Mass Transfer and Equilibrium Parameters on High-Pressure CO2 Extraction of Plant Essential Oils

  • José M. del Valle
  • Juan C. de la Fuente
  • Edgar Uquiche
  • Carsten Zetzl
  • Gerd Brunner
Conference paper
Part of the Food Engineering Series book series (FSES)

Abstract

Supercritical fluids (SCF) in general and supercritical carbon dioxide (CO2) in particular allow convenient and environmentally friendly extraction processes because of their liquid-like solvent properties and gas-like transport properties, that allow efficient and fast extraction processes, and complete elimination of solvent traces from extracts and treated substrates. High-pressure CO2 is an inexpensive gas that offers safe and selective supercritical fluids SCF extraction (SCFE) processes at near-environmental temperatures that can be use to recover high-value compounds in vegetable substrates.

This chapter reviews mass transfer and of phase equilibrium parameters that are required to design industrial SCFE processes for plant essential oils. Relevant mass transfer parameters include an external mass transfer coefficient and an effective diffusivity (De), among others. Values of De range from 102 to 105 times the binary diffusion of plant essential oils in CO2 which suggests pronounced limitations to mass transfer within the solid matrix during SCFE of plant essential oils. A relevant phase equilibrium parameter is the “operational” solubility of plant essential oils in high-pressure CO2, which depends markedly on system temperature and CO2 density, the amount of essential oils in the plant material, the interactions between the many constituents of the essential oils, and the interactions between the essential oil components and the solid matrix, all of which decrease solubility of the essential oil components as compared to their thermodynamic solubility in simple CO2-containing binary and ternary systems.

17.1 Introduction

The production of plant extracts is currently limited by safety and regulatory constraints on the concentration of toxic residues of organic solvents such as n-hexane or methanol (Sanders 1993). Carbon dioxide (CO2) is an excellent alternative to these organic solvents due to its inertness, non-toxicity, non-flammability, and low cost (Brunner 1994; del Valle and Aguilera 1999). The recommended temperature in so-called supercritical fluid (SCF) extraction (SCFE) processes is slightly above the critical temperature (Tc) of the solvent so that a near-environmental temperature is applied when using CO2 (Tc = 304.2 K) in SCFE, thus reducing the requirement of energy for separation as well as the thermal damage of labile bioactive compounds (Brunner 1994). Furthermore, objectionable solvent traces are eliminated from the treated substrate and the extract because, being a gas under normal environmental conditions, CO2 is easily and fully removed following SCFE.

Because of their high compressibility, particularly in the vicinity of the critical point, SCFs exhibit large variations in physical properties, including near-liquid solvent power and near-gas transport properties, and it is possible to take advantage of these improved properties to devise improved (medium-to-high yield, high selectivity, fast) extraction processes (Brunner 1994; del Valle and Aguilera 1999). These advantages of SCFs extend to near-critical liquids and gases. Thus, in this work the use of both supercritical CO2 and near-critical CO2 as extraction solvents will be covered; they will be referred to as high-pressure CO2. The extraction process with high-pressure CO2 will be referred as SCFE.

The typical quality fluctuations of vegetable substrates and difficulties in obtaining the standardized information required for designing selective SCFE processes make the industrial application of CO2 as an extraction solvent for plant materials difficult (Zetzl et al. 2003). In this chapter an attempt is made to bridge the gap between scientific research and industrial application of SCFE for obtaining relevant plant extracts. Specifically, the focus will be on the SCFE of plant essential oils using high-pressure CO2.

Two well-established SCFE applications in the food industry are the decaffeination of coffee (Lack and Seidlitz 1993) and the recovery of bitter compounds from hops to be used in improved beer-producing processes (Hubert and Vitzthum 1978; Gardner 1993). However, in this work it was felt that, viewed from a broader chemical perspective, the two most important types of components extracted from plant materials using high-pressure CO2 are fatty oils (triglycerides) and essential oils (del Valle et al. 2005a). In the specific case of plant essential oils, SCFE allows a higher yield to be attained in a shorter time as compared to steam distillation, hydro-distillation, and conventional solvent extraction, while simultaneously avoiding thermal and hydrolytic degradation of labile compounds, as well as toxic solvent residues in the product (Stahl et al. 1988; Moyler 1993; Reverchon 1997; Mukhopadhyay 2000; Reverchon and De Marco 2006, 2008; Quirin and Gerard 2007).

Authors del Valle and de la Fuente (2006) described SCFE of fatty oils from seeds, including relevant mass transfer and equilibrium parameters. Thus, the purpose of this chapter is to provide similar information for the industrially important case of SCFE of plant essential oils. Because the solubility of essential oils in high-pressure CO2 is great, their selective extraction from a plant requires low-to-medium densities to avoid contamination of the extract with heavier and/or more polar compounds such as, e.g., fatty oils and carotenoids. Thus, for the purpose of this chapter, plant essential oils are defined as those terpenes that can be extracted with high-pressure CO2 at 15 MPa or less.

