

Ras

pber

ry (

Rub

us id

aeus

) se

ed, r

esid

ue a

fter

pre

ssin

gO

il, a

ntio

xida

nts

The

n et

al.

1998

a, L

aroz

e et

al.

2010

Red

ced

ar (

Juni

peru

s vi

rgin

iana

) w

ood

chip

sO

il (

bioa

ctiv

e ag

ent)

Ell

er a

nd K

ing

2000

, Ell

er a

nd T

aylo

r 20

04R

ice

(Ory

za s

ativ

um)

bran

, cor

nO

il, t

riac

ylgl

ycer

ols,

fre

e fa

tty

acid

s,

oryz

anol

s, to

coph

erol

s, s

tero

ls, w

axes

; ar

oma

Ram

say

et a

l. 19

91, S

aito

et a

l. 19

91, G

arci

a et

al.

1996

, Kin

g et

al.

1996

, She

n et

al.

1996

, 199

7, K

uk a

nd D

owd

1998

, Kim

et a

l. 19

99a,

Xu

and

God

ber

2000

, B

hatt

acha

rjee

et a

l. 20

03, P

erre

tti e

t al.

2003

, Dan

iels

ki e

t al.

2005

, Sar

men

to e

t al

. 200

6, S

park

s et

al.

2006

, Bal

acha

ndra

n et

al.

2008

, Che

n et

al.

2008

a,b,

Wan

g et

al.

2008

aR

idol

fi a (

Rid

olfi a

seg

etum

) di

ffer

ent a

eria

l par

ts

Vol

atil

e oi

lM

aron

giu

et a

l. 20

07b

Roc

k ro

se (

Cis

tus

lada

nife

r) le

aves

Vol

atil

e oi

l, w

axes

de L

ucas

et a

l. 19

99, R

inco

n et

al.

2000

Roc

k sa

mph

ire

(Cri

thm

um m

arit

imum

) ae

rial

par

t V

olat

ile

oil:

p-c

ymen

e, β

-phe

llan

dren

e,

γ-te

rpin

ene,

thym

ol m

ethy

l eth

er, d

ill a

piol

eM

aron

giu

et a

l. 20

07c

Ros

e: w

ild

dog

rose

and

sw

eet b

riar

ros

e (R

osa

cani

na,

R. r

ubig

inos

a) f

ruit

, see

d an

d pe

el

Oil

, car

oten

oids

, toc

ophe

rols

Ille

s et

al.

1997

, del

Val

le e

t al.

2000

a, 2

004,

200

6, E

gger

s et

al.

2000

, Rev

erch

on

et a

l. 20

00, d

el V

alle

and

Uqu

iche

200

2, S

zent

mih

alyi

et a

l. 20

02, H

egel

et a

l. 20

07, M

achm

udah

et a

l. 20

07, 2

008a

,b, T

ozzi

et a

l. 20

08R

ose

of J

eric

ho (

Ana

stat

ica

hier

ochu

ntic

a) a

eria

l par

tH

exad

ecan

oic

acid

, 9,1

2-oc

tade

cadi

enoi

c ac

id, h

enei

cosa

ne, h

epta

cosa

neN

orul

aini

et a

l. 20

09

Ros

emar

y (R

osm

arin

us o

ffi c

inal

is)

leav

esV

olat

ile

oil,

phen

olic

dite

rpen

e an

tiox

i-da

nts:

car

nosi

c ac

id, c

arno

sol,

favo

noid

s,

cuti

cula

r w

axes

, ant

imic

robi

als

Haw

thor

ne e

t al.

1988

, Rev

erch

on a

nd S

enat

ore

1992

, Rev

erch

on e

t al.

1993

, R

ever

chon

and

Ses

ti O

sseo

199

4b, W

alke

r et

al.

1994

b, M

ende

s et

al.

1995

, C

oelh

o et

al.

1997

, Ten

a et

al.

1997

, Lop

ez-S

ebas

tian

et a

l. 19

98, B

aum

an e

t al.

1999

, Iba

nez

et a

l. 19

99, 2

000b

, Bic

chi e

t al.

2000

, Sen

oran

s et

al.

2000

, Lea

l et

al. 2

003,

Ram

irez

et a

l. 20

04, C

arva

lho

et a

l. 20

05, P

rest

i et a

l. 20

05, S

anto

yo e

t al

. 200

5, B

ajer

et a

l. 20

07, C

elik

tas

et a

l. 20

07, B

abov

i et a

l. 20

10R

ue (

Rut

a gr

aveo

lens

) ae

rial

par

t, ro

otA

lkal

oids

Stas

henk

o et

al.

2000

Rus

sian

sag

e (P

erov

skia

atr

ipli

cifo

lia)

aer

ial p

art

Vol

atil

e oi

lPo

urm

orta

zavi

et a

l. 20

03

(Tab

le 1

con

tinu

ed)



Plan

t par

tE

xtra

ct c

ompo

nent

sR

efer

ence

s

Rye

(Se

cale

cer

eale

) br

anA

lkyl

reso

rcin

ols

Fran

cisc

o et

al.

2005

Sach

a in

chi (

Plu

kene

tia

volu

bili

s) s

eed

Fatt

y oi

l: li

nole

ic a

cid,

lino

leni

c ac

id,

γ- a

nd δ

-toc

ophe

rol

Foll

egat

ti-R

omer

o et

al.

2009

Sach

alin

fi r

(Abi

es s

acha

line

nsis

) ba

rkD

iterp

enoi

ds: c

is-a

bien

olO

hira

and

Yat

agai

199

4Sa

ffl o

wer

(C

arth

amus

tinc

tori

us)

seed

Oil

Tayl

or e

t al.

1997

Saff

ron

(Cro

cus

sati

vus)

fl ow

ers

Safr

anal

Sem

iond

et a

l. 19

96, L

ozan

o et

al.

2000

Sage

(Sa

lvia

offi

cin

alis

, S. d

esol

eana

) le

aves

Vol

atil

e oi

l, an

tiox

idan

ts, c

utic

ular

wax

esR

ever

chon

et a

l. 19

95c,

Cat

chpo

le e

t al.

1996

a, 1

997,

Rev

erch

on 1

996,

L

embe

rkov

ics

et a

l. 19

98, B

aum

an e

t al.

1999

, Dau

ksas

et a

l. 20

01, M

aron

giu

et

al. 2

001,

Men

aker

et a

l. 20

04, A

leks

ovsk

i and

Sov

ova

2007

, Mic

ic e

t al.

2008

, B

abov

i et a

l. 20

10Sa

lvia

mir

zaya

nii a

eria

l par

tV

olat

ile

oil

Yam

ini e

t al.

2008

Sand

alw

ood

(San

talu

m a

lbum

, S. s

pica

tum

) st

ems,

w

ood

Vol

atil

e oi

l: s

esqu

iterp

enes

san

talo

l, bi

s-ab

olol

, far

neso

l, nu

cife

rol

Nai

k et

al.

1989

, Pig

gott

et a

l. 19

97, M

aron

giu

et a

l. 20

06e

Sant

olin

a in

sula

ris

Vol

atil

e oi

l, w

axes

, cyt

otox

ic a

nd a

ntim

i-cr

obia

l sub

stan

ces

Che

rchi

et a

l. 20

01

Sass

afra

s (S

assa

fras

alb

idum

) ro

ot, b

ark

All

ylbe

nzen

es: s

afro

leH

eike

s 19

94Sa

vory

(Sa

ture

ja h

orte

nsis

), s

hrub

by s

avor

y (S

. fru

tico

sa),

S. m

onta

na le

aves

Vol

atil

e oi

l, an

tiox

idan

ts, i

nsec

tici

des

Haw

thor

ne e

t al.

1993

, Rib

eiro

et a

l. 19

98, E

squi

vel e

t al.

1999

a, K

ubat

ova

et a

l. 20

01, 2

002,

Coe

lho

et a

l. 20

07, Z

orca

et a

l. 20

07, P

avel

a et

al.

2008

, Gro

sso

et a

l. 20

09Sa

w p

alm

etto

(Se

reno

a se

rrul

ata

syn.

S. r

epen

s sy

n.

Saba

l ser

rula

ta)

berr

ies

Fatt

y ac

ids,

β-s

itost

erol

, nut

race

utic

als

Mar

enti

s 19

98, C

atch

pole

et a

l. 20

00, 2

002

Schi

zand

ra (

Schi

sand

ra c

hine

nsis

) fr

uit,

seed

, ste

ms,

le

aves

Lig

nans

, cin

nam

ic a

cid

Loj

kova

et a

l. 19

97, S

lani

na e

t al.

1997

, Cho

i et a

l. 19

98a,

Kim

et a

l. 19

99b,

Dea

n an

d L

iu 2

000,

Bar

tlov

a et

al.

2002

, Huy

ke e

t al.

2007

, Sov

ova

et a

l. 20

07b,

Wan

g et

al.

2008

aSc

opol

ia p

arvi

fl ora

, Sc.

japo

nica

roo

ts, a

eria

l par

tsT

ropa

ne a

lkal

oids

: hyo

scam

ine,

sco

po-

lam

ine

salt

sJo

o et

al.

1994

, Cho

i et a

l. 19

99

Sea

buck

thor

n (H

ippo

phae

rha

mno

ides

) fr

uit,

seed

, pu

lpO

il, p

olyu

nsat

urat

ed f

atty

aci

ds, w

axes

, ca

rote

noid

s, to

coph

erol

s, p

hyto

ster

ols

Shaf

tan

et a

l. 19

86, S

tast

ova

et a

l. 19

96, M

anni

nen

et a

l. 19

97a,

Yin

et a

l. 20

03,

2005

a,b,

Der

evic

h an

d Sh

indy

apki

n 20

04, Y

akim

ishe

n et

al.

2005

, Ari

mbo

or e

t al.

2006

, Vla

se e

t al.

2006

, Cos

suta

et a

l. 20

07, L

i et a

l. 20

07, O

lah

et a

l. 20

07, X

u et

al

. 200

8a,b

, Saj

frto

va e

t al.

2010

Ses

ame

(Ses

amum

indi

cum

) se

edO

il, α

-toc

ophe

rol,

anti

oxid

ants

, lig

nans

Nam

iki e

t al.

2002

, Oda

basi

and

Bal

aban

200

2, H

u et

al.

2004

, Xu

et a

l. 20

05Se

seli

boc

coni

leav

esV

olat

ile

oil

Mar

ongi

u et

al.

2006

bSh

owy

ratt

lebo

x (C

rota

lari

a sp

ecta

bili

s) s

eed

Alk

aloi

d: m

onoc

rota

line

Scha

effe

r et

al.

1988

, 198

9, 1

989a

Smil

ax, C

hina

(Sm

ilax

chi

na)

tube

rsSa

poge

nins

Shu

et a

l. 20

04So

ya (

Gly

cine

max

imus

) be

ans,

fl ak

es, fl

our

, hyp

o-co

tyle

, cak

e, p

ulp

Oil

, toc

ophe

rols

, pho

spho

lipi

ds, i

sofl

avon

es

daid

zein

, gen

iste

in, p

hyto

ster

ols,

phe

noli

c co

mpo

unds

Stah

l et a

l. 19

80, F

ried

rich

et a

l. 19

82, S

nyde

r et

al.

1984

, Egg

ers

et a

l. 19

85,

Tayl

or e

t al.

1993

, Lan

cas

et a

l. 19

94, 1

995,

Rev

erch

on a

nd S

esti

Oss

eo 1

994a

, C

hand

ra a

nd N

air

1996

, Kin

g et

al.

1996

, Mon

tana

ri e

t al.

1996

, 199

9, T

aylo

r et

al

. 199

7, 2

000,

Sie

vers

199

8, B

ruhl

and

Mat

thau

s 19

99, M

atth

aus

and

Bru

hl 1

999,

20

01, N

odar

et a

l. 20

02, R

osta

gno

et a

l. 20

02, L

uque

-Gar

cia

and

de C

astr

o 20

04,

Kle

jdus

et a

l. 20

05, A

rman

do e

t al.

2006

, Qui

tain

et a

l. 20

06, A

rauj

o et

al.

2007

, H

egel

et a

l. 20

07, K

ao e

t al.

2008

, Roc

hova

et a

l. 20

08Sp

iked

thym

e (T

hym

bra

spic

ata)

V

olat

ile

oil

Sons

uzer

et a

l. 20

04

(Tab

le 1

con

tinu

ed)



Plan

t par

tE

xtra

ct c

ompo

nent

sR

efer

ence

s

Spru

ce (

Pic

ea a

bies

, P. o

mor

ica,

P. p

unge

ns)

need

leV

olat

ile

oil

Haw

thor

ne e

t al.

1988

, Ora

v et

al.

1998

, Sed

lako

va e

t al.

2003

bSt

Joh

n’s

wor

t (hy

peri

ci h

erba

) (H

yper

icum

per

fora

-tu

m L

.) a

eria

l par

t, fl o

wer

sV

olat

ile

oil,

alka

nes,

fat

ty a

cids

, wax

es,

phyt

oste

rols

, phl

orog

luci

nols

hyp

erfo

rin,

ad

hype

rfor

in; q

uerc

etin

, rut

in

Cat

chpo

le e

t al.

2000

, 200

2, C

ui a

nd A

ng 2

002,

Man

nila

et a

l. 20

02, 2

003,

D

imit

ries

ka-S

tojk

ovic

and

Zdr

avko

vski

200

3, R

ompp

et a

l. 20

04, S

eger

et a

l. 20

04, S

mel

cero

vic

et a

l. 20

04, W

ang

et a

l. 20

04, G

lisi

c et

al.

2008

St M

ary’

s th

istl

e, m

ilk

this

tle

(Sil

ybum

mar

ianu

m)

frui

t, se

edO

il, s

ilym

arin

, pig

men

ts, t

ocop

hero

ls,

met

als

Szen

tmih

alyi

et a

l. 19

98, G

amse

and

Mar

r 19

99, S

kerg

et e

t al.

2000

, Had

olin

et a

l. 20

01, S

kerg

et a

nd K

nez

2001

Star

ani

se (

Illi

cium

ver

um)

frui

tV

olat

ile

oil:

ane

thol

eSt

ahl a

nd G

erar

d 19

82a,

Liu

199

6, T

uan

and

Ilan

gant

ilek

e 19

97, D

ella

Por

ta e

t al.

1998

aSt

evia

(St

evia

reb

audi

ana)

leav

es

Ole

ores

in: s

esqu

iterp

enes

, fat

ty a

cids

, al

ipha

tic

hydr

ocar

bons

, ste

roid

s, tr

iterp

e-ne

s; g

lyco

side

s: s

tevi

osid

e, r

ebau

dios

ide

A

Liu

et a

l. 19

97, P

asqu

el e

t al.

1999

, 200

0, C

hoi e

t al.

2002

b, Y

oda

et a

l. 20

03

Stin

ging

net

tle

(Urt

ica

dioi

ca)

leav

es, r

oot

Oil

, ole

ores

in: p

igm

ents

, β-s

itost

erol

, sc

opol

etin

Raf

ajlo

vska

et a

l. 20

01, S

ovov

a et

al.

2004

, Saj

frto

va e

t al.

2005

, Hoj

nik

et a

l. 20

07St

oneb

reak

er (

Phy

llan

thus

nir

uri)

ste

ms,

aer

ial p

art

Gal

lic

acid

, ell

agic

aci

d, c

oril

agin

Mar

kom

et a

l. 20

07St

raw

berr

y (F

raga

ria)

fru

itA

rom

aPo

lese

llo

et a

l. 19

93Su

gar

cane

(Sa

ccha

rum

offi

cin

arum

) le

aves

, rin

dW

ax, o

il, r

esin

Gar

cia

et a

l. 19

94, d

e L

ucas

et a

l. 20

07Su

nfl o

wer

(H

elia

nthu

s an

nuus

L.)

see

dO

il, b

ioac

tive

com

poun

dsSt

ahl e

t al.

1980

, Cal

vo e

t al.

1994

, 199

8, F

avat

i et a

l. 19

94, L

anca

s et

al.

1994

, C

ocer

o an

d C

alvo

199

6, P

erru

t et a

l. 19

97, T

aylo

r et

al.

1997

, Bru

hl a

nd M

atth

aus

1999

, Mat

thau

s an

d B

ruhl

199

9, 2

001,

Roy

er a

nd B

arth

200

0, A

ndri

ch e

t al.

2001

, C

ocer

o an

d G

arci

a 20

01, B

ravi

et a

l. 20

02, K

iria

mit

i et a

l. 20

02, L

uque

-Gar

cia

and

de C

astr

o 20

04, S

algi

n et

al.

2006

, Cas

as e

t al.

2007

, 200

8, H

egel

et a

l. 20

07Sw

eet g

ale

(Myr

ica

gale

) fr

uit

Vol

atil

e oi

lSo

kolo

va e

t al.

2005

Swee

t gra

ss (

Hie

roch

loe

odor

ata)

Ant

ioxi

dant

s 5,

8-di

hydr

oxyc

oum

arin

, 5-

hydr

oxy-

8-O

-β-d

-glu

copy

rano

syl-

benz

opyr

anon

e

Gri

goni

s et

al.

2005

Swee

t iri

s (D

alm

atia

n ir

is)

(Iri

s pa

llid

a) r

hizo

mes

Ir

ones

, iri

dals

Bic

chi e

t al.

1993

Swee

t oli

ve (

Osm

anth

us f

ragr

ans)

fl ow

ers

E

ssen

tial

oil

Yao

et a

l. 19

98Sw

eet p

otat

oes

(Ipo

mea

bat

atas

) ro

otC

arot

enoi

ds, α

-toc

ophe

rol

Span

os e

t al.

1993

, Oku

no e

t al.

2002

Swee

t wor

mw

ood

(Art

emis

ia a

nnua

) ae

rial

par

tA

rtem

isin

in (

anti

mal

aric

com

poun

d),

arte

mis

inic

aci

d, s

copo

leti

n K

ohle

r et

al.

1997

a,b,

Hao

et a

l. 20

02, Q

uisp

e-C

ondo

ri e

t al.

2005

, Tze

ng e

t al.

2007

Tabe

rnae

mon

tana

cat

hari

nens

is b

ranc

hes

and

leav

esIn

dole

alk

aloi

ds, a

ntio

xida

nts

Pere

ira

et a

l. 20

04, 2

005,

200

7Ta

gete

s, m

arig

old

(Tag

etes

luci

da, T

. ere

cta,

T. p

atul

a,

T. m

inut

a) fl

ower

pet

als

Vol

atil

e oi

l: in

sect

icid

es; l

utei

nW

ells

et a

l. 19

92, V

asud

evan

et a

l. 19

97, B

icch

i et a

l. 19

99, M

a et

al.

2008

, Gao

et

al. 2

009,

201

0, S

kerg

et e

t al.

2010

Taiw

an p

lum

yew

(C

epha

lota

xus

wil

soni

ana)

leav

esC

epha

lota

xine

Cho

i et a

l. 20

00Ta

mar

ind

(Tam

arin

dus

indi

ca)

frui

t, pu

lp, s

eed

coat

Vol

atil

e oi

l, an

tiox

idan

ts: e

pica

tech

inSa

grer

o et

al.

1994

, Tsu

da e

t al.

1995

, Lue

ngth

anap

hol e

t al.

2004

Tans

y (T

anac

etum

vul

gare

) fl o

wer

sV

olat

ile

oil

Smit

h an

d B

urfo

rd 1

994

Tea

(Cam

elli

a si

nens

is, C

. sas

anqu

a) s

eed,

leav

esO

il, v

olat

ile

oil,

cate

chin

s, c

affe

ine,

gal

lic

acid

Swif

t et a

l. 19

94, B

rare

n an

d K

urzh

als

1998

, Cha

ng e

t al.

1999

, 200

0, R

ajae

i et

al. 2

005,

Hua

ng e

t al.

2007

, Kim

et a

l. 20

07, 2

008,

Lee

et a

l. 20

07, P

ark

et a

l. 20

07a,

b, S

halm

ashi

et a

l. 20

08

Tea

tree

(M

elal

euca

alt

erni

foli

a) le

aves

, ter

min

al

bran

chle

tsV

olat

ile

oil:

terp

inen

-4-o

lG

arau

and

Pit

tau

1998

, Won

g et

al.