17.1.1 Chemistry and Localization of Essential Oils

Essential oils are complex mixtures of many volatile compounds that are responsible for the aroma of herbs and spices. As a group, essential oils do not share common chemical properties beyond conveying the characteristic aroma of the herb or spice and consequently are used for flavoring foods, drinks, perfumes, cosmetics, incense, and bath and house-cleaning products. For applications in foods, a spice is a seed, fruit, root, bark, or leaf that is dried, ground (usually), and used in small amounts as a preservative against deleterious or harmful microorganisms, or as an additive to impart flavor or color to the food. Herbs differ from spices in that they are leafy, green plant parts that are usually chopped into smaller pieces and used in a fresh (undried) condition as food preservatives or flavor additives.

Brielmann et al. (2006) reviewed the chemistry of plant essential oils. The most volatile components in essential oils are terpenes, which are secondary plant metabolites derived from isoprene (2-methyl-1,3-butadiene), a 5-carbon unsaturated hydrocarbon molecule. Terpenes include the 2-isoprene (or 10-carbon) monoterpene hydrocarbons that typically fit a C10H16 molecular formula (e.g., p-cymene, limonene, α-pinene), the 3-isoprene (or 15-carbon) sesquiterpene hydrocarbons that typically fit a C15H24 molecular formula (e.g., β-caryophyllene, α-humulene), and oxygen-containing derivatives of monoterpene and sesquiterpene hydrocarbons (the so-called oxygenated monoterpenes and oxygenated sesquiterpenes, respectively) such as acetates (e.g., linalyl acetate, farnesyl acetate), alcohols (e.g., β-citronellol, geraniol, farnesol, linalool, menthol, patchoulol, verbenol), aldehydes (e.g., p-anisaldehyde, citral), ketones (e.g., camphor, carvone, fenchone), phenols (e.g., carvacrol, eugenol, thymol), and oxides (e.g., artemisinin, 1,8-cineole), among others. Among these compounds the oxygenated monoterpenes are especially important because they are responsible for the characteristic aroma of the herb or spice.

Plant essential oils are encapsulated in specialized secretory structures made of high-molecular-weight nonvolatile waxes (CnH2n+2) and other fatty compounds that protect them against evaporative losses and deleterious oxidative and/or hydrolytic reactions by atmospheric oxygen and water. Essential oils are secreted into specialized structures that can be located in either the surface (the so-called glandular trichomes or glands) or below the outer surface of the plant material (secretory ducts and secretory cavities) depending on the plant family and species (Denny 1991; Zizovic et al. 2007c; Stamenić et al. 2008). The leaves, terminal shoots, and flowers of aromatic herbs of the Lamiaceae family, such as basil (Ocimum basilicum), lavender (Lavandula angustifolia), marjoram (Origanum majorama), oregano (Origanum vulgare), pennyroyal (Mentha pulegium), peppermint (Mentha × piperita), rosemary (Rosmarinus officinalis), sage (Salvia officinalis), spearmint (Mentha spicata), thyme (Thymus vulgaris), and wild thyme (Thymus serpyllum), produce superficial oils that are stored in abundant secretory cells called glandular trichomes or glands (Zizovic et al. 2005, 2007c; Stamenić et al. 2008).

Unlike the aromatic herbs of the Lamiaceae family that secrete oils in superficial glands, herbs and spices of the Apiaceae and Asteraceae families secrete oils into subcutaneous ducts (Zizovic et al. 2007a,b,c; Stamenić et al. 2008). These ducts are elongated cavities that can branch out to create a network of interconnected pores extending from the roots, through the stems, and to the leaves, flowers, and fruits of the plants. In this chapter the Apiaceae family is represented by anise (Pimpinella anisum), caraway (Carum carvi), celery (Apium graveolens), fennel (Foeniculum vulgare), and parsley (Petroselinum crispum), whereas the Asteraceae family is represented by candeia (Eremanthus erythropappus), carqueja (Baccharis trimera), chamomile (Matricaria recutita), and marigold (Calendula officinalis).

Other forms of subcutaneous oils are accumulated in secretory cavities, which are spherical structures lined with essential-oil-producing ephitelium cells (Zizovic et al. 2007c; Stamenić et al. 2008). Secretory cavities can be found in both aerial and underground parts of many plants including roots (valerian, Valeriana officinalis, Valerianaceae), rhizomes (ginger, Zingiber officinale, Zingiberaceae), leaves (alecrim pimenta, Lippia sidoides, Verbenaceae; boldo, Peumus boldus, Monimiaceae; cinnamon of Cunhã, Croton zehntneri, Euphorbiaceae; eucalyptus, Eucalyptus globulus, Myrtaceae; ho-sho, Cinnamomum camphora, Lauraceae), flower buds (clove, Syzygium aromaticum, Myrtaceae) and cones (hop, Humulus lupulus, Cannabaceae), fruit peels (orange, Citrus sinensis, Rutaceae); black pepper, Piper nigrum, Piperaceae), and seeds (nutmeg, Myristica fragrans, Myristicaceae).

17.1.2 Organization of Chapter

Figure 17.1 represents the SCFE of a solid substrate in a packed bed. As will be discussed in Sect. 17.2, the process can be modeled using a differential mass balance equation (Fig. 17.1a) coupled with a mass transfer rate equation. During SCFE of a pre-treated plant material, the partition of solutes between the solid and fluid phases (K), the actual solubility of the solutes in the solvent (Csat), and various resistances to mass transfer play important roles in extraction rates. The effective diffusivity in the solid matrix (De), external mass transfer coefficient (kf), and axial dispersion coefficient (Dax) all influence the concentration gradient-driven mass transfer rates within the solid, the stationary SCF film surrounding each particle, and along the bed, respectively (Fig. 17.1b).
Fig. 17.1

Conceptual model of supercritical fluid extraction of solid substrates in packed beds: (a) differential mass balance along packed bed; and (b) mass transfer phenomena within solid particle (substrate), between particle and CO2 (solvent) phase, and in CO2 phase along bed

Figure 17.2 presents an integral extraction plot of solute yield versus specific solvent consumption resulting from the SCFE of the solid substrate in a packed bed. Although there might be a positive effect of superficial solvent velocity on extraction rates, integral extraction curves generally collapse to a single line, at least initially, with a slope that represents the so-called operational solubility (Cfo) (Fig. 17.2, zone I). Scientific research on SCFE of plant essential oils, aimed at the industrial application of the process, should result in mass transfer (kf, Dax, De) and phase equilibrium or pseudo-equilibrium data (K, Csat, Cfo) that can be applied for process design purposes.
Fig. 17.2

Supercritical fluid extraction curve showing solute yield versus specific solvent consumption. Both the recovered solute and amount of CO2 passed through the packed bed are expressed in a common base, the amount of substrate loaded into the extraction vessel

In Sect. 17.2, mathematical models are presented and discussed for the SCFE of essential oils from a packed bed of plant material, followed by a presentation of the external (kf) and internal (De) mass transfer parameters that have been fitted in the literature to cumulative extraction plots of essential oil yield versus time or specific solvent consumption (Sect. 17.3). Next, reported “operational” solubility (Cfo) values are presented and compared to the “thermodynamic” or true solubility (Csat) values of plant essential oil components in high-pressure CO2 in binary, ternary, and more complex systems (Sect. 17.4). Some concluding remarks are made in Sect. 17.5.

17.2 Mass Transfer Models

This section presents a mathematical model that can be used as a reference to discuss the effect of mass transfer and equilibrium parameters on the SCFE of plant essential oils using high-pressure CO2 as the solvent (Sect. 17.2.1). The so-called diffusion model assumes internal mass transfer by diffusion within solid particles, external mass transfer by convection through a static film of SCF next to the particles, and axial dispersion of dissolved solute in the SCF phase along the bed. This reference model also assumes a packed bed of spherical particles, an essential oil that can be treated as a single substance (pseudo-solute), and a constant partition coefficient for this pseudo-solute between the solid substrate and high-pressure CO2. Discussion follows covering the effect on mass transfer rates of particle shape, localization of the solute in specialized structures within the solid matrix, actual composition of the essential oil, and its partition between the solid matrix and the CO2 that limit the application of the diffusion model (Sect. 2.2). Finally, this section concludes with a discussion of alternative internal mass transfer mechanisms that can compliment diffusion, thus affecting the rate at which essential oils migrate through the solid substrate (Sect. 2.3).

17.2.1 Diffusion Model

The reference model used in this section will be the diffusion model of Goodarznia and Eikani (1998). The assumptions of this diffusion model are as follows: (1) the substrate particles are spherical (diameter dp, radius R = dp/2) and homogeneous; (2) the physical properties of the extract (the essential oil) are those of a representative pseudo-solute; (3) the physical properties of the SCF and the substrate remain unchanged during extraction; (4) the extract partitions between the solid and SCF phases according to a constant coefficient (K) that is concentration-independent; and (5) the solute disperses axially in the SCF as a result of irregularities in the packing of the substrate in the bed and concentration-gradient-driven diffusion of the solute along the packed bed. As a result of these assumptions, solute concentration in the solid matrix (Cs) depends on the radial position within the particle (r), the axial position along the bed (z), and the extraction time (t); whereas solute concentration in the SCF (Cf) depends only on z and t. The assumption of constant physical properties is valid when the density and viscosity of the SCF depend only on the extraction temperature and pressure, and are unaffected by the dissolved pseudo-solute. Because of that, the variations in temperature and pressure should be negligible within the bed, and the concentration of essential oils in the loaded SCF phase should be small (selected process conditions should limit the solubility and/or availability of the solute). On the other hand, the assumption of constant physical properties of the solid phase is valid if the substrate remains unaffected (does not swell or shrink) as a result of CO2 adsorption and solute removal, and this results in a constant bed porosity (ε) and, consequently, in a constant interstitial velocity of the SCF in the packed bed (u = U/ε). These assumptions are valid in the selective extraction of plant essential oils with high-pressure CO2 for several reasons. The availability of solute is small because the content of essential oils in a typical herb or spice is limited to a few percent or below. Recommended values of extraction temperature and pressure (e.g., 323 K and 9 MPa) (Reverchon 1997) place a limit on the solubility of the essential oil in high-pressure CO2, so as to increase the selectivity of the process. A near-environmental extraction temperature is selected to reduce thermal damage of labile compounds as well as energy requirements of the process, which reduces the exchange of heat with the environment and minimizes radial temperature gradients in the extraction vessel. Finally, as for other internally controlled mass transfer processes, small values of superficial solvent velocity (1 ≤ U ≤ 5 mm/s) (Eggers 1996) are recommended to improve economics, and these small velocities reduce losses of energy of the SCF as it passes through the bed of packed substrate, and minimize axial pressures gradients in the extraction vessel.