2001

(Tab

le 1

con

tinu

ed)



Plan

t par

tE

xtra

ct c

ompo

nent

sR

efer

ence

s

Thy

me

(Thy

mus

vul

gari

s, T

. zyg

is, T

. her

ba-b

aron

a)

leav

es, fl

ow

erin

g to

ps

Vol

atil

e oi

l: th

ymol

, pas

ty p

rodu

cts,

an

tiox

idan

tsB

estm

ann

et a

l. 19

85, H

awth

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002,

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Vol

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e oi

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tty

acid

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ydro

carb

ons

Rou

t et a

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07To

bacc

o (N

icot

iana

taba

cum

)Ta

r pr

ecur

sors

, nic

otin

e, N

-nit

rosa

min

es,

vola

tile

oil

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ra-a

cyl s

ucro

se e

ster

sH

uber

t and

Vit

zthu

m 1

978,

Don

si e

t al.

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, Pro

kopc

zyk

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92, 1

995,

U

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t al.

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ei e

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vic

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l. 20

00, P

alic

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02, A

shra

f-K

hora

ssan

i et a

l. 20

05To

mat

o (S

olan

um ly

cope

rsic

um, s

yn. L

ycop

ersi

con

escu

lent

um)

seed

, fru

it pu

lp, s

kin

Oil

, car

oten

oids

: lyc

open

e, β

-car

oten

e;

toco

pher

ols,

sito

ster

ols

Roy

et a

l. 19

94a,

199

6a, F

avat

i et a

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97, I

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98, B

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ez-P

riet

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, 200

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el C

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nch

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sam

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t al.

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Tonk

a be

an tr

ee (

Dip

tery

x od

orat

a, C

oum

arou

na

odor

ata)

bea

nsL

ipop

hili

c to

p ph

ase,

cry

stal

line

bas

e ph

ase,

cou

mar

inE

hler

s et

al.

1996

Tre

e w

orm

woo

d (A

rtem

isia

arb

ores

cens

) ae

rial

par

tV

olat

ile

oil:

tran

s-th

ujon

e, c

amph

or,

cham

azul

ene

Mar

ongi

u et

al.

2006

c

Tri

tica

le (

Trit

icos

ecal

e) s

traw

Wax

: fat

ty a

cids

, pri

mar

y al

coho

ls,

alka

nes,

ste

rols

, dik

eton

esA

thuk

oral

a an

d M

azza

201

0

Tro

pica

l alm

ond

(Ter

min

alia

cat

appa

) le

aves

, see

d V

olat

ile

oil,

anti

oxid

ants

, ant

imut

agen

sK

o et

al.

2002

, 200

3, M

au e

t al.

2003

Tucu

ma

palm

(A

stro

cary

um v

ulga

re)

pulp

Oil

, car

oten

oids

Fra

nca

et a

l. 19

99b

Turm

eric

(C

urcu

ma

long

a, C

. zed

oari

a) r

hizo

mes

Vol

atil

e oi

l, cu

rcum

inoi

ds, t

urm

eron

esSa

nagi

et a

l. 19

93, M

a et

al.

1995

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man

n et

al.

2000

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an e

t al.

2000

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hass

agne

z-M

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z et

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Gop

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raga

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03, L

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t al.

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ng e

t al.

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et a

l. 20

07V

aler

ian

(Val

eria

na w

alli

chii

, V. o

ffi c

inal

is)

root

Vol

atil

e oi

l, va

lepo

tria

tes,

val

eren

ic a

cid,

se

squi

terp

enes

Mur

avle

v an

d Sm

etan

in 1

974,

Sta

hl a

nd S

chut

z 19

80a,

Gam

se a

nd M

arr

1999

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ohet

and

Wil

ls 2

006,

Ziz

ovic

et a

l. 20

07b,

Saf

aral

ie e

t al.

2008

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0, S

alim

i et

al. 2

008,

Hua

ng e

t al.

2009

Van

illa

(V

anil

la p

lani

foli

a) b

eans

Ole

ores

inV

itzt

hum

and

Hub

ert 1

971,

Ngu

yen

et a

l. 19

91, A

nkla

m a

nd M

ulle

r 19

95V

asso

ura

(Bac

char

is d

racu

ncul

ifol

ia)

Vol

atil

e oi

lC

asse

l et a

l. 20

00V

eget

able

s –

vari

ous

α-

and

β-C

arot

ene

Mar

sili

and

Cal

laha

n 19

93V

etiv

er (

Ver

noni

a zi

zani

oide

s) r

oot

Vol

atil

e oi

l: k

husi

nol,

khus

ilal

Nai

k et

al.

1989

, Bla

tt a

nd C

iola

199

1, M

arti

nez

et a

l. 20

04, 2

007,

Tak

euch

i et a

l. 20

08, T

alan

sier

et a

l. 20

08W

alnu

t tre

e (J

ugla

ns n

igra

) nu

tsO

ilC

row

e et

al.

2002

, Oli

veir

a et

al.

2002

, Cro

we

and

Whi

te 2

003,

Sal

gin

and

Salg

in

2006

, Ber

nard

o-G

il a

nd C

asqu

ilho

200

7W

ater

mel

on (

Cit

rull

us la

natu

s) f

ruit

Lyc

open

eV

augh

n et

al.

2008

Wes

t Ind

ian

lant

ana

(Lan

tana

cam

ara)

Vol

atil

e oi

l: b

ioci

des,

ant

ibac

teri

al a

nd

anti

fung

al s

ubst

ance

sV

asud

evan

et a

l. 19

97, M

aron

giu

et a

l. 20

07a

Whe

at (

Trit

icum

vul

gare

, T. a

esti

vum

) ge

rm, fl

our

, pl

umul

eFa

tty

oil:

non

-pol

ar li

pids

, gly

coli

pids

, ph

osph

olip

ids,

toco

pher

ols

Tani

guch

i et a

l. 19

85, S

aito

et a

l. 19

89, A

rtz

and

Saue

r 19

92, L

anca

s et

al.

1994

, K

ing

et a

l. 19

96, G

omez

et a

l. 19

97, Z

hang

et a

l. 19

98a,

Mun

oz e

t al.

1999

, Gom

ez

and

de la

Oss

a 20

00, G

e at

al.

2002

a,b,

Pan

fi li

et a

l. 20

03, H

ubba

rd e

t al.

2004

, E

isen

mer

ger

et a

l. 20

06, Z

acch

i et a

l. 20

06, L

ucas

et a

l. 20

07, E

isen

mer

ger

and

Dun

ford

200

8, S

hao

et a

l. 20

08, P

iras

et a

l. 20

09

(Tab

le 1

con

tinu

ed)



Plan

t par

tE

xtra

ct c

ompo

nent

sR

efer

ence

s

Wor

mw

ood

(Art

emis

ia a

bsin

thiu

m)

Vol

atil

e oi

l: β

-thu

jone

, art

absi

n, a

bsin

thin

Stah

l and

Ger

ard

1982

b, 1

983

Yar

row

(A

chil

lea

mil

lefo

lium

) ae

rial

par

t, fl o

wer

sV

olat

ile

oil,

oleo

resi

nPe

plon

ski e

t al.

1994

, Gam

se a

nd M

arr

1999

, Boc

evsk

a an

d So

vova

200

7,

Bar

gham

adi e

t al.

2009

Yer

ba m

ate

(Ile

x pa

ragu

aren

sis)

her

bs, l

eave

sP

urin

e al

kalo

ids:

caf

fein

e, x

anth

ines

, sq

uale

ne, t

ocop

hero

ls, s

tero

ls, f

atty

aci

ds,

hydr

ocar

bons

, alc

ohol

s

Sald

ana

et a

l. 19

99, 2

000a

,b,c

, 200

2b, E

smel

indr

o et

al.

2004

, Car

dozo

et a

l. 20

07, J

acqu

es e

t al.

2007

Yew

(Ta

xus

brev

ifol

ia, T

. cus

pida

ta, T

. bac

cata

) ne

edle

s, b

ark

Pacl

itax

el (

Taxo

l), t

axic

in, b

acca

tin

III

Jenn

ings

et a

l. 19

92, H

eato

n et

al.

1993

, Chu

n et

al.

1994

, 199

6, V

anda

na a

nd T

eja

1995

, Van

dana

et a

l. 19

96Y

lang

-yla

ng (

Can

anga

odo

rata

) fl o

wer

sV

olat

ile

oil

Stas

henk

o et

al.

1996

aZ

atar

ia m

ulti

fl ora

V

olat

ile

oil

Ebr

ahim

zade

h et

al.

2003

(Tab

le 1

con

tinu

ed)

In the particular case of designing and development of supercritical processes for extraction of valuable botanic sub-stances, the TMF should be able to model and predict mainly the solubility of solid solutes in supercritical solvents, and to a lesser extent the solubility of liquids. However, as discussed in detail by Fornari et al. (2010), this is not a simple task because the modelling of the solubility of condensed non-volatile solutes in supercritical solvents involves a number of diffi culties not usually encountered in other phase equilib-rium calculations. In particular

(i) The vapour pressure is the most important indicator of solubility : However, together with additional pure-component data, it is often unavailable and cannot be measured experimentally for relatively non-volatile com-plex solids, which are most of the solutes of interest. (ii) The proximity to the critical point : The rapid density changes and the anomalous behaviour displayed in the critical region is a challenge to any model applied near the critical point, which is mathematically singular. (iii) SCF solutions are often highly asymmetric : The solute and solvent molecules generally differ greatly in mo-lecular size and in their interaction strengths, leading to highly non-ideal mixtures. As a result, binary inter-action constants must be correlated from data using conventional corresponding states theory based on critical properties. (iv) SCF solutions are highly compressible : This leads to solvent condensation or clustering about the solute even in non-polar systems.

In what follows we will briefl y outline the thermodynamics of the phase equilibria exhibited by the systems SCF + botanic substance without/with an entrainer, followed by a concise description of the different elements of a TMF: namely ther-modynamic mixture models; the methods that are used to estimate the properties of the extracts when they are not avail-able; and the methods, algorithms, and numerical techniques to calculate the phase equilibria.

4.1. The thermodynamics of phase equilibria of

SCF + botanic substances systems

4.1.1. Vapour-liquid equilibria The extraction with SC-CO 2 of valuable vegetable oils consisting mainly of trig-lycerides, with a low fraction of diglycerides, free fatty acids, and a number of minor components (sterols, tocopherols, phospholipids, etc.) that have added value as pharmaceuticals and food additives, and the extraction and fractionation of essential oils with SC-CO 2 requires detailed knowledge of the of the vapour-liquid (and vapour-liquid-liquid) equilibria of the systems under consideration (Franceschi et al. 2004).

For vapour-liquid equilibrium, the general equilibrium relation is

f fi iL V= (1)

where fiL and fi

V are the fugacities of component i in the liq-uid and vapour phases, respectively.



Fugacities are related as

f x P

f y P

i i i

i i i

L L

V V

=

=

ϕ

ϕ

(2)

where P is the pressure, and x i and y i are mole fractions, and

ϕi

L and ϕi

V are fugacity coeffi cients of the i -th component in the liquid and vapour phase, respectively.

Thus, the solubility (mole fraction) of component i in the vapour (SC fl uid) phase can be expressed as follows:

y

xi

i i

i

= ϕϕ

L

V

(3)

Thus, the problem is how to calculate the fugacity coeffi -cient of the i -th component in the liquid and vapour phases.

4.1.2. Solid-SCF The majority of the systems that we focus on involve medium- and large-sized solutes at ambient or slightly elevated temperatures where they are typically pure solids. Four different modelling approaches are typically used to describe the solubility of solids in SCFs. These approaches are density based, dense gas, expanded liquid, and solubility parameter.

The density-based approach is an empirical or semiempiri-cal modelling approach that relies on developing a relation-ship between the solubility and the density of the SCF. The dense gas and expanded liquid approaches are both equation-of-state (EoS) approaches that differ in the way in which the SCF phase is treated. At high pressures and liquid-like den-sities common in SFE, the distinction between a gas and a liquid is diffi cult. SCFs can therefore be treated either as a gas or as a liquid (McHugh et al. 1988, McHugh and Krukonis 1994). The dense gas approach treats the SCF as a gas while the expanded liquid approach treats the SCF as a liquid. The solubility parameter approach is an expanded liquid approach that uses the regular solution theory and the solubility para-meter concept to develop a model for the solubility of solids in SCFs.

The density-based approach for modelling solubilities of sol-ids in SCFs attempts to explain the common observation that the logarithm of the solubility is linearly dependent on the density or the logarithm of the density of the SCFs (Kumar and Johnston 1988). This approach has been studied by many authors, includ-ing Chrastil (1982), Schmitt and Reid (1985), Kumar and Johnston (1988), Harvey (1990), Bartle et al. (1991a), Mitra and Wilson (1991), and Liu and Nagahama (1996).

Chrastil (1982) proposed the following relationship between the solubility and the density:

c

a

Tbk= +⎛

⎝⎜⎞⎠⎟ρ exp (4)

where c is the concentration of the solid in the SCF in g l -1 , ρ is the SCF density, T is the temperature, k is the association number, and a and b are empirical constants. The parameters k , a , and b are obtained performing a multiple linear regres-sion on the experimental solubility data.

Chrastil (1982) identifi ed the constant a with the heat of reaction as the solute associates with the solvent and the con-stant b with a relationship between the molecular weights of the solute and solvent, and used Eq. (4) to successfully correlate solubilities of a variety of different compounds in SC-CO 2 .

Adachi and Lu (1983) used Chrastil ’ s equation to corre-late the solubilities of 37 systems. To obtain reasonable per-formance, they made the parameter k density dependent and added two additional parameters. Yun et al. (1991) correlated cholesterol solubilities in SC-CO 2 using Chrastil ’ s equation and obtained a performance ranging from 1.5 % to 9 % .

Skerget et al. (1995) correlated solubilities of carotene, oleic acid, and capsaicin in SC-CO 2 using Chrastil ’ s equation. The performance of the correlation for these compounds var-ied from 10 % to 34 % . Kumar and Johnston (1988) proposed two new relationships to relate the solubility to the SCF den-sity. The relationships were derived using a dense gas-type approach, expressing the fugacity coeffi cient of the supercrit-ical phase in terms of density rather than pressure.

Chrastil ’ s equation was used to describe the solubility behaviour of fatty acids; mono-, di-, and triglycerides; and fatty acid esters in SC-CO 2 (Guclu-Ustundag and Temelli 2000). The authors point out that mono- and diglycerides are the least studied classes of lipids, although information on their phase behaviour is essential for the design of processes such as fractionation of glyceride mixtures or refi ning of veg-etable oils, which are of great commercial importance.

Brennecke and Eckert (1989) state that Chrastil ’ s equation has been the most successful density-based model, but due to its empirical nature, it is unable to predict phase equilibria. Additional detailed enumeration of the empirical models most often applied for modelling of the solubilities of solids in SCFs can be found in the recent review by Skerget et al. (2011).

4.1.3. The dense gas approach The dense gas approach for modelling solute solubilities in SCFs begins with equat-ing the fugacities of the solid and SCF phase and the stan-dard formulation of this problem is based on the equi-fugacity condition for the solute; that is, assuming an EoS model for the fl uid phase and denoting by the superscript “ S ” the solid solute and by the superscript “ F ” the fl uid phase:

f S ( T , P ) = f F ( T , P , y, V ) (5)

where f S is the fugacity of the solute in the pure solid phase, f F is fugacity of the solute in the fl uid-phase solution, y = ( y 1 , y 2 , … , y Nc )

T is the vector of fl uid-phase mole fractions, and V is the molar volume of the fl uid from an EoS model. Additional relationships that must be satisfi ed are the summation to one of the fl uid-phase mole fractions.

As discussed by Fornari et al. (2010), there have been a number of efforts at introducing mathematical artifi ces for solid-phase fugacity within traditional fl uid-phase equilib-rium EoS descriptions. Some investigators have attempted to modify the EoS so that it may predict the existence of a solid phase. However, it has been more common to take a popular EoS and use it directly in solid-fl uid equilibrium



calculations by introducing a solid-phase fugacity function defi ned in terms of a fl uid-phase reference state. Two differ-ent approaches are popular.

According to the fi rst approach, originally proposed by McHugh et al. (1988), the solid vapour pressure is used as the reference fugacity of the solid. Thus, for the simple case of binary solid-gas equilibria, and if the solid solute in the system is denoted by subscript 2, then:

f Pv dP

RTP

P

2 2 22

2

S s sS

= ∫ϕ exps

(6)

where P2s( T ) is the sublimation (vapour) pressure of the pure

solid, ϕ2S is the fugacity coeffi cient at sublimation pressure, and

v2S is the molar volume of the solid, all at temperature T . The fugacity of the solute in the supercritical phase is

f y PG G2 2 2= ϕ

(7)

where ϕ2G is the fugacity coeffi cient and y 2 is the solubility

(mole fraction) of the solute in the SCF. For phase equilibrium between a high-boiling compound

and a SCF whose critical temperature is low, the following three assumptions are usually introduced: (i) the solid solute remains pure since the size and shape of solute and solvent molecules are ordinarily suffi ciently different and hence solid solutions do not form; (ii) the molar volume of the solid solute can be treated as a constant with respect to pres-sure; and (iii) the saturated vapour of the solid solute-vapour (pure) system behaves as an ideal gas. The fugacity coef-fi cient takes into account deviations of the saturated vapour from ideal gas behaviour and the Poynting factor (the expo-nential term) takes into account the effect of pressure.

Furthermore, since the solid phase is pure (assumption 1), the fugacity of the solute in the solid state is equal to the pure solid fugacity and Eq. (6) can be rewritten as follows:

f P Tv P P T

RT2S S S

Ssub1S-

=( )⎛

⎝⎜

⎞

⎠⎟subl subl( )ϕ exp

( )

(6a)

Applying further assumption 2 and the thermodynamic equilibrium condition [Eq. (5)], the mole fraction of the solid component in the supercritical phase can be expressed as

y

P

PE2

2=s

(8)

where

E

v dP

RT

v P P

RTP

P

G G≡ =

( )⎡

⎣⎢⎢

⎤

⎦⎥⎥∫ϕ

ϕ

ϕ

ϕ

22

2

2

2 2

2

2

sS

s

S s

s

-exp exp

(9)

The enhancement factor E contains three correction terms: ϕ2

s , which takes into account non-ideality of the pure satu-rated vapour; the Poynting correction, which gives the effect

of pressure on the fugacity of the pure solid; and ϕG2. Of all

three correction terms, the last one is by far the most impor-tant. In most practical cases, the sublimation pressure of the solid is quite small and thus ϕ2

s is nearly equal to unity (assumption 3). The Poynting correction is not negligible, but it generally accounts for an enhancement factor < 2 or

3. However, ϕ2G is always far removed from unity and can

produce very large enhancement factors. The solubility in an

ideal gas is y

P

P22=s

; hence, the large solubility enhancements

in SCF ’ s relative to an ideal gas are due to exceptionally small values of ϕG

2. The above equation represents the basis for the dense gas approach for modelling solubilities in SCFs. This equation relies on the adequate evaluation of ϕ2

G, at the

specifi ed conditions of P and T . Therefore, the solute solubility is primarily a function of

the solid solute pure compound physical properties, the sys-tem temperature and pressure, and the fugacity coeffi cient of the solid solute in the SCF. The fugacity coeffi cient is the property calculated by a thermodynamic model.