Equation 17.1 is a differential mass balance for the SCF surrounding the particles of substrate in the packed bed. J, the so-called source-and-transfer term (Zizovic et al. 2007c; Stamenić et al. 2008), is the flux of solute that is transferred from the solid to the SCF, and can be estimated using (17.2). On the other hand, the diffusion of the solute through the solid particles can be estimated using (17.3).
$$ \frac{{\partial {C_{\rm f}}}}{{\partial t}} + u\frac{{\partial {C_{\rm {f}}}}}{{\partial z}} - {D_{\rm {ax}}}\frac{{{\partial^2}{C_{\rm {f}}}}}{{\partial {z^2}}} = \frac{6}{{{d_{\rm {p}}}}}\frac{{\left( {1 - \varepsilon } \right)}}{\varepsilon }J $$
(17.1)
$$ J = - {D_{\rm {e}}}{\left. {\frac{{\partial {C_{\rm {s}}}}}{{\partial r}}} \right|_R} $$
(17.2)
$$ \frac{{\partial {C_{\rm {s}}}}}{{\partial t}} = \frac{{{D_{\rm {e}}}}}{{{r^2}}}\frac{\partial }{{\partial r}}\left( {{r^2}\frac{{\partial {C_{\rm {s}}}}}{{\partial r}}} \right) $$
(17.3)
Goodarznia and Eikani (1998) assumed constant solute concentrations in the solid matrix (initial solute content Cso) and the SCF phase (initial solute content Cfo) in the bed initially (17.4a and 17.4b, respectively), a symmetry condition for the removal of solute from the particles (17.4c), continuity in the flux of solute leaving a solid particle and entering the SCF film around it (17.4d), and the Danckwerts conditions for axial dispersion in packed beds (17.4e and 17.4f).
$$ {C_{\rm s}} = {C_{\rm so}} \quad \left( {t = 0,\, 0 \leq r \leq R} \right) $$
(17.4a)
$$ {C_{\rm f}} = {C_{\rm fo}} \quad \left( {t = 0,\, 0 \leq z \leq H} \right) $$
(17.4b)
$$ {\left. {\frac{{\partial {C_{\rm s}}}}{{\partial r}}} \right|_0} = 0 \quad \left( {t \geq 0,\, 0 \leq z \leq H} \right) $$
(17.4c)
$$ - {D_{\rm e}}{\left. {\frac{{\partial {C_{\rm s}}}}{{\partial r}}} \right|_R} = {k_{\rm f}}\left( {\frac{{{{\left. {{C_{\rm s}}} \right|}_R}}}{K} - {C_{\rm f}}} \right)\quad \left( {t \geq 0,\,0 \leq z \leq H} \right) $$
(17.4d)
$$ u{C_{\rm f}} - {D_{\rm ax}}\frac{{\partial {C_{\rm f}}}}{{\partial z}} = 0 \quad \left( {t \geq 0,\, z = 0} \right) $$
(17.4e)
$$ \frac{{\partial {C_{\rm f}}}}{{\partial z}} = 0 \quad \left( {t \geq 0,\, z = H} \right) $$
(17.4f)

Examination of (17.1)–(17.4) suggests that variations in Cs and Cf as a function of r, z, and t depend on the initial essential oil content in the substrate (Cso), the geometry of the packed bed (diameter, DE; height, H; porosity, ε) and the particles (diameter, dp), and the conditions of the SCF (interstitial velocity, u; temperature, T; and pressure, P).

A closer examination of (17.1)–(17.4) also suggests that the extraction rate and yield depend on both kinetic (or mass transfer) parameters and equilibrium (or solubility) parameters. The former category includes an internal mass transfer coefficient (the effective diffusivity of the extract in the solid matrix, De), an external mass transfer coefficient (the SCF film coefficient, kf), and an axial dispersion coefficient (Dax) (Fig. 17.1b). Phase equilibrium parameters include the solubility of the essential oils in high-pressure CO2 at T and P (Csat), and their partition between the solid matrix and the SCF phase (K). Border condition 17.4b implicitly requires extraction to be preceded by a static period (unaccounted for by the model) so as to equilibrate the vessel to the required process temperature and pressure conditions, and to dissolve free solute in the solid phase. The SCF phase becomes saturated (initial solute concentration Csat) only if there is enough free solute in the substrate; when there is less solute, the concentration Cfo is determined by the ratio between the total amount of free solute and the total void volume occupied by the SCF in the bed.

Some of the simplifications of the diffusion model applied in the literature include the following (Table 17.1): neglecting the effect of axial dispersion in mass transfer (model Diff/PF of Araus et al. 2009); treating the packed bed as a perfectly mixed extraction vessel (model Diff-Sph/PM of Reverchon et al. 1993a; models Diff-Slab/PM and Diff-Slab/IC of Gaspar et al. 2003; model Diff-Sph/IC of Campos et al. 2005); and neglecting the external resistance to mass transfer (model Diff-Slab/IC of Gaspar et al. 2003; model Diff-Sph/IC of Campos et al. 2005).
Table 17.1

Summary of mathematical models used in the literature for high-pressure CO2 extraction of plant essential oils in packed beds

Mass transfer model

Substrate particlesa

Hydrodynamics in packed bedb

External mass transfer coefficientc

Axial dispersion coefficientd

Sorption/“operational” solubility modele

Diffusion (Diff or D) models

Diff/ADPF (Goodarznia and Eikani 1998)

Sphere

Axially dispersed plug flow

Literature correlation

Literature correlation

Linear isotherm

Diff/PF (Araus et al. 2009; Uquiche et al. submitted)

Infinite slab

Plug flow

Literature correlation

Neglected

Linear isotherm

Diff-Sph/PM (Reverchon et al. 1993a)

Sphere

Perfect mixing

Literature correlation

Neglected

Neglected

Diff-Slab/PM (Gaspar et al. 2003)

Infinite slab

Perfect mixing

Literature correlation

Neglected

Neglected

Diff-Sph/IC (Campos et al. 2005)

Sphere

Perfect mixing

Neglected

Neglected

Neglected

Diff-Slab/IC (Gaspar et al. 2003; Campos et al. 2005)

Infinite slab

Perfect mixing

Neglected

Neglected

Neglected

Shrinking-Core (SC) models

SC/ADPF (Spricigo et al. 2001;

Machmudah et al. 2006)

Porous sphere

Axially dispersed plug flow

Literature correlation

Literature correlation

Limited by saturation

SC/ADPF (Steffani et al. 2006)

Porous sphere

Axially dispersed plug flow

Fitted to data

Literature correlation

Limited by saturation

SC/PF (Akgun et al. 2000; Germain et al. 2005)

Porous sphere

Plug flow

Literature correlation

Neglected

Limited by saturation

SC/PF (Germain et al. 2005)

Porous sphere

Plug flow

Fitted to data

Neglected

Limited by saturation

Desorption-Dissolution-Diffusion (DDD or D3) models

DDD/ADPF/BET (Ruetsch et al. 2003)

Porous sphere

Axially dispersed plug flow

Literature correlation

Literature correlation

BET isotherm

DDD/ADPF/Lang (Daghero et al. 2004)

Porous sphere

Axially dispersed plug flow

Literature correlation

Literature correlation

Langmuir isotherm

DDD/ADPF (Salimi et al. 2008)

Porous sphere

Axially dispersed plug flow

Literature correlation

Literature correlation

Several isotherms

DDD/PM (Kim and Hong 2002)

Porous sphere

Perfect mixing

Fitted to data

Neglected

Linear isotherm, K = 1

Intact-and-Broken-Cell (IBC) models

IBC-Diff (Kim and Hong 2002)

Sphere

Plug flow

Neglected

Literature correlation

Neglected

IBC/PF/PCPR (Machmudah et al. 2006; Sovová 2005;

Langa et al. 2009)

Unaccounted for

Plug flow

Fitted to first stage

Neglected

PCPR isotherm

IBC/PF (Louli et al. 2004)

Unaccounted for

Plug flow

Fitted to first stage

Neglected

Limited by saturation

IBC/PFNA (Sovová et al. 1994a)

Unaccounted for

PF with no accumulation

Fitted to first stage

Neglected

Decreasing solubility

Sovová (Campos et al. 2005;Louli et al. 2004; Mira et al. (1996, 1999); Papamichail et al. 2000; Povh et al. 2001; Ferreira and Meireles 2002; Sousa et al. 2002; Martínez et al. 2003; Rodrigues et al. 2003; Sousa et al. 2005; Vargas et al. 2006; Martínez et al. 2007; Bensebia et al. 2009)