The second approach, introduced originally by Kikic et al. (1997), implements the fugacity of a hypothetical subcooled liquid phase, as the reference of the solid phase fugacity. Thus, the solid-phase fugacity function, for a pure solute solid phase at temperature T and pressure P , defi ned in terms of a hypothetical liquid-phase fugacity as a reference state, and disregarding the change in specifi c heat because of its negli-gible effect, is given as follows:

f f P TV V

RTdP

H

R T TP

PS SCL

S SCLfus

m

--

subls

= +⎛⎝⎜

⎞⎠⎟

⎛

⎝⎜

⎞

⎠∫( , )exp

∆ 1 1⎟⎟

(10)

Implicitly assuming that there are no solid-solid phase transitions and provided the solid specifi c volume at the sub-cooled liquid state V SCL is weakly dependent on pressure, Eq. (10) can be written as follows:

f f P T

V V

RTP P T

H

R T T

S SCL

S SCL

sublS fus

m

-- -

=

( ) ( )( )+ ⎛⎝⎜

⎞⎠⎟

( , )exp

∆ 1 1⎛⎛

⎝⎜

⎞

⎠⎟

(10a)

In Eq. (10), f SCL is the fugacity of the pure subcooled liquid, ∆ H fus is the enthalpy of fusion, ∆ V fus = V S - V SCL is the change in volume, all taken for the solute at its triple point.

Often the second approach should be preferred because of the following reasons:

With the use of Eq. (6a) for the calculation of solid fu-(i) gacity, it is not usually possible to fi t the normal melting point ( T fus ) of the solid compound. On the other hand, use of Eq. (10a) reproduces the normal melting point of the solid compound since it is an input parameter for this approach. The fi rst part of the exponential term in Eq. (10a), (ii) ∆ V fus = V S - V SCL , is important at higher pressures and should not be eliminated.



In Eq. (10a), the data that are required for calculating the fugacity of the pure solid phase are as follows: the fugacity of the pure solute in the subcooled liquid phase (calculated from a thermodynamic model), the enthalpy of fusion at the triple point ( ∆ H TP ), the triple point temperature ( T TP ), the triple point pressure ( P TP ), and the change in molar volume assumed to be a constant upon fusion ( ∆ V TP ).

4.1.4. Lattice gas models The theory behind lattice gas models is based on the fact that the molecules are distributed over a three-dimensional lattice (Brennecke and Eckert 1989) and that these molecules interact with a mean-fi eld-type inter-molecular potential (McHugh and Krukonis 1994). A number of “ holes ” are placed at specifi c lattice sites to obtain the cor-rect density (McHugh and Krukonis 1994). Lattice gas mod-els are reviewed by Johnston et al. (1989), Brennecke and Eckert (1989) and McHugh and Krukonis (1994). Brennecke and Eckert (1989) conclude in their review that, although the lattice gas equations are theoretically based, their perfor-mance in terms of modelling solubilities is poorer than the performance of cubic and perturbed EoSs.

4.1.5. Expanded liquid approach The expanded liquid approach for modelling solute solubilities in SCFs begins with equating the fugacities of the solid and SCF phase. Assuming the solid is pure, the fugacity of the solid is calculated using the same equation as in the dense gas approach. The fugacity of the SCF phase, treated as an expanded liquid, is written as follows:

f y f2 2 2

SCFpureSCF= γ

(11)

where γ 2 is the activity coeffi cient of the solute in the liquid phase.

The expanded liquid approach has an advantage over the dense gas approach in that it does not require integration through the critical region. The expanded liquid approach, however, requires the evaluation of two parameters, the activ-ity coeffi cient and the partial molar volume of the solute at infi -nite dilution, versus one parameter in the dense gas approach. Mackay and Paulaitis (1979) found that the expanded liquid approach did not provide better solubility correlation perfor-mance than the dense gas approach and therefore the intro-duction of a second parameter is not warranted.

4.1.6. Solubility parameter approaches The solubility parameter approach is an expanded liquid approach that uses the regular solution theory to determine the solubility and activity coeffi cient, according to the following relations:

ln lnyH

RT

T

Tfus

m

m

2 2

2

2 1=⎛⎝⎜

⎞⎠⎟

- - -∆

γ

(12)

ln ( )γ φ δ δ2

212

1 22= V

RT-

(13)

where V 2 is the solute molar volume in a hypothetical liq-uid state, φ 1 = ( x 1 V 1 )/( x 1 V 1 + x 2 V 2 ) is the volume fraction of the

solvent, V 1 is the molar volume of the liquid solvent, and δ 1 and δ 2 are, respectively, the solvent and solute solubility parameters, defi ned by:

δii

i

U

Vi=

⎡

⎣⎢

⎤

⎦⎥ =∆

1 2

1 2

/

,

(14)

where ∆ U i is the vapourisation energy and V i is the liquid

molar volume. Thus, Eqs. (12) and (13) represent the func-tional form of the RST, using solubility parameters to calcu-late the solubility.

Ekart et al. (1991) and Brennecke and Eckert (1989), in summarising the efforts that have been made to use the RST in correlating solubilities in SCFs, point out that semiempiri-cal modifi cations of the theory have been required.

4.2. Thermodynamic models

Reliable thermodynamics mixture models that are able to describe the extremely complex phase behaviour of the sys-tems studied are a vital element of the TMF. An ideal thermo-dynamic model is a model that uses easily measured physical properties to predict phase equilibria at all conditions and is theoretically based. Still, up to the present time, no current model fi ts these criteria. Existing correlations of phase equi-libria data contain many regressed parameters, are semiem-pirical at best, and may succeed in fi tting the data in portions of the phase diagram with some accuracy (Ekart et al. 1991).

The dense gas approach is an EoS approach that treats the supercritical phase as a gas and is currently the most widely used for representing the phase equilibria of asymmetric sys-tems at high pressures. It requires the evaluation of the fugac-ity coeffi cient using an EoS valid over the entire density range studied, and hence an adequate relationship to describe the P-V-T behaviour of the SCF phase.

The dense gas approach requires the evaluation of the fugacity coeffi cient and hence a variety of different relation-ships exist to describe this relationship. The most commonly used are the cubic equations of state.

4.2.1. Equations of state Both cubic and noncubic EoSs have been used to model the solubility of solids in SCFs, and a summary of the models and methods used can be found in Ashour et al. (2000).

Cubic EoSs are derived from the equation, which takes attractive and repulsive forces into account, and was pro-posed for the fi rst time by van der Waals. Currently, cubic EoSs, in combination with different mixing rules, are the most widely used models for the calculation of solubilities of solid solutes in SCF. The recent contribution of Fornari et al. (2010) is devoted entirely to the application of cubic EoSs to correlating the solubility of solid compounds in SCFs. The authors offer a detailed critical analysis of the cubic EoSs advantages and shortcomings in fulfi lling the above tasks and stress that to model adequately SC fl uid-solid phase equilibria or SCF + liquid equilibria using an EoS approach, the EoSs employed must be able to describe both the fl uid-phase and



the solid (liquid) phase behaviour reliably. To realize that, two avenues are usually pursued – improvement of mixing rules and improvement of the existing EoS and development of new models – and Fornari et al. (2010) present an analysis of van der Waals one-fl uid mixing rule and its modifi cations.

Haselow et al. (1986) evaluated seven cubic EoSs and two non-cubic EoSs for the prediction of SFE. They suggested that there is a need to develop new mixing rules, otherwise no existing cubic EoS with the traditional van der Waals mixing rules can yield good predictions. Yamamoto et al. (1987) eval-uated two EoSs, namely the perturbed hard sphere (PHS) EoS that comprises the Carnahan-Starling equation repulsive term and the Soave attractive term, and the Soave-Redlich-Kwong (SRK) EoS (Soave 1972) for the prediction of the solubilities of high-boiling compounds in SCFs. They reported that the performance of the SRK-EoS seems slightly better than that of the PHS-EoS, and it was pointed out that the selection of mixing rules is more important than the equation itself. Lee et al. (1989) conducted a similar study to examine three cubic EoSs for the prediction of solid solubilities in SCFs with co-solvent. Weber et al. (1999) modelled the solubility of tristearin, tripalmitin, and triolein with the Redlich-Kwong-Aspen EoS and the Mathias-Klotz-Prausnitz mixing rule: the relative deviation of calculated and experimental solubility in the gas-phase was high, whereas the absolute deviation was considerably small. Yamamoto et al. (2000) correlated solubilities and entrainer effects for fatty acids and higher alcohols in SC-CO 2 using SRK EoS with association model. Ismadji and Bhatia (2003) demonstrated that the one- or two-parameter van der Waals mixing rule with the Peng-Robinson (PR) EoS model failed to predict the solubility of some esters in SC-CO 2 , but the Stryjek-Vera mixing rules were able to correlate the experimental data fairly well.

One empirical approach to eliminate the shortcomings of the van der Waals one-fl uid model for a cubic EoS has been to provide additional composition dependence by adding para-meters to the combining rule for the parameter a mix , gener-ally leaving the mixing rule for the parameter b mix unchanged. Some examples are the combining rules of Panagiotopoulos et al. (1986), Adachi and Sugie (1986), Sandoval et al. (1989) and Schwartzentruber and Renon (1989a,b). However, there are several problems associated with this multipara-meter combining rules that limit their use. One is that because of added composition dependence in the parameter a mix , this group of combining rules fails to satisfy the theo-retical quadratic composition dependence of the second virial coeffi cient.

Ashour et al. (2000) have shown that incorporating addi-tional parameters in the cubic EoS does not signifi cantly improve the prediction of the solubility of the solid in the SCF. However, this study did not take into account the depen-dence of the interaction EoS parameters with respect to tem-perature. Nicolas et al. (2005) considered different mixing rules associated with the Sanchez-Lacombe EoS, and the results were compared with those obtained with the PR equa-tion. For this purpose, binary mixtures of solids with SC-CO 2 , ethane, ethylene, and xenon were investigated. Several mix-ing rules were considered, among which classical “ k ij and l ij ”

and the generalised composition-dependent mixing rule origi-nally proposed by Adachi and Sugie (1986) and generalised by Hernandez-Garduza et al. (2001), to avoid the invariance problem pointed out by Michelsen and Kistenmacher (1990).

With Sanchez-Lacombe EoS, two versions were studied: kij( )0 ,

kij( )1 mixing rule associated with a linear co-volume b , and kij

( )0 ,

kij( )1 , l ij mixing rule where b is a quadratic function of molar

fractions. It was shown that, in many cases, the range of solu-

bility data was too narrow to allow estimating meaningful kij( )0 ,

kij( )1 values. The correlation of data in a large range of tem-

peratures by means of classical mixing rules requires taking into account a temperature dependence of binary interaction parameters. It was observed that, with the proposed tem-perature function, only three parameters associated with the “ k ij ( T ) and l ij ” , or “ k ij and l ij ( T ) ” mixing rules allow to predict solubility data with an accuracy comparable to that of isother-mal correlation. The PR-EoS results at the same conditions were of the same accuracy, provided a temperature depen-dence of EoS parameters was considered.

Another interesting approach was advocated by Ruckensh-tein and Shulgin (2001) who suggested a family of mixing rules for the cubic EoS in which the empirical binary inter-action parameter k 12 in the van der Waals mixing rule was replaced by a physically more meaningful parameter. In the new mixing rules, some mole fractions in the expressions of parameters a mix and b mix in the van der Waals mixing rules were replaced with various expressions for the local mole fractions. The family of the new mixing rules can contain one, two, or even three parameters, and thus they are quite fl exible regard-ing the number of adjustable parameters. In particular, it was shown that the new mixing rules with two or three adjustable parameters provided better correlations of the experimental data for the solubilities of the antibiotic penicillin in SCF CO 2 than the conventional mixing rules or the empirical expres-sions containing many more parameters.

To avoid the two principal limitations of the dense-gas/cubic EoS approach and in an attempt to improve the mod-elling success that is, in some cases , only semiquantitative, researchers have focused on developing more sophisticated mixing rules and EoS (Colussi et al. 1992), e.g., Rao and Mukhopadhyay (1989), Sheng et al. (1992), Bartle et al. (1992a) and Carleson et al. (1993). Rao and Mukhopadhyay (1989) and Sheng et al. (1992) proposed new mixing rules to attempt to improve correlation results. Nishiumi et al. (1988), Bartle et al. (1992a), and Carleson et al. (1993) devel-oped new relationships for the binary interaction parameter that avoid the need for experimental data. Schmitt and Reid (1986) therefore adopt a new approach that still remains a dense gas approach, which uses the PR-EoS to evaluate the fugacity coeffi cient but the EoS parameters of the mixture are not calculated in the conventional manner.

Another alternative to van der Waals one-fl uid mixing rules and a very attractive route to developing better mixing rules is to combine EoS with activity coeffi cient models thus combining the advantages of successful cubic EoS and G E models, such as the Universal Functional Activity Coeffi cient (UNIFAC) model (Fornari et al. 2010). A number of models



that are essentially all mixing rules for the energy parameter of cubic EoS has appeared (see, e.g., Huron and Vidal 1979, Mollerup 1986, Dahl and Michelsen 1990, Michelsen 1990a, Dahl et al. 1991, Holderbaum and Gmehling 1991, Wong and Sandler 1992).

EoS/ G E models have been applied mainly to modelling vapour-liquid systems and only to a limited extent to solid-gas systems (see, e.g., Sheng et al. 1992, Spiliotis et al. 1994, Chen et al. 1995, Escobedo-Alvarado et al. 2001, Huang et al. 2001, Sovova et al. 2001a, to name a few). Tochigi et al. (1998) applied the PR-EoS with the analytical solutions of group (PRASOG) method to estimate solid solubilities in SC-CO 2 and indicated its applicability. Coutsikos et al. (2003) evaluate the linear combination of Vidal and Michelsen mix-ing rules (LCVM) EoS model (Boukouvalas et al. 1994, Voutsas et al. 1996), which combines the PR-EoS with origi-nal UNIFAC using an EoS/ G E type mixing rule, for solid-gas equilibria applications including systems with co-solvents, and studied the infl uence of using vapor-liquid equilibria (VLE)-based parameters for making SGE predictions. The LCVM model has a large parameter table including gases and it has been shown to yield quantitatively satisfactory predictions for binary solid + gas systems involving aromatic hydrocarbons, aliphatic acids, and some alcohols. Poor results were obtained, however, for complex solids, e.g., naproxen and cholesterol. Another model that can be used successfully to calculate and predict the solubility of a solid solute in SCFs is the predictive SRK (PSRK) EoS (Holderbaum and Gmehling 1991). PSRK has also a large parameter table available enabling the repre-sentation of a wide variety of complex natural products.

Jaubert et al. (1999) performed phase equilibria calculations of mixtures involving SC-CO 2 and fatty acid esters (FAE) by combining at a constant packing fraction the PR-EoS and the Van Laar G E model. A new group O = C-O was added, and the fully predictive model thus obtained was used to predict the phase behaviour of a real fi sh oil containing 30 different fatty acid ethyl esters. In a further study, Jaubert et al. (2001) com-pared the phase equilibria predictions for systems of carbon dioxide and two different fatty acid ethyl esters – eicosap-entaenoic acid and docosahexaenoic acid ethyl esters of the Jaubert et al. (1999) model with that developed by Coniglio et al. (1995), namely the MHV1-QB approach. The MHV1-QB approach combines the SRK-EoS with a quadratic expres-sion for the mixture b parameter, and a constant value for the binary interaction parameter l ij = 0.3, with the fi rst order modifi ed Huron-Vidal mixing rule (MHV1) proposed by Michelsen (1990b). It was demonstrated that the MHV1-QB model lead to very good results at low pressures but overesti-mated the bubble point pressures in the vicinity of the critical point and all the dew point pressures. Jaubert et al. (1999) model performed better in the vicinity of the critical point and for the dew point prediction, which was explained by some intrinsic features of the two models.

Araujo and Meireles (2000) applied the PR equation with van der Waals mixing rules and combining rules with two parameters and three binary parameters of Kwak and Mansoori (1986) and Park et al. (1987) to the systems containing fat- and oil-related compounds in SC-CO 2 . Preference was given

to correlating experimental data for both phases, which is per-haps the most diffi cult form of correlating vapour-liquid equi-librium data with cubic EoS considering the importance of this information for the design of supercritical fractionation systems. On the basis of the absolute mean deviation for mole fractions, it was concluded that the PR equation with van der Waals mixing rules for the three different combining rules described qualitatively all the important characteristics of the vapour-liquid equilibrium of the systems studied. The differ-ences among the results obtained with the analysed combin-ing rules were not signifi cant. On the other hand, the absolute mean deviations for the vapour phase obtained were smaller compared with the Soave equation and the mixing rules of MHV1 and MHV2, and the LCVM model for the majority of the binary and ternary systems studied. Therefore, concluded the authors, if experimental data are available, a simple model as the one discussed predicts the phase equilibrium of com-plex system within the required accuracy for project design. On the other hand, in the absence of experimental data, the entirely predictive EoS/ G E models are very useful.

Huang et al. (2001) applied the PR-EoS and a modifi ed Huron-Vidal type mixing model with a volume correction term to calculate the solid solubilities of aromatic, fatty acid, and heavy alcohol compounds in SC-CO 2 . The UNIFAC activity coeffi cient model with its optimally fi tted binary interaction parameters was used and a volume correction term was employed, and its parameters were correlated as func-tions of the solid molar volume for both non-polar and polar systems.

Escobedo-Alvarado et al. (2001) used the Wong-Sandler mixing rule and the PR-EoS to model the solubility of solid phases in SCFs. More recently, Vieira de Melo et al. (2005) applied the PR-LCVM-UNIFAC model to model the solubil-ity of caffeic acid and l -dopa in the SC-CO 2 -rich phase.

Gracin et al. (2002) examined the ability of the original UNIFAC method to predict solubilities of very different solid organic fi ne and specialty chemicals, organic intermediates, and pharmaceutically important compounds in 15 industrially important solvents.

Valderrama et al. (2003) proposed a model that includes an EoS and an excess Gibbs free energy model and applied it to the correlation of phase equilibria in gas + solid systems containing SC-CO 2 . A modifi ed “ regular solution ” model for the excess Gibbs free energy that considers nonpolar, polar, and hydrogen-bonding contributions and a generalised three-constant EoS was advocated. The mixing rule derived for the model includes a concentration-dependent interaction para-meter and an interaction parameter into one of the volume constants of the EoS. Literature data for nine binary gas + solid systems containing SC-CO 2 were used for testing the pro-posed model.

Espinosa et al. (2002) applied the group contribution (GC) EoS proposed by Skjold-Jorgensen (1988) to model high-pressure phase equilibria in mixtures of fatty oils and acid alkyl esters with SCFs. The GC-EoS is based on the genera-lised van der Waals partition function and a group contribu-tion principle. The repulsive term is a Carnahan-Starling-type expression, which is characterised by the critical hard-sphere



diameter, and it is considered a function of the molecular size of the pure component. The attractive term is calculated using the non-random two liquid (NRTL) model with density-de-pendent mixing rules. Espinosa et al. (2002) represented the fatty oil by a pseudo-triacylglyceride with the same molecu-lar weight and degree of unsaturation of the natural oil. The critical hard sphere diameter of the oil, i.e., the size-related parameter, was determined from the correlation of infi nite dilution activity coeffi cients of n -alkanes in high molecular weight triacylglycerides and hydrocarbons. Good predic-tions of vapour-liquid, liquid-liquid, and vapour-liquid-liquid equilibria in mixtures of supercritical solvents (propane, eth-ane, and CO 2 ) with pure triacylglycerides, natural vegetable oils, and fatty acid alkyl esters were obtained. The authors conclude that the results obtained show the capability of the GC-EoS model to describe the phase equilibria of size-asym-metric mixtures and its potential for modelling supercritical processes involving oils and derivatives.

In new developments, Chafer et al. (2004, 2005) and de la Fuente et al. (2005) also applied the GC-EoS to model the solubility of quercetin and carnosic acid, and capsaicin in SC-CO 2 and compared its capabilities with those of SRK.

Still, the use of this group contribution approach can be considered to be quite demanding while dealing with the amount of necessary regressed parameters and with the cal-culation of the association contributions for multiple associat-ing groups.

At this stage, we feel that the following should be under-lined: the key assumption of all group contribution approaches such as UNIFAC is that molecules can be broken down into functional groups that can be treated as being independent of the rest of the molecule. Interaction parameters between groups are determined by correlation of the model to experi-mental data. For UNIFAC parameters, for example, more than 60 different functional groups are determined simultaneously in an extensive optimisation where the total deviation between the UNIFAC model and huge amounts of experimental data is minimised. Because of the complexity of this optimisation, parameter values are primarily correlation values rather than describing the actual physics in each particular interaction, and of course this limits the possibility to extrapolate the use into new situations. Furthermore, the values of the UNIFAC parameters to be used have been determined from vapour-liq-uid equilibrium data because these are the most extensive data that are available. From a physical point of view these interac-tion parameters should be equally useful for solid-liquid equi-libria. However, because of deviations from the underlying assumptions and because of the complexity of the parameter determination, the extrapolation to solid-liquid systems is not necessarily valid.

The practical problems associated with the application of the UNIFAC-based mixing rules are that many solid solute compound molecules extracted from natural matrices are more complex than the molecules normally encountered in gas-liquid equilibria. In addition, these molecules sometimes contain functional groups for which UNIFAC parameters are unavailable. Also, even if all group defi nitions exist, a subset of the relevant parameters is unavailable. These problems can

be eliminated with suffi cient and accurate experimental data. Frequently, however, this involves a rather large number of parameters compared with the amount of data available.

Finally, all group contribution methods discussed thus far treat the light gases, such as CO 2 , as individual groups, and hence the volume and surface area parameters for these groups must be determined. In some cases, as pointed out by Fornari et al. (2010), these structural parameters are estimated using semitheoretical methods like those of Bondi (1964) and Apostolou et al. (1995) but their values are essentially arbi-trary and differ from those given by Dahl et al. (1991), the size parameters of the latter being about twice the size of the gases of Apostolou et al. (1995). There has not been a thor-ough analysis of which values are the best. In addition, these values must be set before the optimum values of the group interaction parameters of the UNIFAC model can be found, and hence any defi ciency that exists in the selection of these structural parameters will inevitably affect the group interac-tion parameters (Orbey and Sandler 1998).

4.2.2. Other models Cubic EoSs are exceedingly simple and have been remarkably successful in modelling SCF-phase behaviour and are probably the most widely used in analysing experimental data. Moreover, the cubic EoS must be the equation of choice for process design of any complex system because the interactions are too involved to justify the use of a more fundamentally based equation. However, all of the cubic EoSs were originally developed to characterise hydrocarbons, and they embody a very wrong component of the corresponding state theory. This theory assumes similar-ity of molecular size and force constant – an assumption that does not work for the highly asymmetric in force constant and size SC systems. Furthermore, cubic EoSs are least pre-cise in the region near the critical point, and are completely inapplicable right at the critical point, which is mathemati-cally singular. This is because many cubic EoSs predict com-mon value for the critical compressibility factor for all fl uids, Z c = 0.303, while real values vary from 0.2 to 0.5 (Valderrama 2003, Valderrama and Alvarez 2004).

Furthermore, the rapid density changes and the anomalous behaviour displayed in the critical region are a further chal-lenge for EoS models. Thus, attempts to modify mixing rules, making them variable in density, temperature, or composition may be useful, but are stopgap solutions. The real need is to develop better EoSs. One response to this challenge is the application of the statistical associating fl uid theory (SAFT) to model SFE.

To overcome the use of empirical corrections to cubic EoSs or G E mixing rules, the breakthrough in the modelling of polar and highly non-ideal systems came with the development of more rigorous explicit association models. A semiempirical EoS that was developed in the late 1980s and has gained con-siderable popularity in both the academic and industrial com-munities is the SAFT. SAFT is derived from the fi rst-order thermodynamic perturbation theory of Wertheim (1984a,b, 1986a,b), where the reference fl uid is a hard sphere and the perturbation consists of the relatively weak dispersive attrac-tions. In SAFT, the Helmholtz free energy is written as the



sum of contributions due to hard-sphere repulsive interac-tions, due to chain formation through bonding of a number of hard spheres, and due to association and dispersion. From the several successful modifi cations of SAFT that have been advocated, the one suggested by Huang and Radosz (1990, 1991) should be mentioned in particular.

Although the approach is very successful in modelling the phase equilibria of complex systems, research dealing with its application to the modelling of the solubility of solids in SCFs is rather scarce (Muller and Gubbins 2001). Economou et al. (1992) used the SAFT EoS to correlate the solubility of polynuclear aromatics in supercritical ethylene and ethane, where a total of six systems were adopted and the correlated results showed that good agreement with experimental data can be obtained with the SAFT EoS.

Zhong and Yang (2002) carried out a comprehensive inves-tigation of the capability of the SAFT approach for modelling the solubility of solids in SCFs. They adopted an extended SAFT EoS combined with eight mixing rules to evaluate the capability of the SAFT approach. The results show that the SAFT approach gives good correlative accuracy in general, and that it can be used to model solid-SCF equilibria, which gives slightly better correlative accuracy than the cubic EoSs. In their further work, the authors apply the SAFT approach to model the solubility of solid aromatic compounds in SCFs with co-solvents (Yang and Zhong 2005).

Efforts to develop new models and improve the existing ones with the view to represent in a more comprehensive manner the complex interaction between the solid + SCF are continuing. We will briefl y discuss some of them without either the ambition to be exhaustive or that all new models are covered.

Vetere (1998) presented an empirical correlation with two parameters, namely molecular weight and melting point for the prediction of solid solubility. In a similar development, Mendez-Santiago and Teja (1999) showed that a simple linear expression, based on the theory of dilute solutions, can be used to correlate solid solubility data. The linear relationship may also be used to check the consistency of experimental data. The proposed equation for solid solubility requires knowledge of the sublimation pressure of the solid of interest, and the authors advocated another relationship for the solid solubility that incorporates a Clausius-Clapeyron equation for the sublima-tion pressure. Although the resulting expression contains three parameters, it was demonstrated that these parameters are inde-pendent of temperature and pressure. The proposed expres-sion may therefore be used to extrapolate data to temperatures where experimental information may not be available.

The molecular interactions near the critical point and high pressures have recently been studied intensively. The solute-solvent interactions near the critical point are strong. The studies that show these phenomena observed clusters in solu-tions – aggregates of solvent around solute of dilute organ-ics in SCFs (see, e.g., Walsh et al. 1987, Eckert and Knutson 1993, Zhang et al. 1995a). Cheng et al. (2003) calculated solid solubility by applying the equilibrium criteria for the cluster formation process. The simplifi ed cluster-solvation model has two temperature-independent binary parameters, and it was observed that the overall deviation in solid solubility

calculations from this model is comparable to that from other semiempirical models with more optimally fi tted parameters.

Solute-solute interactions are also important, as observed by Kurnik and Reid (1982) and Kwiatkowski et al. (1984). Brennecke and Eckert (1989) presented evidence for both solute-solvent and solute-solute interactions, due to the for-mation of dimers, even at very low concentrations using spectroscopic studies. They recommended using solute-solute interactions to develop EoSs.

Zhong et al. (1998) suggested a model for correlating the sol-ubility of solids in SCFs. This model is based on the fact that the free solute molecules, the solvent molecules, and the solvent-solute clusters in such solid-SCF systems are in chemical equi-librium. The local density of the solvent surrounding a solute is used as a one parameter. The model can correlate the solubility data that are not in immediate region to the critical point of the solvent. Jiang et al. (1998) presented an equation for solubility behaviour representation derived from the solvation concept.

Cheng et al. (2002) also explored the application of a mod-ifi ed regular solution model as an alternative method with-out the need of critical constants to the modelling of solid solubility of complex biological compounds, including ste-roids, antioxidants, xanthines, drugs, and heavy aromatic in SC-CO 2 . They compared their results with those obtained using semiempirical equations and EoS approaches. It was demonstrated that with two or with a single parameter in the solution model, satisfactory results are obtained that are com-parable to those from other methods with more parameters. The optimally fi tted parameters in the solution model method are presented and the generalisation of the solution model parameters as a function of pure solid property is illustrated.

Ruckenstein and Shulgin (2002) developed a predictive method for the solubility of a solid in a SCF containing an entrainer at any concentration. They presented a method based on the Kirkwood-Buff formalism, and expressions for the derivatives of the fugacity coeffi cient of the solute in a ter-nary mixture with respect to the mole fractions were obtained. On the basis of these expressions, an algebraic equation, which allowed one to predict the solubility of a solid solute in terms of its solubilities in the SCF and in the entrainer, was derived. The equation was compared with the experimental results available in the literature regarding the solubility in a mixture of SCFs and good agreement was obtained.

Li et al. (2003) studied the solubility of solids in SCFs by chemical association reaction method, and both cases of with and without co-solvent were considered. On the basis of the thermodynamic and association reaction equilibrium theories, a model for the solubility of solids in SCFs under association reactions was developed. It reduces to normal solubility cal-culation model when there are no co-solvent and association reactions. The model was tested with the experimental data collected from the literature, and the results show that it is more accurate than other models.

4.3. Solute properties estimation

The systems that we focus on involve medium- and large-sized solutes at ambient or slightly elevated temperatures



where they are typically pure solids. Such substances usually have the following characteristics: molar mass > 100 g mol -1 ; polyfunctionality (two or more functional groups); multiple molecular conformations; complex molecular interactions, such as large dipoles, high polarisability, hydrogen bonding, and charge-transfer complexes; and, very importantly, limited amounts of reliable measured data, as their critical parameters and/or melting properties cannot be determined experimen-tally (Fornari et al. 2010).

Correlation of solubility requires not only robust thermo-dynamic models but reliable methods to estimate the values of the solid compounds thermophysical properties (e.g., critical and melting properties) because inaccuracy in the properties plays a major role in the quality of the SFE predictions. This is a very challenging task on its own, moreover that there are very big deviations between the values estimated and reported by the different authors applying different methods. In view of this, a range of effective methods to estimate the solute properties should be available within the TMF.

The two groups of properties of the pure solid solute required for modelling its solubility in SCF are its critical parameters and melting properties. For a liquid solute (such as essential oils, and di- and triglycerides), only critical para-meters are required, while for a solid solute both the critical and the melting properties are needed.

4.3.1. Critical parameters For most of the solutes extracted from vegetable material, the critical properties may not be experimentally accessible because of thermal crack-ing below their critical temperature. Hence, the values of the critical para meters and normal boiling temperatures should be considered as hypothetical quantities rather than properties with any physical meaning, which have to be estimated either by correlations or group contribution methods.

A concise but critical analysis of the methods applied to estimate the critical parameters of solid solutes can be found in Fornari et al. (2010), and we will not further pursue this topic here. Still, it should be noted that usually there are no experimental data available with which to compare the esti-mated values. In view of this, it is recommendable to apply as an assessment tool of the reliability of the properties esti-mated the generalised semitheoretical expression advocated by Zbogar et al. (2006):

T c / P c = 9.0673 + 0.43309 ( Q w 1.3 + Q w 1.95 ) (15)

where T c is in Kelvin and P c is in bar. The dimensionless parameter Q w is a measure of the van der Waals molecular surface area and is calculated as the sum of the group area parameters, Q k :

Q Qw k k

k

=∑ ν

(16)

where ν k is the number of times group k appears in the mol-ecule. The group area parameters Q k are available in the UNIFAC tables.

The infl uence of the uncertainties in the values of the criti-cal parameters is explored in detail by Gordillo et al. (2005b)

although for a different type of solid solutes, namely dyes. The authors employ several methods to estimate the criti-cal parameters of blue 14, a disperse anthraquinone dye, and demonstrate that the choice of a particular group contribu-tion method was more important than the choice of the EoS; for example, for the SRK cubic EoS, the Lydersen (1955) method, combined with Meissner group contribution method, leads to a better value for the AARD of the dye solubility than Joback and Reid ’ s (1987) method. The latter is not surprising taking into consideration that the former gives an excellent approximation to the theoretically calculated T c / P c ratio for blue 14 (31.56), namely 32.11 versus 42.85 for the latter.

4.3.2. Melting properties It has been demonstrated that the sublimation pressure plays a dominant role in the correla-tion of solubility data and that, in many cases, the only way to obtain a reasonable calculation of these data is to consider the sublimation pressure as an adjustable parameter (Reverchon et al. 1995a, Neau et al. 1996). It has also been shown that, in the case of high molar mass compounds for which subli-mation pressures cannot be measured, the safest way to esti-mate them is to correlate experimental vapour pressure data through an analytical relation and to use normal fusion prop-erties in order to settle the sublimation pressure equation with respect to temperature (Neau et al. 1999).

Thus, a possible route to estimate the sublimation pressure of a solid compound is to integrate the Clapeyron relation from the triple-point temperature T t and pressure P t , assum-ing a negligible dependence of the sublimation enthalpy with respect to temperature (Neau et al. 1999):

ln

P

P

H

R T T

s

t

s

t

⎛⎝⎜

⎞⎠⎟

=⎛⎝⎜

⎞⎠⎟

- -∆ 1 1

(17)

where ∆ H s is the sublimation enthalpy at the triple point of the pure component, which can be expressed with respect to the fusion and vapourisation enthalpies as

∆ H s = ∆ H fus + ∆ H vap (18)

The practical interest of this method is thus to require, besides an EoS, fusion property data that can be either mea-sured, found in the literature, or estimated (Garnier et al. 1999).

In most cases the triple-point conditions (the temperature and pressure at the triple point) for the solute are unknown experimentally. However, for almost all heavy compounds, there is little difference between the triple-point temperature and the normal melting temperature. Indeed, this difference is usually < 0.1 K, which is less than the scattering of experimen-tal values of transition temperatures found in the literature. Furthermore, the difference in the heats of fusion at these two temperatures is also often negligible (Perry and Green 1999). Under this assumption, the enthalpy of fusion in Eq. (17) can be estimated with the fusion enthalpy measured at the normal melting temperature. Hence, if the melting temperature of the compound of interest is known it is possible to calculate P t and ∆ H vap from an EoS.



Coniglio (1993), Trassy (1998), and more recently Neau et al. (1999) and Crampon et al. (2004) discuss in detail the reliable methods, among the numerous ones devoted to this subject. We would like, however, to mention also the con-tribution of Valderrama and Zavaleta (2005) who propose to calculate the sublimation pressures of pure solids from high-pressure solubility data using genetic algorithms. The sublimation pressure is considered as a parameter to be deter-mined by regression analysis of experimental solubility data, and hence an optimisation problem, in which the difference between the correlated and experimental data of solubility is to be minimised, is solved using a method that applies bio-logically derived techniques such as inheritance, mutation, natural selection, and recombination to fi nd the optimum solution.

In the case of compounds that may decompose before the melting point, all fusion properties have to be estimated. For example, Jain et al. (2004) advocate a combination of additive group contributions and non-additive molecular parameters to estimate the normal melting points of 1215 organic compounds. The melting points are calculated from the ratio of the total phase change enthalpy and entropy of melting. The total phase change enthalpy of melting is cal-culated from the enthalpic group contributions, whereas the total phase change entropy of melting is estimated using a semiempirical equation based on only two non-additive molecular parameters.

If, however, the melting temperature is known, then it is possible to estimate ∆ H fus from the following empirical equation:

∆ H fus = 4.184 kT fus (19)

where k is an empirical parameter related to the properties of the solute, and for organic compounds it is usually in the range 10 – 16 (Chen and Ma 2004). Yet another possibility is to estimate the sublimation enthalpy solely on the basis of the value for ∆ H vap , taking into consideration that ∆ H fus is usually less than one quarter of the sum given by Eq. (16) (Prausnitz et al. 1999).

Another route to pursue is presented by Coutsikos et al. (2003) who advocate a group contribution method for the pre-diction of the vapour pressures of organic solids, based on the concept of the hypothetical liquid:

ln lnP PS

R

T

TS L

fusm-= + ⎛

⎝⎜⎞⎠⎟

∆1

(20)

The vapour pressure of the hypothetical liquid is obtained using the Abrams-Massaldi-Prausnitz equation developed for liquids (Abrams et al. 1974), and the entropy of fusion is estimated applying a group contribution method. Coutsikos et al. (2003) underline that experimental values for the entropy of fusion for most of the compounds are not avail-able and reliable predictions of these values are extremely diffi cult and the few available correlations are cumbersome to use (e.g., Chickos et al. 1990, 1991, Dannenfelser and Yalkowsky 1996). Thus, the authors advocate a group con-tribution method to predict values for the entropy of fusion

with typical deviations from the experimental ones, where available, of about ± 10 % to ± 25 % . Taking into consideration the simplicity of the proposed method for such a diffi cult task, it appears suffi cient for the needs for sublimation pres-sure predictions. The overall error for the families of organic compounds considered (hydrocarbons, halogenated aromat-ics, nitro-aromatics, alkanols, phenols, acids, ketones, and multifunctional ones) is in the range of 10 – 40 % , and the error for the total of about 2650 data points exceeds one order of magnitude in very few cases.

Finally, if no experimental data for the solid molar volume is available, a value can be estimated according to the fol-lowing extended relationship (Goodman et al. 2004), which allows including temperature dependence for solid density from T t to substantially lower temperatures:

ρ ρsolid

t

liquidt-( ) . .T

T

TT=

⎛⎝⎜

⎞⎠⎟

( )1 28 0 16

(21)

where ρ solid is the solid density and ρ liquid ( T t ) is the liquid den-sity at the triple point, which is calculated from an EoS.

Needless to say that the lack of reliable experimental data for most of the solutes extracted from vegetable matrices forces the application of correlations and estimation methods. The latter, of course, inevitably leads to uncertainties in the values obtained.

The uncertainties in the values of the parameters of the pure components can seriously infl uence the quality of SFE predictions. Sovova et al. (2001a) show on the example of the triolein + CO 2 binary that the uncertainties in the val-ues of the critical parameters might have a dramatic effect on the phase behaviour calculations and on the predicted extent of the VL region. Thus, applying some of the estima-tions of triolein critical parameters, the system was errone-ously predicted to be homogeneous at very low values of the pressure.

However, it should be underlined that to perform a detailed analysis of the infl uence of the thermophysical properties uncertainties on the phase behaviour predictions and calcula-tions of a solute + SC solvent binary is a very complex task and must be explored from many different angles.

4.4. Computational techniques to solve the

equilibrium relations

The third vital element of a TMF comprises methods, algo-rithms, and numerical routines to model the complex phase behaviour of the solid + SCF ( + entrainer) systems solve the equilibrium relations and calculate the solubility.

Fornari et al. (2010) point out that correlating the solubility even for the simplest cases can be a very challenging task as the weakness of phase equilibrium predictions using an EoS are resulting not only from the weakness of the equation itself but also from the computational techniques applied. Xu et al. (2000) underline that when calculating the solubility of a solid at new conditions using a particular EoS model, there are two computational pitfalls that can be encountered in the calculation of solid-fl uid equilibrium:



Solid solubilities in SCFs are usually computed by lo-(i) cating a mole fraction, which satisfi es the equi-fugacity equation relating the solute fugacity in the SCF, as pre-dicted by the EoS, and the fugacity of the pure solid [see Eq. (5)]. However, at certain values of temperature, pressure, and k ij , there can exist multiple solutions to the equi-fugacity condition. A common method for solving the equi-fugacity equation is successive substitution or some similar approach, using some small value of the solid solubility in the fl uid phase as the initial guess. In general, this strategy will only fi nd the smallest solubil-ity root and may miss any larger values, if present, that satisfy the equi-fugacity equation. Thus, what is needed is a completely reliable method to determine all the roots to the equi-fugacity equation. Equi-fugacity is a necessary but not suffi cient condi-(ii) tion for stable solid-fl uid equilibrium. Solutions to the equi-fugacity equation must be tested for global thermo-dynamic phase stability.