Unaccounted for

PF with no accumulation

Fitted to first stage

Neglected

Limited by saturation

Microscale (μS) models

μS/SGl (Zizovic et al. 2005; 2007c; Stamenić et al. 2008)

Surface glands

Axially dispersed plug flow

Literature correlation

Literature correlation

Limited by saturation

μS/SDuct (Zizovic et al. 2007b, c; Stamenić et al. 2008)

Secretory ducts

Axially dispersed plug flow

Literature correlation

Literature correlation

Limited by saturation

μS/SCav (Zizovic et al. 2007a, c; Stamenić et al. 2008)

Secretory cavities

Axially dispersed plug flow

Literature correlation

Literature correlation

Limited by saturation

Diffusion models using Linear Driving Force (LDF)

LDF/ADPF (Reverchon and Marrone 1997)

Unaccounted for

Axially dispersed plug flow

Hidden in kg

Literature chart

Linear isotherm

LDF/ADPF (Reis-Vasco et al. 2000)

Unaccounted for

Axially dispersed plug flow

Hidden in kg

Fitted to data

Linear isotherm

LDF/PF/CDIC (Coelho et al. 1997)

Unaccounted for

Plug flow

Hidden in variable kg

Neglected

Limited by saturation

LDF-Sph/PF (Esquivel et al. 1996)

Sphere

Plug flow

Hidden in kg

Neglected

Limited by saturation

LDF/PF (Reverchon et al. 1999)

Unaccounted for

Plug flow

Hidden in kg

Neglected

Linear isotherm

LDF/IMTC (Catchpole et al. 1996b)

Sphere

Plug flow

Neglected

Neglected

Linear isotherm, K « 1

LDF-Slab/PMMS (Reverchon 1996)

Infinite slab

Perfectly mixed multistages

Hidden in kg

Neglected

Linear isotherm

LDF/PMMS (Esquivel et al. 1996)

Unaccounted for

Perfectly mixed multistages

Hidden in kg

Neglected

Linear isotherm

LDF/UENA (Louli et al. 2004; Papamichail et al. 2000)

Sphere

Uniform extraction NA

Hidden in kg

Neglected

PCPR isotherm

R-SO (Louli et al. 2004; Papamichail et al. 2000; Vargas et al. 2006; Reverchon et al. 1995a; Zekovic et al. 2001; Pfaf-Šovljanski et al. 2005)

Sphere

Uniform extraction NA

Neglected

Neglected

Neglected

DDD models using LDF

LDF-D3/DB/BET (Goto et al. 1998)

Infinite slab

Differential bed

Literature correlation

Neglected

BET isotherm

LDF-D3-Sph/DB (Perakis et al. 2005)

Sphere

Differential bed

Literature correlation

Neglected

Linear isotherm

LDF-D3-Slab/DB (Sousa et al. 2005; Goto et al. 1993)

Infinite slab

Differential bed

Literature correlation

Neglected

Linear isotherm

Equilibrium Desorption (ED), Internal-Mass-Transfer-Control (IMTC), and External-Mass-Transfer-Control (EMTC) models

ED (Reis-Vasco et al. 2000)

Unaccounted for

Plug flow

Neglected

Fitted to data

Linear isotherm

IMTC (Ferreira et al. 1999)

Sphere

Perfect mixing

Neglected

Neglected

Limited by saturation

EMTC (Ferreira et al. 1999; Kotnik et al. 2007)

Sphere

Simplified diff. mass balance

Fitted to first stage

Neglected

Limited by saturation

aThe particles were treated as solid or porous spheres (Sph) or infinite slabs (Slab); or else their shape as an inner structure was unaccounted for

bFlow conditions in extraction vessel are assumed to be axially dispersed plug flow (ADPF), plug flow (PF), perfect mixing (PM), or perfectly mixed multistages (PMMS). For simplification, the packed bed was treated as a differential bed (DB), and the differential mass balance assumed plug flow with no accumulation (PFNA) or uniform extraction with no accumulation (UENA)

cThe external mass transfer and was estimated from correlations in the literature, then fitted to data, or neglected. The internal-mass-transfer-control (IMTC) models neglected the external resistance to mass transfer. The external mass transfer coefficient was sometimes hidden in a global mass transfer coefficient (kg), either implicitly or explicitly; and in some cases (Reis-Vasco et al. 2000; Coelho et al. 1997; Ferreira et al. 1999; Kotnik et al. 2007) kg was assumed to be an internal mass transfer coefficient (in IMTC models), and in others (Reverchon and Marrone 1997; Ferreira et al. 1999) (external-mass-transfer-control or EMTC models), an external mass transfer coefficient

dThe axial dispersion coefficient was also estimated from correlations or charts in the literature, fitted to data, or neglected

eThe equilibrium concentration of essential oils in the SCF phase was assumed to be limited by saturation (solubility), or to depend on the residual concentration of the oils in the solid substrate by a sorption isotherm given by a linear model, BET model, a Langmuir (Lang) model, or Perrut-Clavier-Poletto-Reverchon (PCPR) model of Perrut et al. (1997), among others

The diffusion model adopted in this chapter as the reference model (this section) makes several simplifying assumptions about the particle geometry (spherical), the solid matrix (homogeneous), the localization of the solute in the solid matrix (homogeneous), the composition of the solute (fully characterized by a pseudo-solute), the partition of the solute between the solid matrix and the CO2 (constant and independent of solute concentration), and the mass transfer mechanism for the extraction process (diffusion). As discussed in the following sections, some of these simplifying assumptions should be avoided to improve the physical picture of the extraction process.