The problem can become even more complex, because a molecularly dissimilar system (different molecular size and force interactions) can exhibit very complex phase behav-iour in the PT thermodynamic phase space. For example, the onset of liquid-liquid immiscibility can occur either as a “ break ” in the critical point locus or can outgrow from the solid-liquid-gas (SLG) locus. This “ outgrowth ” of the liquid-liquid-gas (LLG) behaviour changes the nature of the SLG locus from a continuous one to one of two branches (with dif-ferent composition of the liquid phases), and is accompanied by the formation of a quadruple point (solid-liquid-liquid-gas, SLLG), from which four three phase loci originate. As molecular differences between the pure components become more pronounced, and the melting temperature of the heavier component is higher than the critical temperature of the sol-vent, the l = g critical point locus becomes discontinuous. Further molecular dissimilarities will cause the pure compo-nent phase equilibria in the PT space to draw further apart and the LLG will be replaced by two separate liquid-vapour regions, and the two disconnected SLG loci, terminating at an upper critical end point and at a lower critical end point, respectively, will have markedly different compositions. The PT diagram of the latter phase behaviour is usually referred to as typical for a solid + solute binary (Garcia and Luks 1999, Labadie et al. 2000).

Moreover, in the presence of the solvent, the melting curve of the solute can be depressed, lowering its melting point. There are cases known of up to 70 ° C depression of the melt-ing point of a solute (Lemert and Johnston 1989). If this fact is not taken into consideration, and particularly when there is no optical view cell to observe the sample, then there is a strong possibility to mistakenly accept and report the experi-mental data as solid-fl uid equilibrium, while in reality it is vapour-liquid, and there is no solid present.

Furthermore, for solid + SCF binaries, for which the dif-ference between the melting temperature of the solute is not much higher than the critical temperature of the solvent CO 2 (304.2 K), any of the PT diagrams discussed above is feasible

and the possibility to mistakenly interpret the solubility data measured is even stronger. For example, the solubility mea-surements for naphthalene (melting temperature 353.65 K) and biphenyl (melting temperature 344.15 K) in SC-CO 2 were initially reported as representing solid-fl uid equilibrium because it was not realised that the experiments were carried out at temperatures in the vapour-liquid region (at temper-atures above the upper critical end point). It was only later acknowledged that these measurements were actually rep-resenting the composition of a vapour phase in equilibrium with a liquid and that there was no solid present (McHugh and Paulaitis 1980, Xu et al. 2000).

Thus, to have a viable and detailed description of the phase behaviour of a solid + SCF system in the thermodynamic phase space, and to correlate reliably the solid solubility, in addition to solute physical properties and a thermodynamic model, a variety of robust, effective, and effi cient fl ash routines (SLG, LLG, LG, etc.), algorithms, and numerical procedures are required.

When three phases, namely solid, liquid, and vapour, are in equilibrium, the following equations must be satisfi ed:

T S = T L = T V (22)

P S = P L = P V (23)

f Si = f Li = f Vi i = 1, 2 (24)

The liquid-vapour equilibrium conditions for the CO 2 + solid solute binary system, applying the above equations, are

ϕ ϕ1 1 1 1

L Vx y= (25)

ϕ ϕ2 2 2 2

L Vx y= (26)

where the subscript 1 corresponds to SC-CO 2 and subscript 2 to the solid solute. Furthermore, it is assumed that the solid phase is pure solute, and hence for the solid-liquid equilib-rium the following holds:

ϕ ϕ2 2 2S L= x (27)

The following constraints also apply for the liquid and vapour phases:

xi

i

==∑ 1

1

2

(28)

yi

i

==∑ 1

1

2

(28a)

The fugacity coeffi cient of the solid solute is calculated according to (Prausnitz et al. 1999):

ln lnϕ ϕ2 2

1 1S PSL TP

TP

TPTP- -= +

⎛⎝⎜

⎞⎠⎟

+ ( )∆ ∆H

R T T

V

RTP P

(29)

Equation (29) relates the fugacity coeffi cient of the solid solute to the fugacity coeffi cient of the pure solute in the



subcooled liquid phase at temperature T and pressure P ( ϕ2PSL),

and it is assumed implicitly that there are no solid-solid phase transitions and that the solid phase is incompressible.

The above system of equations is strongly non-linear and may have several solutions. The non-uniqueness is a particu-lar problem and is a result of the mathematical presence of local minima and maxima in the Gibbs energy surface. This, in turn, relates to convergence to a local rather than global minimum, and to the impossibility to distinguish among thermodynamically stable and unstable equilibrium states. As pointed out previously, the equality of chemical poten-tials represents a necessary but not a suffi cient condition for equilibrium, and hence a stability analysis routine and a phase identifi cation procedure must be employed at each step to fi nd with guarantee the phase confi guration with the minimum Gibbs energy, which is particularly important in regions of the thermodynamic phase space where the EoS has multiple roots as is the case around the SLG locus.

Somewhat surprisingly, the practice of searching for all roots to the equi-fugacity condition and testing for phase sta-bility appears not to be widespread among those who mea-sure, model, and compute high-pressure solid-fl uid equilibria (Xu et al. 2000).

Still, the need to test for stability and its infl uence on phase diagrams has been an area of interest to some researchers. We will like to mention particularly the works of Xu et al. (2000) and Scurto et al. (2003) who described a new method for reliably computing solid-fl uid equilibrium without and with co-solvents at constant temperature and pressure based on interval analysis, in particular, an interval Newton/genera-lised bisection algorithm; Marcilla et al. (1997), who focused on low-pressure solid-liquid equilibrium and the need for stability analysis and were able to carefully map out the full phase diagrams for their selected systems, as well as the con-tributions by Corazza et al. (2004) and Sovova et al. (2007a). However, as pointed out by Fornari et al. (2010), it is only fair to say that some of the above-mentioned researchers applied local, initialisation-dependent solvers, which in general nei-ther provide guarantee that all equi-fugacity roots are found nor that phase stability analysis is done correctly, while Xu et al. (2000) and Scurto et al. (2003) were the fi rst to pres-ent a technique that provides a mathematical and computa-tional guarantee that all roots to the equi-fugacity equation are enclosed and that phase stability analysis is performed cor-rectly and thus the stable solution to the solid-fl uid problem is determined with certainty.

5. Mathematical models for SFE kinetics

Mathematical models that effectively describe the extraction kinetics of solid substrates in packed beds operating with SCFs are useful tools for the design and scale-up of SFE processes, with predictive models being of special interest to assess pro-cess feasibility preliminarily, and/or to validate experimen-tal data for process scale-up (del Valle et al. 2006). Several aspects distinguish the SFE from plants from the extraction with conventional solvents. First, the external mass transfer

from plant surface to bulk fl uid is much faster due to the excellent transport properties of SCFs. Thus, as long as there is enough solute near the plant surface, the solution fl owing out of the extractor is saturated or near saturated. Second, a dry solvent such as pure carbon dioxide gradually removes from the plant the moisture remaining there after drying usu-ally in the concentration of 8 – 10 wt. % . The permeability of an overdried plant tissue is extremely low, the diffusion of a solute through the plant surface is very slow, and thus it is easy to distinguish between the initial period of fast extrac-tion of easily accessible solute and the fi nal period with much slower extraction. Brunner (1994) explains the sensitivity of cell walls to the moisture by the properties of an elementary membrane. The membrane consists, according to Danielli, of three bimolecular lipid layers with pores that can be passed by water and by lipids. If there is not enough water in the system, the pores are closed and the membrane becomes imperme-able. Third, the low kinematic viscosity makes SCFs prone to natural convection induced by even small density gradi-ents related to the differences in concentration (due to the extraction) or in temperature (due to the heat transfer through the wall of extractor). As a result, the fl ow pattern could dif-fer signifi cantly from the plug fl ow, which ensures the best extractor performance.

The most easily available experimental data on extraction kinetics are the extraction curves, the dependence of extrac-tion yield on either extraction time, or the solvent-to-feed ratio, directly proportional to the time. These curves are compared with a mathematical model to adjust its param-eters and to check whether it corresponds to the reality. To distinguish better between different models, del Valle et al. (2000b) recommend a multiobjective fi tting strategy when both experimental extraction curves and experimental resid-ual concentration profi les in solid phase should be fi tted by the models.

A phenomenological model for SFE from plant materials is a mathematical description of extraction kinetics in the form of equation or a set of equations defi ning the solute concen-trations in the extractor in dependence on extraction time and spatial coordinates. The extraction yield is then calculated from the outlet concentration. The models are usually not pre-dictive; some of their parameters can be estimated according to literature correlations but at least one parameter is adjusted to fi t experimental data.

The extraction process comprises phase equilibrium or adsorption/desorption kinetics, diffusion through the plant particles to their surface, external mass transfer from particle surface to the bulk fl uid, and displacement with the fl owing solvent. Different types of models are obtained combining different expressions for these steps. Probably the most thor-ough overview was published by del Valle and de la Fuente (2006), who focus on the extraction of vegetable oils but also mention the models for other types of solutes. The paper also contains a valuable survey of published correlations used to estimate some model parameters: binary diffusion coeffi cient of extracted substance in supercritical solvent, external mass transfer coeffi cient, coeffi cient of axial dispersion, effective internal diffusion coeffi cient, and also the relationships for



the extract solubility in SCF and/or for its adsorption iso-therm, when it is adsorbed on vegetable matrix. del Valle and de la Fuente (2006) started with a complex model and showed different possibilities for its simplifi cation.

Al-Jabari (2002) regarded the models as sets of blocks describing individual extraction steps; one or more blocks could be deleted when the corresponding step was marginal under given conditions. In the present paper, we follow the scenario advocated by Al-Jabari (2002) and judge on the importance of individual steps according to their character-istic times. Where possible, the relationships are presented in dimensionless form to facilitate comparison of the results from the papers using different notation.

5.1. Mass balance for solute

The basis for phenomenological SFE models is a differential mass balance equation for the solute in the packed bed (del Valle and de la Fuente 2006). On the assumption of plug fl ow, the mass balance equation for the fl uid phase is

ε

∂∂

+ ∂∂

⎛⎝⎜

⎞⎠⎟

=c

t

c

hJ c h c t cu , ( 0) 0, ( 0) 0= = = =

(30)

where ε is the free void of extraction bed, c is the fl uid phase concentration (kg m -3 ), t is the extraction time, u is the inter-stitial velocity, h is the axial co-ordinate, J is the mass transfer rate per unit volume of bed, and the subscript 0 denotes the state at t = 0. The mass balance equation for the solute in the solid phase is

1 0- - 0ε( ) = =( )=∂

∂c

J c t cs ss

t,

(31)

where cs is the average solid phase concentration (kg m -3 ). Time-dependent concentration profi les for fl uid and solid phase are obtained by integration of these equations. The extraction yield is calculated from the fl uid phase concentra-tion at the extractor outlet:

eq

c h H dtf

t

= ′ =( )∫ρ 0

, e ( t = 0) = 0 (32)

where e is the extraction yield in terms of mass of extract over the mass of plant inserted into extractor, q ′ is the spe-cifi c fl ow rate in terms of the solvent mass fl ow rate over the mass of plant, ρ f is the solvent density, and H is the height of the packed bed. Eqs. (30) and (31) contain the mass transfer rate per unit volume of the extractor, J , which is given by the equation for external mass transfer:

J = k f a ( c + - c ) (33)

where the superscript + indicates the surface of a plant par-ticle, k f is the fl uid phase (external) mass transfer coeffi cient, and a is the specifi c surface area. The concentrations at the particle surface are usually assumed to satisfy an equilibrium relationship:

c c c+ += ( )* s

(34)

where c s is the local concentration within the particles and the superscript * denotes equilibrium. The solid phase concentration at particle surface, cs

+ , is related through an internal mass transfer relationship to the average particle concentration. For example, the mass balance for a spheri-cal particle of radius R and effective internal diffusion coef-fi cient D e is

∂∂

= ∂∂

==

c

t

D

R

c

r

J

r R

s e s3

1-ε

(35)

where r is the radial co-ordinate (Esqu í vel et al. 1999, del Valle et al. 2000b).

The initial concentrations at t = 0 when the outlet valve opens and the solution begins fl owing out of the extractor are related to the content of the solute in the plant put into the extractor, c

u (kg m -3 ):

c c cu s-

-0 01= ε

ε. (36)

They are usually chosen either on the assumption that no mass transfer has taken place until t = 0, it is c 0 = 0 and cs0 = c u , or, on the opposite, on the assumption that phase equilibrium has been established during the static extraction before the solvent starts fl owing out of the extractor. The real initial concentrations may be between these limits and depend on the rate of mass transfer during the period of static extraction before t = 0. The models for the mass transfer during static extraction were published by Al-Jabari (2002) and Steffani et al. (2006).

The content of solute in the plant loaded into the extrac-tor is primarily expressed in mass fraction x

u , (kg solute)(kg plant) -1 , which can be converted to units (kg solute)(kg matrix) -1 , where matrix is the insoluble part of the plant. Similarly, the contents of solute in both phases in the extractor are often expressed in mass ratio y (kg solute)(kg solvent) -1 and either mass fraction or mass ratio x , x expressed as (kg solute)(kg plant) -1 or (kg solute)(kg matrix) -1 , respectively. The conversion between the volume-related and mass-related quantities is via densities ρ f and ρ s , where ρ s is the density of plant particles calculated as either mass of plant or the mass of matrix over the volume of plant:

c y x c xf s s s s= = =ρ ρ ρ, , . c (37)

(The solute, the volume of solid phase, and also the specifi c fl ow rate are related to the mass of matrix when the initial content of solute in the plant is high and thus the mass of the plant varies considerably during the extraction.) The alternative form of the model equations expressed in y and x is

ερf

y

tu

y

hJ y h y t y

∂∂

+ ∂∂

⎛⎝⎜

⎞⎠⎟

= = = = =, ( 0) 0, ( 0) 0

(30a)



1 0 0-ε ρ( ) ∂

∂= =( )=s

x

tJ x t x- ,

(31a)

e q y dt e tout

0

t

= ′∫ , ( =0 = 0 )

(32a)

J = k f a ρ

f ( y + - y ) (33a)

y + = y *( x + ) (34a)

∂∂

= ∂∂ =

x

t

D

R

x

r r R

3 e

(35a)

x x y yu

f

s

--0 0 01

= ( ) =ρ ε

ρ εγ .

(36a)

5.2. Extraction steps and their characteristic times

5.2.1. Washing out (fl uid displacement) For any fl ow pattern, the characteristic time of washing out is equal to the mean residence time, t r = H / u . The course of washing out of a solute from the extractor is, however, not only a function of the dimensionless extraction time τ = t / t r but is also closely related to the fl ow pattern, as shown in Figure 3 . Plug fl ow is an idealisation. In reality, axial dispersion is always present in the extractor, at least the dispersion by molecular diffusion and small-scale mixing due to the fl ow between the particles. The mass balance for the fl uid phase with the coeffi cient of axial dispersion D ax , combined with the Danckwerts ’ boundary conditions, is

ε

∂∂

+ ∂∂

∂∂

⎛⎝⎜

⎞⎠⎟

=c

tu

c

hD

c

hJ- ax

2

2 ,

uc D

c

h- ax

∂∂

=0 for h = 0,

∂∂

=c

h0

for h = H.

(30b)

The value of D ax for SFE from plants is usually estimated from literature correlations for Peclet number, such as those developed by Tan and Liou (1989), Catchpole et al. (1996b), Funazukuri et al. (1998), or Yu et al. (1999).

It seems, however, that these correlations based on the data measured without mass transfer may not be always valid in the situation of mass transfer in the extractor because the mass transfer causes concentration gradients leading to density gra-dients, which can invoke or suppress mixing, as mentioned below in Section 5.2.3. Reis-Vasco et al. (2000) extracted with CO 2 the essential oil from leaves and observed that the axial dispersion coeffi cient was by one order of magnitude larger than according to the correlations and still the effect of axial dispersion on extraction kinetics was quite small. On the other hand, Zwiefelhofer and Brunner (1993), who extracted theobromine from cocoa shells, found a stronger dependence of the coeffi cient of axial dispersion on Reynolds number than according to the correlations.

Another form of the fl uid phase mass balance frequently used for short (small) extractors is the lumped parameter model:

ε

dc

dt

c

tJ

r

+⎛⎝⎜

⎞⎠⎟

= ,

c ( t = 0) = c 0 . (30c)

Mathematically, this model is identical to the model for continuous stirred tank extractor (ideal mixer).

The axial mixing can also be expressed by a series of n ideal mixers into which the extractor is divided along its height (Clavier et al. 1995, Reverchon 1996, Sovova 2005). The model is identical to the lumped parameter model for n = 1 and approaches the model with plug fl ow for a high number of mixers.

Another fl ow pattern was used in a model for extractor divided on its cross section into zones with parallel plug fl ows of different rates. When the extractor is scaled-up, attention should be paid to fl ow patterns because the fl ow in the packed vessels of larger diameter becomes less homogeneous. Brunner (1994) showed that the local degree of extraction depends also on the radial coordinate of extractor. Particularly at small fl ow velocities, the local velocity and mass transfer are higher near the wall and thus the residual concentration in the particles is higher close to the axis of the extractor. Brunner (1994) suggests using the model with axial disper-sion separately for the centre and the rim, with the amount of solvent for each section as an additional parameter, to simu-late the radial distribution. A similar solution with the extrac-tor divided into up to six parallel sections with plug fl ow of different fl ow rates was proposed by Sovova et al. (1994a) to fi t experimental extraction curves affected by natural convec-tion in the extractor where the SC-CO 2 dissolving vegetable oil fl owed from the bottom to the top. When del Valle et al. (2004a) extracted oil from milled seeds in a laboratory-scale extractor of 20 mm inner diameter and in a pilot extractor with a sample holder of 90 mm inner diameter, they found that the plug fl ow pattern was adequate for the smaller extrac-tor (the axial dispersion was too low to affect the extraction rate), while the simulation of extraction rate in the larger extractor required dividing the extractor into inner and outer

1.2

1.0

0.8

0.6

0.4

0.2

e/x,

g/g

00 1 2

τ, -3

Figure 3 The effect of fl ow pattern on washing out of the solute from the extractor: ( – – ) plug fl ow, ( – + – + – ) ideal mixer.



zones of different fl ow rates. A review of the literature on the scale-up of pressurised fl uid extractors was recently published by Pronyk and Mazza (2009).

Catchpole et al. (1996a) investigated the effect of extrac-tor geometry on the extraction rate, comparing the extraction curves measured in the standard extractor with axial fl ow and in an extractor with radial horizontal fl ow through the bed of particles. When the extraction was controlled by external mass transfer, the extraction with the horizontal solvent fl ow was much slower than with the axial fl ow. The residual oil content in the particles was signifi cantly higher at the bottom than at the top of the bed, indicating that the bottom was bypassed.

5.2.2. Phase equilibrium With respect to the extraction from plants, it is necessary to mention that phase equilibrium, in addition to its dependence on pressure and temperature, is often affected also by the solute interaction with the plant matrix, particularly when the content of the solute in the plant is low – a few weight per cent or less. The equilibrium fl uid phase concentration then decreases during the extraction, as sketched in Figure 4 . The solubility, c

sat , as a characteristic of solute-solvent equilibrium can be applied particularly in the extraction of oils from seeds where the initial content of solute is expressed in tens of per cent. A widely accepted correlation for the solubility of common vegetable oils composed mostly of C18 fatty acids in dense CO 2 was published by del Valle and Aguilera (1988):

cT Tsat f= +⎛

⎝⎜⎞⎠⎟

ρ10 742226 810

18708 2186840. exp .- -

(38)

where T is the temperature in kelvins and both c sat

and ρ f are

in kg m -3 . The equation is valid for pressures from 15.2 to 89.2 MPa, temperatures from 20 ° C to 80 ° C, and oil solubility below 100 kg m -3 .

If there is no solute-matrix interaction, the equilibrium fl uid phase concentration remains constant as long as there is still any solute in the solid phase:

c* = c sat for c s * > 0, c* = 0 for c s * = 0, or y* = y

sat for x * > 0, y* = 0 for x * = 0. (39)

Such discontinuous relationship could complicate numeri-cal solution of differential equations of SFE models. Lee

c* c*

csat

cs cs

csat

ct

Figure 4 Equilibrium relationships: ( – – ) no solute-matrix interac-tion, Eq. (10); (---) transition to linear equilibrium, Eq. (11); ( – + – + – ) solute-matrix interaction with linear equilibrium, Eq. (12).

et al. (1986) proved experimentally that the fl uid phase concen-tration of canola oil extracted from seed fl akes with SC-CO 2 was constant and in agreement with Eq. (38) in the range of initial oil content, 0.2 – 0.7 g (g oil-free seed) -1 . However, a decrease of equilibrium oil concentration was described in other works after the oil content in seeds decreased below approximately 25 % (Bulley et al. 1984) or 15 % (King et al. 1987), as depicted in the review of del Valle and de la Fuente (2006). This phenomenon was observed also by Perrut et al. (1997) who extracted sunfl ower seed oil. They proposed a simple equilibrium relationship combining the oil solubility y sat

for oil content in seed higher than a transition value x t and

a linear equilibrium corresponding to oil-matrix interaction for lower oil content in seed, with a mass-related partition coeffi cient K m :

y* = y sat for x * > x t , y* = K m x for x ≤ x t , K m x t < y sat (40)

Equation (40) can be readily converted to the relationship of volumetric concentrations c , c s . The more general Eq. (40) is reduced to Eq. (39) when the transition concentration x t is set to zero.

The most frequently used relationship in the case of solute-matrix interaction is a linear sorption isotherm with a constant partition coeffi cient K :

c Kc*= s or y K x* ,= m K Km s f= ρ ρ . (41)

More complicated equilibrium relationships in the models for SFE are different adsorption isotherms such as Langmuir isotherm applied by Clavier et al. (1995) and Subra et al. (1998), Freundlich isotherm applied in the VTII model (Zwiefelhofer and Brunner 1993, Brunner 1994) and later, e.g., by Ghoreishi and Sharifi (2001), or the BET isotherm applied by Goto et al. (1998). Different equilibrium relationships were mutually compared (Salimi et al. 2008). Araus et al. (2009) propose that the sorption isotherms should be experimentally determined when modelling a given extraction process instead of selecting a certain equilibrium relationship in advance.

5.2.2.1. Equilibrium extraction The equilibrium extraction is an extraction with negligible mass transfer resistance. The characteristic time of equilibrium extraction is based on the assumption that the extraction rate is limited only by the initial fl uid phase equilibrium concentration established at t = 0 when c 0 = c *( c s0 ). Thus, the characteristic time t eq and the dimension-less time of equilibrium extraction Θ eq are, respectively

t

c

cteq

sr=1 0

0

-εε

,

Θeqeq

r

t

t=

(42)

Particularly, for the two cases without solute-matrix inter-action and with linear equilibrium:

Θeq

u

sat

=11

--

εε

c

c when c * = c sat ,

Θeq K

=1-εε

when c * = Kc s . (43)



The expression Θ eq for linear equilibrium is a reciprocal value of the dimensionless parameter Γ introduced by Poletto and Reverchon (1996) in their parametric analysis of a model for the SFE with plug fl ow, internal or external mass transfer resistance, and linear equilibrium. The paper contains also the analytical solution of equilibrium extraction equations for plug fl ow, which is valid for both equilibrium relationships from Eq. (40). The concentration profi le in the extractor is a discontinuous function of dimensionless axial co-ordinate z = h / H :

c

c

c

c0 0

1= =s

s for

z ≥

+τ

1 Θeq

and τ< +1 Θeq ,

c

c

c

c0 0

0= =s

s else,

(44)

and the extraction yield increases linearly until the extraction is complete:

e

xu eq

=+

τ1 Θ

for τ< +1 Θeq ,

e x= u else. (45)

On the other hand, the analytical solution of equilibrium extraction with linear equilibrium described by the lumped parameter model is

e

xu eq

=+

⎛

⎝⎜

⎞

⎠⎟1

1- -exp

τΘ

(46)

(Goto et al. 1993, Al-Jabari 2002). Both extraction curves are compared in Figure 5 . Evidently, the shape of the equilibrium extraction curve is determined by fl ow pattern in the same way as in the case of a simple washing out of a solute.

5.2.3. External mass transfer and extraction from

particle surface It follows from Eqs. (30) and (33) that the characteristic external mass transfer time and the dimensionless external resistance are, respectively:

t

k a kff f

= =ε λ εε1-

, Θ f

f

r f r

= =t

t k at

ε,

(47)

1.2

1.0

0.8

0.6

0.4

0.2

00

e/x,

g/g

τ, -1+Θeq

Figure 5 Equilibrium extraction with linear equilibrium: ( – – ) plug fl ow, ( – + – + – ) ideal mixer.

where λ is the characteristic dimension of a particle equal to its volume-to-surface ratio ( λ = R /3 for a spherical particle of radius R ). The models for the extraction from particle surface (or from the particles with negligible internal mass transfer resistance) are obtained combining mass balance equations for both phases, Eq. (33) for the external mass transfer, and phase equilibrium relationship. As the internal mass transfer resistance is neglected, the concentration is assumed to be uniform across the particle and Eq. (34) is modifi ed to the relationship

c c c+ = ( )* s . (34b)

5.2.3.1. Model for plug fl ow + no solute-matrix interac-tion Brunner (1984) introduced into the modelling of SFE from plants a relationship valid for plug fl ow and no solute-matrix interaction (when the equilibrium fl uid phase con-centration equals the solubility of solute in the solvent, c sat ), which reads in the nomenclature of the present paper

c

c

z

sat f

=⎛

⎝⎜

⎞

⎠⎟1- -exp ,

Θ

e

xu eq f

=+

⎛

⎝⎜

⎞

⎠⎟

⎡

⎣⎢⎢

⎤

⎦⎥⎥

τ1

11

Θ Θ- -exp . (48)

Brunner (1984) used this relationship to describe the initial period of oil extraction from pre-pressed seed. According to Eq. (48), the extraction rate is constant and the corresponding section of extraction curve is a straight line. This equation is valid as long as all particles contain the solute. Lee et al. (1986) solved the mass balance equa-tions numerically for both the initial period and the second extraction period, when the solute is exhausted fi rst at the extractor inlet and then the region free of solute extends until it reaches the extractor outlet. The model was fi tted to both experimental extraction curves and experimental solid phase concentration profi les c s ( h , t ). The experiments with oil extracted from crushed seed with SC-CO 2 were conducted in a wide range of fl ow rates and the evaluated external mass transfer coeffi cient was found to be directly proportional to u 0.54 .

Although the extraction rate of oil from seed usually agrees with Eq. (48), S-shaped extraction curves were sometimes observed (Cocero and Garc í a 2001). This could be related to the mixing in the empty volume between the extractor and the separator. When a basket with the plant particles was placed into the extractor and a large empty space remained behind the basket in the fl ow direction, the outlet concentration was much lower than the oil solubility, although the residence time in the basket was suffi cient to saturate the solution (Fiori 2007). This again could be explained by mixing of the saturated solution with pure solvent fi lling initially the empty place.

5.2.3.2. Model for plug fl ow + partial solute-matrix interaction Perrut et al. (1997) extracted sunfl ower oil from seeds and observed that the slower extraction in the second period, following the fi rst constant rate period, was still controlled by phase equilibrium. They used therefore in the model for SFE the equilibrium relationship given by Eq. (40). The numerical solution of the model was compared



with experimental curves, and the equilibrium parameters and k f were adjusted.

5.2.3.3. Model for plug fl ow + linear equilibrium Cocero and Garc í a (2001) adapted a model for desorption from par-ticle surface to simulate the extraction of oil from seed with SC-CO 2 modifi ed with alcohols. The mass balance equations were integrated numerically. The analytical solution of the model equations, which evaluation however requires numeri-cal methods, was published by Lucas et al. (2007).

5.2.3.4. Model for mixer + linear equilibrium Neglecting the accumulation term in Eq. (30c) and using the equilibrium relationship according to Eq. (41), Papamichail et al. (2000) obtained analytical solution of the ordinary differential equa-tions (in the present nomenclature):

cKc e

xu eq f

outu

f eq f

=+ +( )

⎛

⎝⎜⎜

⎞

⎠⎟⎟

=+( )

⎛

⎝⎜

1 11

1Θ Θ Θ Θ Θexp , exp- - -

τ τ⎜⎜

⎞

⎠⎟⎟

(49)

5.2.3.5. Model for mixer + partial solute-matrix interac-tion Moreover, Papamichail et al. (2000) solved the SFE model for the conditions of negligible internal mass resis-tance, lumped parameters, and the equilibrium relationship given by Eq. (40). The accumulation term in mass balance for the fl uid phase, Eq. (30c), was again neglected to obtain the approximate analytical solution:

y

y

e

x

y

xx x yout

sat f u

sat

u ff u t sa=

+=

+≤ = +( )( )1

1 11

Θ ΘΘ,

γ ττ τ γ for -t tt( ),

y

x K Kout

t m

f

m t

f

=+

( )+

⎛

⎝⎜

⎞

⎠⎟1 1Θ Θ

exp ,--γ τ τ

e

x

x

x

K

u

t

u

m t

f

= ( )+

⎛

⎝⎜

⎞

⎠⎟1

1- -

-exp .

γ τ τ

Θfor tτ>τ

(50)

where γ is the solvent-to-matrix mass ratio in the extraction bed, γ = ρ f ε /[(1- ε ) ρ s ]. The models for SFE from particle sur-face enable, among others, calculation of k f from experimen-tal extraction curves. The initial y ( h = H )/ y sat or c ( h = H )/ c sat ratio can be determined experimentally from initial slopes of

Table 2 CO2 extraction from plants: external mass transfer coeffi cients based on experimental data for different solutes, particle sizes, pressures and temperatures, and fl ow velocities.

Solute/plant Substrate kf × 105 m s-1 kf a0 × 102 s-1 References

Fatty oil Flaked canola seed – 0.6–7 Lee et al. 1986Fatty oil Milled tomato seed 0.2–1.4 – Roy et al. 1994Fatty oil Milled grape seed 0.4–0.6 4–10 Sovova et al. 1994aFatty oil Milled sea buckthorn berries – 0.05–1 Stastova et al. 1996Fatty oil Milled sunfl ower seed – 1–9 Cocero and Garcia 2001Fatty oil Milled wheat germ – 0.3–1 Lucas et al. 2007Fatty oil Crushed sunfl ower seed 2.2 – Perrut et al. 1997Essential oil Ground clove buds 0.25–1.6 – Reverchon and Marrone 1997Oleoresin Milled black pepper berries – 0.3–2 Sovova et al. 1995Oleoresin Milled black pepper berries – 0.03–0.08 Ferreira et al. 1999

extraction curves measured once at a given fl ow rate and once at a very low fl ow rate, when the solution at the extractor out-let is saturated. Several results of k

f evaluation from experi-mental extraction curves are shown in Table 2. The k

f values

are usually of the order of magnitude 10 -6 m s -1 , the volumetric mass transfer coeffi cient is not far from 1 min -1 , and the char-acteristic time of external mass transfer in SC-CO 2 , t f , is usu-ally close to 1 min or even less. It is a common practice to use Eq. (48) to evaluate k

f via Θ f . Nevertheless, it is evident from Eqs. (48) – (50) that the effect of external mass transfer resis-tance on the outlet concentration depends on the fl ow pattern, as illustrated also in Figure 6 and discussed in the literature (Sovova 2005). Thus, Eq. (48) should be used to evaluate k

f only when the fl ow pattern is close to plug fl ow. The lower values of k f a obtained by Ferreira et al. (1999) are based on experiments in a horizontal extractor where the fl ow pattern was most probably different, as indicated by the results on SFE in a horizontal extractor published by Catchpole et al. (1996a).

Channelling is an exception from the rule that the charac-teristic time of external mass transfer in the SFE from plants is only a few minutes or even tenths of minutes. When the particles forming the extraction bed stick closely together, the solvent breaks several channels in the bed and passes through them with a high velocity. As the specifi c interfacial

1.2

1.0

0.8

0.6

0.4

c out

/cO, -

0.2

00 1 2 3

Θf, -

Figure 6 Extraction from particle surface: the dependence of out-let concentration on dimensionless external mass transfer resistance: ( – – ) plug fl ow, ( – + – + – ) ideal mixer.



area is extremely small, the external volumetric mass transfer coeffi cient k

f a decreases and t

f increases by several orders of

magnitude against usual values. So it was for example in the extraction of essential oil from sticky particles in a large-scale extractor (Berna et al. 2000).

The external mass transfer coeffi cient in packed beds was correlated with the physical properties of solute and sol-vent, fl ow velocity, and particle size d in terms of Sherwood, Reynolds, and Schmidt numbers. The most frequently used correlations to estimate k

f in SFE models are listed in Table 3 together with references to some of their applications; more extensive reviews of k

f correlations together with ranges of their validity are offered by del Valle and de la Fuente (2006) and particularly by Puiggene et al. (1997). The last lines of Table 3 indicate the correlations that include also the Grashoff number, Gr, which is proportional to the density differences in the fl uid phase which induce natural convection. The natu-ral (free) convection can enter the models for SFE either by changing fl ow pattern, as mentioned above in Section 5.2.1, or by changing k

f as proposed in a series of papers by Stuber et al. (1996), Puigenne et al. (1997), and Germain et al. (2005). In the calculation of Sherwood number, the term containing Gr is either added to the term for the forced convection in the case of gravity assisted mass transfer (usually solvent down-fl ow) or subtracted from it in the case of gravity opposed mass transfer (usually solvent up-fl ow).

The numbers Sh and Sc include the binary diffusion coef-fi cient of a solute in supercritical solvent, D . Although D depends on pressure, temperature, and chemical composi-tion, its value does not vary substantially under the conditions of SFE. Its order of magnitude is usually 10 -9 m 2 s -1 or close to this value. For example, D of essential oils in CO 2 under pressure of 9 – 10 MPa and at temperature 40 ° C was found in the range 1 × 10 -8 – 2 × 10 -8 m 2 s -1 , and D of fatty oils in CO 2 at 28 – 30 MPa and 40 ° C was 3 × 10 -9 m 2 s -1 (Germain et al. 2005). Typical k

f values under the conditions of SFE from plants, calculated from the correlations, are then of the order of mag-nitude 10 -6 or 10 -5 m s -1 .

5.2.4. Internal and overall mass transfer The internal mass transfer is characterised in the models by either effective diffusion coeffi cient, D

e , or solid phase (internal) mass transfer coeffi cient, k

s , the later one in analogy to the external mass transfer coeffi cient.

5.2.4.1. Effective diffusivity According to Fick ’ s second law, the equation for symmetrical diffusion in a spherical par-ticle of radius R is

∂∂

= ∂∂

∂∂

⎛⎝⎜

⎞⎠⎟

∂∂

= = = ∂∂ =

c

t

D

r rr

c

r

c

rr J D a

c

r r

s e s se

s2

2 0 0, , for -RR

(51)

Bartle et al. (1990) simulated the SFE controlled by inter-nal diffusion using this equation with initial and bound-ary conditions c

s = c

u for t = 0, c

s = 0 for r = R. The solution

was taken from an analogical case of heat transfer from a sphere:

e x x x c c

e

x nn

D t

Rnu u s u

u

e= = = ⎛⎝⎜

⎞⎠⎟=

∞

∑1 1 16 1

2 22 2

21

- - - -, expπ

π

(52)

The model is therefore called the “ hot ball model. ” The higher terms of the infi nite series become negligible after a short time and the extraction curve is then

e

x

D t

Ru

e= ⎛⎝⎜

⎞⎠⎟

16

22

2- -π

πexp .

(53a)

Thus, the effective diffusivity can be estimated from the slope of a plot of ln(1- e / x u ) against the extraction time at suf-fi ciently high extraction times. The solution of a model for mass transfer from a slab-like particle (Bartle et al. 1991b) is of a similar form as Eq. (52).

The next step was made by Reverchon et al. (1993, 1994b) who adapted for the SFE of essential oils a mathematical description of heat transfer from a sphere that takes into account also the external mass transfer. No interface was assumed at particle surface as the internal diffusion was assumed to take place in the pores of a porous particle that are fi lled with solvent. The solution of model equations shows that the external mass transfer resistance is important only in the very beginning of the extraction and later it does not affect the extraction kinetics because it is negligible in comparison with increasing internal mass transfer resistance.

In their third paper on the hot ball model, Bartle et al. (1992b) extended Eq. (52) by an expression including the solubility of solute in the solvent, respecting the fact that the fl uid phase concentration is limited by the solubility. It is evident, however, that the models where mass transfer and

Table 3 Correlations for the external mass transfer coeffi cient (Sh = kf d/D, Re = udρf /(εµ), Sc = µ/ρf D).

Correlation Published by Applied by

Sh=2+1.1 Re0.6Sc1/3 Wakao and Funazkri 1978,Wakao and Kaguei 1982

Brunner 1984, Recasens et al. 1989, Peker et al. 1992, Goto et al. 1993, 1996, Ghoreishi and Sharifi 2001, Skerget and Knez 2001, Vedaraman et al. 2005

Sh=0.38 Re0.83 Sc1/3 Tan et al. 1988 Reverchon et al. 1993, 1994a, Reverchon and Sesti Osseo 1994a, Goodarznia and Eikani 1998, del Valle et al. 2004a, Perakis et al. 2005

Sh=0.839 Re0.667 Sc1/3 Catchpole 1991 (PhD thesis), cited in Brunner 1994, p. 160

Gaspar et al. 2003, Lu et al. 2007

Sh=0.206 Re0.8Sc1/3 Puiggené et al. 1997 del Valle et al. 2006, Araus et al. 2009Sh=Sh(Re, Sc, Gr) Lim et al. 1990 Roethe et al. 1992Sh=Sh(Re, Sc, Gr) Puiggené et al. 1997 Germain et al. 2005



phase equilibrium are expressed independently, such as those discussed below in Sections 5.3 – 5.6, correspond better to the situation where both steps control the extraction kinetics.

5.2.4.2. Mass transfer coeffi cient The internal mass transfer rate is often approximated by a function of the aver-age solid phase concentration:

J k a x x k a c c= ( )= ( )+ +

s s s s sρ - - .

(53)

The solution of Eq. (53) together with Eq. (31) and with initial and boundary conditions c

s = c

u for t = 0, c

s + = 0 is

e

x

t

tt

k

t

tii

ru ii

s

=⎛⎝⎜

⎞⎠⎟

= =1- -exp , ,λ Θ

(54)

where t i is the characteristic time of internal mass transfer.

The dimensionless internal mass transfer resistance Θ i was

used, e.g., by Poletto and Reverchon (1996) in the analysis of extraction kinetics. It can be shown that a formally identi-cal result is obtained when a parabolic concentration profi le is assumed in the particles. After the parabolic concentration profi le substitution into Eq. (51) for spherical particle, into analogous equations for diffusion in a long cylindrical par-ticle, and in a slab-like particle, and after integration of these equations with the above-mentioned initial and boundary conditions one obtains

e

x

t

tu i

=⎛⎝⎜

⎞⎠⎟

1- -exp , t

Die

= µλ2

(54a)

where µ is equal to 3/5 for a sphere, 1/2 for a cylinder, and 1/3 for a slab (Catchpole et al. 1996a, Reverchon 1996). Thus, a conversion between the estimates of D

e and k s is possible:

k

Ds

e=µλ

; k s = 5 D e / R for a sphere,

k s = 3 D e / R for a slab of thickness 2 R .

(55)

The internal-to-external mass transfer resistance ratio is often expressed in terms of Biot number Bi = k

f R/ D

e :

Bi = 5 k f / k s for a sphere, Bi = 3 k f / k s for a slab of thickness 2 R . (56)

5.2.4.3. Applications The internal mass transfer was a controlling step in the extraction of caffeine with nitrous oxide from water-soaked coffee beans, where D

e in the pores

fi lled with water was as high as 1 × 10 -10 m 2 s -1 (Brunner 1984). When essential oil is extracted with CO 2 from dry plants, the mass transfer resistance is by orders of magnitude higher. Thus, the effective diffusivity of vanilla essential oil extracted from chopped beans was estimated to 3 × 10 -13 m 2 s -1 (Nguyen et al. 1991), essential oils from basil, marjoram, and rose-mary leaves were extracted with D

e 1.2 × 10 -13 – 2.8 × 10 -13 m 2

s -1 (Reverchon et al. 1993, 1994a), and D e of essential oils from sage and celery aerial parts and from coriander seed was 1.4 × 10 -12 – 5.1 × 10 -12 m 2 s -1 (Catchpole et al. 1996a).