17.2.2 Limitations of the Diffusion Model

When extracting herbs and spices it is important to consider the geometry of the tissue following application of pretreatments aimed at increasing the speed and/or final yield of the process. Mild pretreatments, such as coarse milling, are typically applied prior to SCFE to take full advantage of the natural barriers within the plant material to selectively extract the essential oils. Coarse milling of leaves and similar plant parts results in large particles having a slab rather than a spherical geometry as assumed in the diffusion model, so that the fitting of mathematical models to the data improves when using the diffusion equation for an infinite slab instead of (17.3) (Goto et al. 1993, 1998; Reverchon 1996; Gaspar et al. 2003; Araus et al. 2009). Stüber et al. (1997) derived analytical solutions for other regular geometries such as disks and cylinders having different aspect ratios by combining the analytic solutions for basic geometries such as infinite cylinders and infinite slabs using superposition theorems. However, the model for spherical particles still can be used to represent mass transfer from particles of various shapes (including disks and cylinders with different aspect ratios) if a characteristic dimension is computed as three times the volume-to-surface area ratio for a representative particle (dp/2, in the case of a sphere) (Ma and Evans 1968).

When extracting herbs and spices it is important to consider the microstructure of the native tissue. Unlike the assumptions in Sect. 17.2.1, herbs and spices are heterogeneous when observed under the microscope. This is important to consider because SCFE of plant materials depends, among other factors, on the location of the solute within the plant tissue, with essential oils being encapsulated in isolated glands, secretory cells, or cavities, or in interconnected pore networks (Zizovic et al. 2007c; Stamenić et al. 2008). Furthermore, the physical properties of the solid may change during extraction as a result of impregnation of CO2 and removal of essential oils (Eggers 1996).

Also, unlike the assumptions in Sect. 17.2.1, essential oils are not single compounds but mixtures of many different volatile terpenoids. During SCFE of herbs and spices, the waxy constituents of the specialized encapsulating structures of the essential oils are dissolved so that CO2 extracts also include waxes and other compounds besides terpenoids. Thus, the components of CO2 extracts of herbs and spices can be grouped as monoterpene hydrocarbons, oxygenated monoterpenes, sesquiterpene hydrocarbons, oxygenated sesquiterpenes, waxes, and other substrate specific families of compounds such as gingerols in ginger and phenylpropanoids in parsley. In this work, for the purpose of estimating the value of physical properties of CO2 extracts, the authors selected representative compounds of some of these groups, assigned the properties of representative compounds to whole groups, and represented extracts as pseudo-solutes whose properties were estimated as the weighted average of the properties of the representative compounds in each considered group.

The assumption of a constant coefficient for the partition of the solute (linear sorption isotherm) between the solid substrate and the high-pressure CO2 is invalid when a fraction of the solute in the substrate, e.g., contained in broken cells or cavities, is freely available to the CO2, so that its concentration in the fluid phase is determined by availability or solubility constraints. It is also invalid in the final stages of the extraction process, when all remaining solute is strongly bound to the solid substrate (del Valle and de la Fuente 2006). Consequently, Araus et al. (2009) claimed the necessity of relaxing the assumption of a constant partition coefficient of the pseudo-solute between the solid substrate and the CO2 to improve modeling of SCFE of plant essential oils.

The internal mass transfer mechanism may be different from that stated in Sect. 17.2.1, since solute desorption from the solid, solubilization in the SCF, and/or migration by diffusion through the pores of the solid matrix may control mass transfer in the solid. The subject of the internal mass transfer mechanism is analyzed in the following section.

17.2.3 Alternative Internal Mass Transfer Mechanisms

Considering plant tissue as a multiphase material constituted of interconnected or isolated cells and a network of fully or partially interconnected pores (Zizovic et al. 2007c; Stamenić et al. 2008), and how its microstructure is affected by milling and other pretreatments applied prior to SCFE, alternative mass transfer models picture pretreated herbs and spices as porous solid matrices constituted of intact and broken cells (Sovová 1994, 2005; Zizovic et al. 2007c; Stamenić et al. 2008). del Valle and de la Fuente (2006) reviewed most of these models and others with alternative internal mass transfer mechanisms in detail.