5.2.4.4. Overall mass transfer resistance and linear driving force When linear equilibrium and parabolic con-centration profi les in particles are assumed, the two driving forces represented by the concentration differences between the average solid phase concentration and the solid phase con-centration at particle surface, Eq. (53), and between the fl uid phase concentrations at particle surface and in bulk fl uid, Eq. (33), are combined into a linear driving force and multiplied by the combined mass transfer coeffi cient, k

comb , to calculate the mass transfer rate:

J k a Kc ck k

K

k

kk

KBi

comb scomb f s

combf

= ( ) = +

=+

-

for a sphere

, ,1 1

1 5,,

k

k

KBif

comb =+1 3

for a slab

(57)

(Recasens et al. 1989, Goto et al. 1990, Peker et al. 1992). A combined mass transfer resistance in terms of character-

istic times can be introduced as

t t

Kt t tcomb f s f s eq comb f s eq= + = + = +ε

ε1-Θ Θ Θ Θ Θ, . (58)

It is evident from Eq. (58) that when the partition coeffi -cient K is low, the external mass transfer resistance may affect the overall mass transfer rate more than the internal mass transfer resistance, although t

f is much smaller than t s , or in other words, although the external mass transfer coeffi cient is considerably bigger than the internal mass transfer coeffi cient (Peker et al. 1992). The dependence of extraction rate on both mass transfer resistances was evident also in the extraction of theobromine from cocoa shells, where the equilibrium is described by Freundlich isotherm (Zwiefelhofer and Brunner 1993, Brunner 1994).

A good approximation of extraction curves calculated with linear driving force and lumped parameter model offers Eq. (49) when Θ

comb is substituted for Θ f :

e

xu eq f s

=+( )+

⎛

⎝⎜⎜

⎞

⎠⎟⎟

11

- -expτ

Θ Θ Θ. (49a)

5.3. One-stage models

5.3.1. Diffusion model

5.3.1.1. Model equations The model includes the internal diffusion in a homogeneous and usually non-porous solid, phase equilibrium at particle surface characterised by a parti-tion coeffi cient, external mass transfer to bulk fl uid, and fl ow with the fl uid to the extractor outlet.

Goodarznia and Eikani (1998) solved model equations for linear equilibrium and fl ow with axial dispersion, using the method of fi nite differences for the three independent variables: time, axial coordinate of the extractor, and radial



coordinate of spherical particles. del Valle et al. (2000b) assumed a plug fl ow pattern in the extractor, divided the extraction bed and the substrate particles into several disc- and spherical-shell-shaped volume elements, respectively, and integrated the obtained ordinary differential equations in time using a fourth-order Runge-Kutta method. This numeri-cal solution technique was used also by Araus et al. (2009) to integrate model equations for the fl ow with axial dispersion.

5.3.1.2. Simplifi ed forms The diffusion model equations are simplifi ed using the assumption of parabolic concentration pro-fi le in the particles, enabling further combining the internal and external mass transfer resistances using the linear driving force. The concentration in the solid phase is then characterised by the average solid phase concentration and the number of inde-pendent variables is reduced to two, the time and the axial coor-dinate. Brunner (1994) presented the VTII model with linear driving force, Freundlich isotherm, and fl ow with axial disper-sion . Catchpole et al. (1996a) published analytical solution of equations of the diffusion model with linear driving force and plug fl ow. The dimensionless fl uid phase concentration pro-fi le is a function of two dimensionless variables, ε z / Θ comb and ( t / t r - ε z )/( Θ eq Θ comb ). Its approximations are presented, too, and it is shown that the extraction curve is reduced to Eq. (54a) when the extraction is controlled solely by the internal mass transfer and thus the fl ow pattern does not affect the extraction rate. The model with plug fl ow, linear equilibrium, and neglected external mass transfer resistance was derived by Reverchon (1996) to simulate the extraction of sage; the model equa-tions were solved using the method of characteristics or, alter-natively, dividing the extractor axially into a series of mixed extractors and integrating the set of ordinary differential equa-tions by a fourth-order Runge-Kutta method. This model with linear equilibrium, neglected external mass transfer resistance, and plug fl ow pattern was analysed by Poletto and Reverchon (1996) who evaluated the concentration profi les and extrac-tion curves for different values of two dimensionless param-eters Γ = 1/ Θ eq and Θ s . They concluded that the mass transfer resistance can be neglected and equilibrium model can be used when Θ s / Θ eq ≥ 0.02. When Θ s / Θ eq ≥ 2, the mass transfer resis-tance prevails, the concentration profi les in the extractor are fl at, and therefore the fl ow pattern has little effect on the overall extraction rate; the mathematically simpler lumped parameter model is then recommended. When Θ s / Θ eq is between 0.02 and 2, both equilibrium and mass transfer resistance must be taken into account. These results are easily generalised to overall mass transfer resistance when Θ s is substituted by Θ eq Θ comb .

The lumped parameter model has analytical solution dependent on initial conditions. The extraction curve for zero fl uid phase concentration at t = 0 is

e

x

p p p p

p pu

= ( ) ( )1 1 2 2 1

1 2

--

-

exp expτ τ

where

p b b B1

21

24= +⎡

⎣⎤⎦- - ,

p b b B2

21

24= ⎡

⎣⎤⎦- - - ,

b B

comb

= + +11

Θ,

B

comb eq

= 1

Θ Θ. (59)

The dimensionless parameter Φ used in the paper of Peker et al. (1992) where this analytical solution was published is equal to 1/[ Θ

comb (1- ε )] in the present notation.

5.3.1.3. Model parameters The adjustable model param-eter is the effective internal diffusivity D

e , which is evaluated

by fi tting the calculated extraction curves to experimental data. The other model parameters are usually estimated from cor-relations (the external mass transfer coeffi cient and the axial dispersion coeffi cient) or from an experimental extraction curve, where the initial equilibrium fl uid phase concentration is read from its initial slope and the content of extractable sol-ute from its horizontal asymptote; these two values are used to estimate the partition coeffi cient. Alternatively, the parti-tion coeffi cient is taken from the literature (Reverchon 1996, Goodarznia and Eikani 1998).

5.3.1.4. Applications del Valle et al. (2000b) examined two modifi cations of the model neglecting either the external mass transfer resistance or the internal mass transfer resis-tance (for the extraction from particle surface). The sensitiv-ity analysis of the effect of Θ

f and Θ s resulted in fi nding that the extraction curves are almost identical for different internal and external mass transfer characteristic times as long as the combined characteristic time is constant, but the solid phase concentration profi le in the axial direction is fl atter when the contribution of external resistance increases. Thus, a multiob-jective fi t to both experimental extraction curves and experi-mental solid phase concentration profi les was recommended to identify the major mass transfer resistance.

The results of application of the model on the extraction of different essential oils are listed in Table 4. It is interesting to compare the different D

e values obtained from the same

slightly scattered experimental data, in one instance assum-ing slab-like particles and in another – spherical particles (see the fi rst two lines of the table). Evidently, the assumption of spherical particles is not correct when pieces of leaves or fl owers of size larger than about 0.5 mm are extracted. When the result calculated for inadequate particle shape is skipped, the values of D

e are in the range 2 × 10 -13 – 7 × 10 -13 m 2 s -1 . The diffusion model was successfully applied also to the

extraction of theobromine from cocoa seed shells (Brunner 1994) or the extraction of caffeine from water-soaked coffee beans (Peker et al. 1992).

To sum up, the diffusion model is appropriate when the mass transfer resistance is mainly inside the plant particles and the equilibrium is characterised by partition coeffi cient. The model, however, does not fi t the broken extraction curves of the SFE of fatty oils (triglycerides) from seeds where the equilibrium fl uid phase concentration is equal to the oil solu-bility in the solvent, at least in the fi rst extraction period, while the diffusion model is based on the proportionality between the equilibrium solid and fl uid phase concentrations.

5.3.2. Desorption model

5.3.2.1. Model equations The desorption model, also called DDD (desorption-dissolution-diffusion) model, is a model for porous particles with pores fi lled with the solvent.



It consists of solute desorption on the pore walls, its internal diffusion to particle surface, external mass transfer, and dis-placement with bulk fl uid. With respect to the solute trans-port, there is no interface at particle surface, and therefore K = 1 is substituted into the formula for linear driving force, Eq. (57). Two mass balance equations are written for the par-ticles, one for the pores and one for the solid matrix. Recasens et al. (1989) formulated a general model for SCF regeneration of a porous adsorbent in a packed bed of spherical particles where the solvent fl ows with axial dispersion. A nonlinear Langmuir-type kinetics of adsorbate desorption from the pore walls was assumed. [The Langmuir-type kinetics on particle surface was later considered by Al-Jabari (2003) in a model for SFE.] Recasens et al. (1989) derived also two simplifi ed versions of the general model, based on linear driving force and plug fl ow: the model with instantaneously established equilibrium and the model with irreversible desorption, and derived their analytical solutions. These models have only two parameters, the overall mass transfer coeffi cient and either partition coeffi cient or desorp tion rate constant. The linear equilibrium between the solid phase and the fl uid fi ll-ing the pores enables a reduction of two mass balances for particles to one equation.

Srinivasan et al. (1990) proved that a fi rst-order, reversible adsorption model (containing both equilibrium constant and desorption rate constant) successfully fi ts the detailed experi-mental data on desorption of ethyl acetate from activated car-bon with SC-CO 2 .

Numerical solution of model equations is described in more details in several papers. For the fl ow with axial dispersion, Ghoreishi and Sharifi (2001) assumed the Freundlich adsorp-tion isotherm and used the technique of orthogonal colloca-tion on fi nite elements, and Meireles et al. (2009) assumed the linear equilibrium and applied the fi nite difference method. The lumped parameter model is usually combined with linear driving force, which leads to an analytical solution formally identical with the solution for the diffusion model, Eq. (59), where Θ comb is given by Eq. (58) and Θ eq by Eq. (43); how-ever, the partition coeffi cient K in Eq. (43) that was written for the interface at particle surface must be substituted by K pp for a porous particle:

K

K

Kpp =+1-β β

(60)

where K is the partition coeffi cient on the pore walls (inversed adsorption equilibrium constant) and β is the porosity of the particle (Peker et al. 1992, Goto et al. 1994). When a more complex phase equilibrium relationship such as the BET iso-therm applied by Goto et al. (1998) is used, the ordinary dif-ferential equations of the lumped parameter model are solved numerically.

5.3.2.2. Model parameters The axial dispersion coeffi -cient is calculated from literature correlations. The effective internal diffusivity D e in the particles of porosity β and tortu-osity l tor is estimated as

D

lDe

tor

= β

(61)

(del Valle et al. 2006). The estimation of D e is even simpler

when the tortuosity is assumed to be equal to 1/ β :

D e = β 2 D (61a)

(Goto et al. 1993, Skerget and Knez 2001, Meireles et al. 2009). The resulting internal mass transfer resistance is even smaller than the external resistance based on the external mass transfer coeffi cient k f calculated from literature correla-tions. Thus, the overall mass transfer resistance is low and the extraction kinetics is close to that of equilibrium extraction. The most important model parameter, the partition coeffi cient, is determined by fi tting the experimental extraction curves.

5.3.2.3. Applications to SFE The model with irreversible desorption rate was tested in the study on SFE of β -carotene from carrots published by Subra et al. (1998) with the conclu-sion that the model based on adsorption equilibrium would be more adequate. The model with adsorption equilibrium corresponds better to experimental data measured for dif-ferent fl ow rates, is applied most frequently, and only this model will be discussed below. Goto et al. (1993) simulated the extraction of peppermint volatile oil with SC-CO 2 . The peppermint leaves were regarded as slabs. The process could be simulated as equilibrium extraction due to the negligible effect of mass transfer resistance. The only model parameter, the equilibrium constant of the linear equilibrium relationship, was evaluated in dependence on extraction pressure and tem-perature. A more general equilibrium relationship, the BET isotherm, was introduced into the model by Goto et al. (1998)

Table 4 Effective diffusion coeffi cients of volatile oils extracted with SC-CO2, evaluated from experimental extraction curves using the diffusion model.

Herb Particle size (mm)

Pressure/temperature (MPa/°C)

De × 1012 (m2 s-1)

References Source of data

Sage leaves 0.25–3.1 9/50 0.6a Reverchon 1996 Reverchon 1996Sage leaves 0.25–3.1 9/50 8.5 Araus et al. 2009 Reverchon 1996Pennyroyal leaves 0.3–0.7 10/50 58.2 Araus et al. 2009 Reis-Vasco et al. 2000Basil leaves 0.17 10/40 0.2 del Valle et al. 2000a Reverchon et al. 1993Basil and marjoram leaves 0.17 10/40 0.2 Goodarznia and Eikani 1998 Reverchon et al. 1993Caraway seed 0.5 9–10/40 0.5–0.7 Goodarznia and Eikani 1998 Sovova et al. 1994baSlab-like particles were assumed, in contrast to spherical particles in other calculations.



and applied on the same set of experimental data. Adjusting the equilibrium parameters, the volatile oil extraction could be simulated as desorption while only a weak solute-matrix interaction was assumed for the initial period of the extraction of cuticular wax.

Meireles et al. (2009) used the desorption model with lin-ear equilibrium and axial dispersion to simulate the extraction of vetiver oil from particles as small as 0.18 mm. The effect of mass transfer resistance was almost negligible according to the model. The experimental data, however, showed a decrease in the extraction rate after about 80 % of solute had been extracted. The model ability to predict the effects of scale-up was proved by fi tting the partition coeffi cient to experimental data from a smaller extractor, prediction of extraction kinet-ics in a larger equipment, and comparison of the results with experimental extraction curves in this equipment.

Skerget and Knez (2001) applied the desorption model to evaluate extraction curves measured for different plants: cocoa, paprika, pepper, and Silybum mariannum ; the solvents used were CO 2 and propane. The effect of pressure and tem-perature on the extraction kinetics was investigated. More details on the extraction of S. mariannum and its model can be found in the paper published by Hadolin et al. (2001). Again, the controlling factor in the model was the equilibrium. The model simulates tightly the initial sections of extraction curves but the agreement is not as good in the following sec-tion of some of the curves.

Mongkholkhajornsilp et al. (2005) matched the model to experimental extraction curves of nimbin extracted from neem seeds with CO 2 . The seed was ground to different par-ticle sizes ranging from 0.575 to 1.85 mm. The extraction rate decreased with increasing particle size but the model could not simulate this behaviour as long as the mass transfer resistance [based on the correlations of Wakao and Funazkri (1978) and Tan et al. (1988), and on D e according to Eq. (61a)] was neg-ligible. Instead of considering a larger internal mass transfer resistance, the authors decided to decrease the external mass transfer coeffi cient and developed a new correlation for k

f .

5.3.2.4. Comment The porous and tortuous structure of dif-ferent pre-pressed vegetable substrates was evidenced by del Valle et al. (2006). Generally, however, natural materials have cellular structure and thus diffusion across the cell walls may be slower than through the pores of a porous substrate (Roy et al. 1996a). Roethe et al. (1992) proposed a detailed model for parallel mass transfer through the pores and through the cells, each of them characterised by its own effective diffusiv-ity. On the basis of a comparison between scanning electron microscope (SEM) images of the substrate structure and the results of Hg-porosity measurement, they drew a conclusion about the volumetric fraction of pores open for mass transfer in green coffee beans.

5.3.3. Shrinking core model

5.3.3.1. Model equations The shrinking core model assumes a sharp boundary within a porous spherical particle between extracted part and inner non-extracted part, the core. The pores in the core are fi lled with condensed solute up to

the boundary, where the solute dissolves in the solvent and diffuses then through the external shell to the particle surface. The core initially fi lls the whole particle; as the extraction proceeds, the core boundary moves to the centre. Equilibrium is assumed at the core boundary; the fl uid phase concentra-tion is equal to c

sat . The internal mass transfer resistance is located in the shell surrounding the core and increases as the core shrinks. The complete model consists of the description of internal diffusion, external mass transfer, mass balance for fl uid, and mass balance for the particles, which is limited on the core. Zero concentration in the fl uid phase outside par-ticles is assumed at t = 0. The model was formulated for the fl ow with axial dispersion and the partial differential equa-tions were solved numerically by Crank Nicholson ’ s method (Goto et al. 1996, Roy et al. 1996a). The equations of the model for plug fl ow were integrated in time using a modi-fi ed Rosembrock formula after the spatial derivatives had been substituted by fi nite differences (Germain et al. 2005, del Valle et al. 2006).

5.3.3.2. Simplifi ed form When some slow changes of the core radius are neglected in the equations of the model for plug fl ow, a quasi-steady-state analytical solution is obtained as a dependence of the core radius r

c on extraction time and axial coordinate (King and Catchpole 1993, p. 184, Goto et al. 1996):

ξ

τc

u com eq comb

x

x

z z3 11

1= =

+⎛⎝⎜

⎞⎠⎟

--

-Θ Θ Θ

exp where

ξc

cr

R= ,

Θeq

s

sat

c

c= 0 -1 ε

ε, Θ Θ Θcomb f s

c

= +⎛⎝⎜

⎞⎠⎟

51

11

εε ξ-

- . (62)

5.3.3.3. Model parameters Goto et al. (1996) analysed the effects of internal and external mass transfer resistance and of axial dispersion on extraction kinetics. As expected, the extraction is slower and occurs similarly in the whole extrac-tor when Θ

s is large. The effect of axial dispersion is therefore observed only when the mass transfer resistance is low, as shown for Θ

s = 0.67 (parameter a in the paper equals to 15 Θ s ) and for Peclet number < 100. The extraction rate according to the quasi-steady state solution is higher than the rate calcu-lated with the complete model; the agreement of both models increases with decreasing Bi . For large Bi , the sudden initial change of the concentration at the particle surface contradicts to the assumption for quasi-steady solution.

The model parameters are usually obtained from the lit-erature except for the effective internal diffusivity D

e , which is determined by fi tting the calculated extraction curves to experimental data (Goto et al. 1996).

5.3.3.4. Applications Goto et al. (1996) simulated with the model the literature data published by Brunner (1984) on the SFE of rapeseed oil from pre-pressed seeds. The values of model parameters were taken from the paper together with the data, except for D

ax , which was estimated according to other literature sources and the only adjusted model parameter, D

e , which was found to be 0.75 × 10 -10 – 1.5 × 10 -10 m 2 s -1 . The com-plete model equations were solved numerically because the



corresponding Θ s in the range 0.33 – 0.47 was too small for the simplifi ed analytical solution.

The shrinking core model was found suitable to describe the extraction of lipids from pre-pressed or fl aked seeds also by del Valle et al. (2006). The solubility of vegetable oils in CO 2 at given pressure and temperature, c

sat or y

sat , which

can be obtained from a literature correlation, really fi ts the experimental extraction curves and gives evidence that the equilibrium is, at least in the initial extraction period, inde-pendent of the substrate. The model was used to predict D

e

from the particle microstructure and binary diffusion coeffi -cient D according to Eq. (60) for both new experimental data and data from the literature. The extraction kinetics was not far from the equilibrium extraction because of high values of D

e between 1.8 × 10 -11 and 8.6 × 10 -10 m 2 s -1 . The amount of

extractable oil varied according to the technique of seed pre-treatment. The agreement of predicted extraction curves with experimental ones was very good.

Germain et al. (2005) simulated the extraction of oil from pre-pressed rapeseeds with the shrinking core model to exam-ine the effect of solvent fl ow direction in the extractor on the extraction kinetics. The topic is related to natural convection occurring at low fl uid velocities, when the mass transfer could be either assisted by gravity (under solvent down-fl ow for solu-tions denser than pure solvent) or opposed by gravity (usually under solvent up-fl ow). They fi tted the model for plug fl ow to experimental extraction curves and evaluated the decrease in the external mass transfer coeffi cient when the solvent fl ow direction was changed to the up-fl ow. The decrease was from 7.4 × 10 -6 to 2 × 10 -6 m s -1 for the superfi cial velocity as small as 0.17 mm s -1 but no change was observed at the velocity 1.5 mm s -1 when k f was 1.9×10 -5 m s -1 for both fl ow directions.

The model was applied also to other vegetable substrates and solutes, mostly volatile oils. Roy et al. (1996a) simulated the SFE of volatile oil from freeze-dried ginger root with CO 2 at 24.5 MPa and 40 ° C. The particles of ginger were sieved into size fractions from 0.35 to 2.56 mm; the initial content of oil in the root was 3.8 wt. % and the porosity of the particles was 0.81. The parameters determined by fi tting the model to experimental extraction curves were D

e = 2.5 × 10 -10 m 2 s -1 and c

sat = 1.23 kg m -3 ( y

sat = 1.38 g kg -1 ). The authors observed that

the experimental data for smaller particle size could not be simulated with this model as the fi nal part of extraction was much slower than predicted. Akgun et al. (2000) integrated the equations of the model for plug fl ow numerically to simu-late the extraction of volatile oil from lavender fl owers fro-zen in liquid nitrogen before being crushed. The agreement of experimental extraction curves and the curves calculated with adjusted model parameter D e = 1.2 × 10 -11 m s -2 was satis-factory. Spricigo et al. (2001) used the shrinking core model to represent the nutmeg essential oil extraction with liquid CO 2 . The adjusted effective diffusion coeffi cient varied from 1.5 × 10 -12 to 2.5 × 10 -11 m 2 s -1 .

An unusual form of the shrinking core model where the solute is initially present in both pores and solid part of a par-ticle was described by Doker et al. (2004) and applied later by Salgin et al. (2006). Some model equations were probably distorted by typographical errors. The adjusted D

e was of the

order 10 -11 to 10 -10 m 2 s -1 in the fi rst paper and 10 -10 m 2 s -1 or even 10 -9 m 2 s -1 in the second study, and thus the internal dif-fusion had little effect on the extraction kinetics. Steffani et al. (2006) simulated the extraction of volatile oil from the leaves of ho-sho, a tree native in East Asia, using two models: the shrinking core model and a model of porous particles where the rate of diffusion from the pore wall into the bulk pore is proportional to a kinetic parameter and no volatile oil-matrix interaction is assumed.

To sum up, the shrinking core model appropriately simu-lates the extraction from porous substrates rich in solute, such as vegetable oils from pre-pressed seeds or essential oils fi ll-ing glandular ducts of leaves or fl owers. The effective dif-fusivity is usually of the order of 10 -11 to 10 -10 m 2 s -1 and thus t s < t

eq and the extraction is governed by equilibrium, except

for extremely large particles where the effect of internal mass transfer prevails. Although the equilibrium in the shrinking core model is characterised by solubility, the model is applied also to the extraction of essential oils where it is known that solute-matrix interaction exists.

5.4. Models based on complex structure of plant

particles

5.4.1. Broken and intact cell models Vegetable oil is extracted from seed particles obtained by milling. The SEM images of a surface of particles after the extraction shows a layer of broken “ cells ” , the cavities from where the oil was removed (Marrone et al. 1998, Reverchon and Marrone 2001). The SFE begins as the extraction from particle surface (see Section 5.2.3), it means from the mechanically damaged cells with broken walls, which may be in several layers below particle surface, and then it continues from intact cells in the particle core where the oil diffuses through low permeable cell walls and the extraction is therefore slower. The broken and intact cell (BIC) models describe this process. An important parameter of BIC models is the initial fraction of easily accessible solute, G , which is equal to the solute in broken cells over the solute in broken and intact cells and which value is therefore between 0 and 1.

The observed extraction periods correspond to characteristic times of extraction steps. As the relation of characteristic times is usually t f < t r < t eq and t eq < t i , the extraction in the fi rst period of extraction from broken cells is governed by equilibrium and the controlling step in the second period is the internal mass transfer. (An exception is the extraction from extremely small particles or from the particles with low mass transfer resistance; in such case, t eq > t i , the effect of internal diffusion is marginal, and a simple one-stage model should be applied.)

When this mass transfer mechanism is built into a SFE model for plug fl ow, the extraction curves calculated using the model consist of three parts, denoted by Povh et al. (2001) as the constant extraction rate period, when all particles in the extractor contain easily accessible solute, the falling extrac-tion rate period, when the particles near to the solvent inlet are already free of easily accessible solute which is still present near the solvent outlet, and the diffusion controlled extraction period, where the mass transfer is governed solely by internal diffusion.



The BIC models were developed gradually. Semi-empirical models (Goodrum et al. 1996, Hong et al. 1990, Yoo and Hong 1996) described extraction curves composed of two sections, the fi rst one given by Eq. (48) for the extraction from par-ticle surface and the second section by Eq. (54) or (54a) for internal diffusion. Alternatively, Cygnarowicz-Provost (1996) introduced into the model an empirical mass transfer coeffi cient, the initial value of which is equal to k

f and, in

dependence on the solute content in particles, was monoto-nously decreasing. Lack (1985) under supervision of Prof. Marr utilised the analogy of SFE with a drying process and modifi ed the relevant equations for drying. In the SFE model written for plug fl ow, J according to Eq. (33) is multiplied by a function of average solute concentration in the particles, x , which is equal to unity until the easily accessible solute is depleted and then it monotonously decreases with decreasing x. The shape of the function can be adjusted to fi t different experimental extraction curves; when J in the second period is directly proportional to x and when the accumulation term in the mass balance for the fl uid phase with plug fl ow pattern is neglected, the model has analytical solution.

Sovova (1994) modifi ed the term J so that it after the deple-tion of free oil describes the internal mass transfer, on the condition that t

i > > t f and therefore cs+ can be set equal to zero,

and used this analytical solution. This approximate model for SFE, more consistently described later (Stastova et al. 1996), is frequently used to evaluate model parameters from experimental extraction curves. It yields good results when applied to the SFE of vegetable oil from seeds; however, with respect to the conditions used in its derivation, it should not be applied when the solubility of the solute is high or when a solute-matrix interaction exists.

Gaspar et al. (2003) derived a simple and effi cient version of the BIC model for the SFE of essential oil from oregano bracts, where the easily accessible solute from disrupted glands dissolves completely before t = 0 and then the solute from intact cells diffuses to the interface with a rate derived by Bartle et al. (1991b) in the version of hot ball model for slabs. No equilibrium relationship is necessary in this model as the fi rst period is a simple washing out and the second part is controlled by internal diffusion. The fraction of free sol-ute was G = 0.51, the effective diffusivity was D

e = 2 × 10 -14 – 4 × 10 -14 m 2 s -1 .

Reis-Vasco et al. (2000) applied the BIC model to the extraction of essential oil from pennyroyal leaves where two kinds of trichomes contain the essential oil: peltate trichomes that are on the surface, assumed to be broken, and capitate trichomes protected by cell wall and cuticle, representing the intact cells. Extraction curves e ( q ) measured at different fl ow rates overlapped until ∼ 70 % essential oil were extracted; moreover, the curves measured for different particle sizes overlapped up to this point. Thus it was assumed that the extraction of 70 % of essential oil was the equilibrium extrac-tion. The model was written for the fl ow with axial dispersion and for the linear equilibrium. When the easily accessible essential oil was depleted, the extraction from the capitate trichomes was controlled by internal mass transfer resistance. The only adjusted model parameter, k

s , was 1.4 × 10 -7 m s -1 for

average particle diameters 0.3, 0.5, and 0.7 mm. The D e range, estimated from these values, is 4 × 10 -12 –8 × 10 -12 m 2 s -1 .

In their versatile software for numerical simulation of SFE, most probably of the BIC type, Clavier et al. (1995) used the linear driving force. The equilibrium was represented by either solubility (no solute-matrix interaction) or Langmuir-type adsorption isotherm, and the fl uid fl ow was simulated by a series of mixers, allowing taking into account the length of the bed (for an extremely short laboratory extractor the num-ber of mixers is reduced to one).

To describe the mass transfer inside the particles in more detail, three mass balance equations are integrated: for the fl uid phase, for the region of broken cells, and for the region of intact cells. The solute from intact cells diffuses to the region of broken cells, and from broken cells to bulk fl uid (Sovova et al. 1994b). The mass transfer resistance in the region of broken cells can be neglected and equilibrium is established between the concentration in broken cells and the fl uid phase concentration at particle surface. When essential oil is extracted from seed, it is partitioned between the liquid vegetable oil in seed and the supercritical solvent (Sovova et al. 2001b).

Perrut et al. (1997) observed a solute-matrix interaction in the second period of SFE of vegetable oil from seed with SC-CO 2 . The slope of the extraction curves was fi rst deter-mined by oil solubility in CO 2 , and when the free oil was depleted, it decreased to a value corresponding to the equi-librium fl uid phase concentration of oil adsorbed on matrix. The solution fl owing out of the extractor was saturated in both extraction periods, as indicated by the extraction experi-ments, when the extraction curves e ( q ) measured under the conditions of different residence times of the solvent in the extractor overlapped in both periods. It seems probable that the solute-matrix interaction exists also in the SFE of veg-etable oils, such as in the extraction of other solutes, at least for a part of oil initially present in the seed. A versatile BIC model could therefore incorporate the equilibrium relation-ship given by Eq. (40), which allows simulating the transition from the extraction of free solute to the extraction of bound solute, and includes the simpler case when the bound solute is extracted from the very beginning. Such BIC model was derived for different fl ow patterns, analysed, and simplifi ed relationships for calculation of approximate extraction curves were derived (Sovova 2005). The analysis of the model for plug fl ow shows that the existing solute-matrix interaction practically is not visible on the shape of extraction curve when the characteristic time of its equilibrium extraction is smaller than the characteristic time of equilibrium extraction calculated on the basis of solubility. According to Eq. (43), the condition is Kc

s0 > c sat . Marrone et al. (1998) modifi ed the BIC model with three

mass balance equations assuming that the oil inside the intact cells is adsorbed on the matrix (with linear equilibrium), in contrast to the free oil in broken cells, and diffuses directly to the SCF. The number of adjustable parameters was reduced estimating G from SEM images of extracted particles. The free easily accessible oil was assumed to fi ll the surface layer of broken cells which depth was determined from the shape



and size of oil-bearing cells, which was typically 20 – 30 µ m according to the species. This approach was applied by Reverchon and Marrone (2001) to evaluate the internal mass transfer resistance from experimental data measured in their laboratory and also different sets of extraction curves avail-able in the literature. The resulting D e values were relatively high. The reason could be that when G is fi xed at a lower value than the real fraction of free oil is, the effective dif-fusivity is automatically adjusted to a value ensuring that the extraction will not be slowed down after depletion of free sol-ute (in terms of characteristic times, t f < < t

eq and t

i < < t

eq ) and

the extraction is controlled by equilibrium in both periods. This BIC model was further applied and analysed by Fiori and colleagues (Fiori 2007, Fiori et al. 2007) who found that the depth of the region with easily accessible oil is approxi-mately two layers of cells. They also improved the accuracy of modelling, simulating simultaneous extraction from the particles of a wide size distribution (Fiori et al. 2008). Finally they developed and further applied a new model for SFE of oil from seed where, after the oil from broken cells is removed, the oil from the fi rst layer of intact cells diffusing through one cell wall is extracted. After its depletion, the oil from the sec-ond intact layer diffusing through two cell walls is extracted, etc. Thus the model combines the feature of BIC model and shrinking core model (Fiori et al. 2009, Fiori 2010).

5.4.2. Models for SFE of essential oils tailored to plant

microstructure Ž i ž ovi � and co-workers linked the models for SFE of essential oils with the shape, structure, and location of secretory structures from where they are extracted and with behaviour of these structures during the extraction, studied on SEM images. Thus, a model including the mechanism of breakage of peltate glandular trichomes on the surface of leaves of Lamiaceae family plants was derived and adjusted to experimental data ( Ž i ž ovi c et al. 2005). The next extracted plants were those from Asteraceae family where the essential oil is extracted from secretory ducts and the mass transfer resistance is relatively low ( Ž i ž ovi c et al. 2007) and, in contrast, the valerian root where the secretory cells have a thick cuticularised lining and the extraction rate depends on its breakage ( Ž i ž ovi c et al. 2007a). The results for different types of secretory structures are summarised and the models are further developed in the last paper (Stamenic et al. 2008).

5.5. Models for SFE of mixtures

All extracts from plants are mixtures of many substances. When mixture components are similar, such as triglycerides in vegetable oils, the mixture can be regarded as a pseudo-component and the above-described models can be applied directly. When, however, the major components of extract are of very different solubilities, the overall extraction curve will be composed of several extraction curves of different shapes and the fi rst decrease in extraction rate may correspond to the point when the more soluble component was depleted but the extraction of easily accessible less soluble components con-tinues. Moreover, the extracted components can affect each

other, for example, when the more soluble component acts as entrainer for the less soluble component.

The gradual changes in extract composition are denoted as fractionation in time. The fractionation in time was observed for example during CO 2 extraction of sage essential oil con-sisting of monoterpenes, oxygenated monoterpenes, sesqui-terpenes, and oxygenated sesquiterpenes (Reverchon et al. 1995b), while the extraction of three oxygenated monoter-penes, the major components of peppermint oil, was simul-taneous (Goto et al. 1993). Also the extraction of savory oleoresin with subcritical water showed a strong fraction-ation in time among individual components of essential oil (Kubatova et al. 2001).

One group of models for multicomponent SFE from plants includes the models that describe the extraction of each selected component or each group of components as not affected by co-extracted substances. The BIC model was applied to simulate CO 2 extraction of essential oil, piperine, and lipids from black pepper seed, each component with its own model parameters (Sovova et al. 1995). Franca and Meireles (2000) used an empirical expression with different parameters for extraction curves of free fatty acids, triglycer-ides, and β -carotene to simulate time fractionation of vegeta-ble oil extracted from pressed palm oil fi bres. This approach was applied also by Martinez et al. (2003) to simulate the extraction of oleoresin from ginger rhizome, composed of mono terpenes, sesquiterpenes, and other hydrocarbons. Goto et al. (1994) proposed a modifi cation of the lumped parameter desorption model with linear driving force, where a continu-ous mixture is extracted instead of one extracted substance. The concept of the continuous mixture simulates a mixture of groups of a large number of components as continuous func-tions of some mixture property, in this case as the Gaussian function of molecular mass. The partition coeffi cient defi ned in the paper as K = c

s / c was assumed to be directly propor-tional to the molecular mass and the kinetics of the extraction of two groups of components was predicted.

In the second group of models, the equilibrium of a mix-ture of extracted substances with the solvent is taken into account. The initial extraction of easily accessible extract is simulated as the equilibrium extraction based on separation factors known from the models for SFE of liquids in counter-current columns. Shen et al. (1997), who extracted oil from rice bran with SC-CO 2 , recognised that the rate of extraction of minor oil components was related to the rate of extrac-tion of major component and evaluated their separation fac-tors towards triglycerides from the ratio of initial slopes of extraction curves. Gaspar (2002) studied the CO 2 extraction of volatile oil from oregano bracts under different extraction conditions and evaluated the selectivity of individual essential oil components. Sovova et al. (2010) implemented the separa-tion factor of β -sitosterol to triglycerides into a model for the extraction of sea buckthorn oil from particle surface.

Another possibility is to link the different rates of extrac-tion of different extract components with their diffusion coef-fi cients. Machmudah et al. (2006) applied the shrinking core model to the CO 2 extraction of nutmeg oil, distinguishing between components with lower molecular weight (terpene



hydrocarbons) and components with higher molecular weight (oxygenated terpenes and myristicin), the effective diffusivity of which was adjusted to approximately 2.5 lower value than the diffusivity of the hydrocarbons, to fi t experimental data on overall extraction yield and on the changes in extract com-position. The ability of the shrinking core model to simulate the fractionation in time was studied in detail by Tezel et al. (2000) who assumed that the components differ in both solu-bility and effective diffusivity. They also took into account that due to the different rates of extraction of two compo-nents, there are two shrinking cores in the spherical particles – the inner core containing both condensed components and the outer core where only the slower extracted component is condensed. The faster extracted component must diffuse through the outer core before it is dissolved in the solvent fi lling the pores outside the outer core. Moreover, Tezel et al. (2000) adapted for the extraction of mixtures the desorp-tion model with a Langmuir-like adsorption isotherm where several extract components compete for active sites; the components differ in both adsorption isotherm constants and effective diffusivities.

6. Conclusions

Large-scale SFE from plant materials is considered nowadays a standard process. It has extended from the fi rst applications – extraction of fl avour and aroma from hops, extraction of caffeine from raw coffee beans, and the extraction of spices – to other branches as, for example, the extraction of biologi-cally active substances from medical plants and the extrac-tion of herbicides from rice. More and more plant materials are tested for extraction with SC-CO 2 in laboratories around the world. SFE with SC-CO 2 modifi ed with entrainers is fi nd-ing application as a fast and easy to be automated technique for the extraction of analytes from plant matrix prior to their chromatographic analysis.

As the SFE from plants is more and more widely applied in practice, its theory is often regarded as more or less complete, and its further research superfl uous (redundant) and marginal. The contemporary research is fi nding new and fascinating applications of supercritical solvents in formation of micro- and nanoparticles, in chemical and enzymatic reactions as reaction medium, in the production and treatment of polymers, and oth-ers. Nevertheless, new tasks arise with practical applications of SFE from plants, as the optimisation of operating conditions and of plant pre-treatment with the aim to increase the extrac-tion yield, reduce the extraction time or the solvent consump-tion, and/or to increase the concentration of effi cient substances in the extract or maintain their level constant extract despite of changing quality of the extracted plant material.

While in other chemical engineering branches with lon-ger history, the engineers and technicians can solve such tasks using a set of equations and formulae that are based on a comprehensive theory, supercritical extraction from plants still lacks such widely accepted theory and recommended mathematical relationships. Moreover, there is a lack of such theory in the extraction of valuable substances from plant

materials generally, even for the extraction with liquid sol-vents at atmospheric pressure despite of its long tradition. As shown in the present review, extensive experimental and theo-retical research has been carried out by tremendous number of researchers and a large amount of knowledge on supercritical extraction from plants has been collected. It is, thus, probably time to synthesise the knowledge and formulate practically applicable mathematical relationships describing the process generally. Phase equilibrium has been measured for many sub-stances and can be understood with the help of thermodynamic modelling. There are correlations enabling estimation of the mass transfer resistance in SCF, and the internal mass transfer resistance has been evaluated from the course of extraction. Attention is being paid also to the effect of fl ow pattern on the extraction rate, which is important especially in the scale-up process. However, the most intriguing features concerning the extract composition, such as mutual interactions of the com-ponents of extracted mixtures or solute-to-matrix interaction in dependence on extraction conditions, have not yet been studied suffi ciently to be included into the theory to make it complete. Although the representation of botanical materials by mathematical relationships applicable in engineering prac-tice requires severe simplifi cations, the authors believe that the chemical engineering approach to the extraction of plants will enable its rational optimisation and development of new effi -cient procedures and new products of high quality.

Acknowledgements

Financial support by the Ministry of Education, Youth and Sports of the Czech Republic (projects 2B06024 and 2B06049) is gratefully acknowledged.

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Helena Sovová is a scien-tist in the fi eld of supercriti-cal fl uid extraction at the Institute of Chemical Process Fundamentals (ICPF) in Prague, CR. Her primary research interest is in the modelling and simulation of kinetics of extractions. She studied at the Institute of Chemical Technology in Prague where she received a Master’s degree in 1970, and at the ICPF where she recei-

ved a CSc (PhD) degree in chemical engineering in 1975. She is a member of the working party of High Pressure Technology of the European Federation of Chemical Engineering.

Roumiana P. Stateva is a professor at the Institute of Chemical Engineering, Bulgarian Academy of Sciences. She has an MSc in chemical cybernetics and a PhD in chemical engineer-ing from the Mendeleev University of Chemical Technology, Moscow, Russia. Her research is devoted to the modelling and effi cient cal-

culation of phase equilibria of complex systems, and to the development of original methods for the prediction of proper-ties from the chemical structure of pure substances.


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Supercritical fl uid extraction from vegetable materials