When the solid matrix where mass transfer takes place is assumed to be a network of interconnected pores, two important models that can be applied are the so-called shrinking-core (SC) and desorption-dissolution-diffusion (DDD) models. The shrinking-core hypothesis assumes that the solute is retained in the pores of the solid matrix by mechanical or capillary forces, so that pore space is divided into an inner core filled with condensed solute and an outer region containing a solution of the solute in high-pressure CO2 that are separated by a moving boundary. Roy et al. (1996) first applied the shrinking-core hypothesis to model SCFE of ginger essential and fatty oils at >15 MPa (data not included), and there are several examples in the literature on this hypothesis to model the extraction of plant essential oils. Of these models (Table 17.1), that of Machmudah et al. (2006) is different in that they assumed that the extract is a mixture of two pseudo-components, namely the monoterpene and sesquiterpene hydrocarbons, on the one hand, and their oxygenated derivatives (oxygenated monoterpenes and sesquiterpenes), on the other hand (Sect. 17.3.2), that are extracted separately at rates defined by two independent values of De. Reverchon (1997) questioned the validity of the shrinking-core hypothesis to model SCFE of substrates containing little solute bound to the solid matrix, as it could be the case for essential oils in most herbs and spices, where the driving force for the extraction depends little on the solubility of the essential oil in high-pressure CO2 under extraction conditions.

On the other hand, the desorption-dissolution-diffusion hypothesis assumes that the solute is partially adsorbed on the solid matrix within the pores, so that a fraction of the solute is adsorbed on the solid matrix and the rest is dissolved in the SCF phase within the inner pores of the solid, which are related by an equilibrium sorption isotherm (see Table 17.1 for a summary of DDD models applied in literature). Goto et al. (1993) assumed a linear sorption isotherm (or a constant equilibrium-partition coefficient K), Ruetsch et al. (2003) applied a Brunauer-Emmet-Teller (or BET) isotherm, Daghero et al. (2004) applied a Langmuir isotherm for solute concentrations below the saturation concentration in the high-pressure CO2, and Salimi et al. (2008) compared a linear isotherm with several other sorption models including those of Langmuir, Freundlich, and Langmuir Freunlich. Kim and Hong (2002) did not differentiate between the solute adsorbed on the solid and dissolved in the gas phase within the pores, which implicitly implied a unitary equilibrium-partition coefficient (K = 1).

Sovová (1994) proposed the hypothesis of intact and broken cells (IBC), which assumes that as a result of a mild pretreatment such as size reduction, particles of milled plant material have broken cells on the surface, and intact cells in the interior. An external (convective) mass transfer coefficient controls transfer of solute from the broken cells to the SCF in the bed, whereas an internal (diffusive) mass transfer coefficient controls transfer of solute from the intact cells (see Table 17.1 for a summary of IBC models applied in literature). Reverchon et al. (1999) considered the simultaneous extraction of free solute and bound solute using separate coefficients for external mass transfer and internal mass transfer, respectively, and separate equilibrium-partition coefficients for free solute between the broken cells and the SCF in the bed, and between the bound solute in intact cells and the SCF in the bed. The model (LDF/PF) of Reverchon et al. (1999) (Table 17.1) is a simplification of this general IBC model, which they applied SCFE of lipids from milled fennel seeds; the simplifying assumption was that there is no free essential oil in milled fennel seeds and that all was bound to the solid matrix. Unlike Reverchon et al. (1999), Sovová (2005) and Machmudah et al. (2006) assumed that the driving force for the extraction of free essential oil is the difference between an equilibrium concentration of the oil in high-pressure CO2 that depends on the oil concentration in broken cells according to the so-called PCPR isotherm of Perrut et al. (1997), as described in Sect. 17.4.4, and its concentration in the SCF phase, whereas the driving force for extraction of bound essential oil is the difference in oil concentration between the intact and broken cells (model IBC/PF/PCPR in Table 17.1).

More advanced models differentiate the effect of the pretreatment on the substrate depending on the localization of the essential oil in specialized structures in the herb or spice, which are ruptured (surface glands or SGl, inner secretory ducts or SDuct, inner secretory cavities or SCav) during milling, or burst (surface glands) as a result of swelling of the glands by dissolution of high-pressure CO2 in the gland contents (essential oils) (Zizovic et al. 2005, 2007a,b,c; Stamenić et al. 2008). Table 17.1 classifies these so-called Micro-Scale (μS) models, which are further described in Sect. 17.3.3.

Table 17.1 also summarizes several simplifications of the basic mass balance and rate equations of mass transfer models used in the literature to simulate SCFE curves of plant essential oils. Several of these simplifications pertain to the differential mass balance equation. When assuming a so-called differential bed (DB), which is valid if the height of the packed bed is comparable with the inner diameter of the extraction vessel, the second term on the right of the differential mass balance equation (17.1) is replaced by an expression reflecting a linear variation in the concentration of the solute in the SCF with the axial position along the bed (Goto et al. 1993, 1998; Perakis et al. 2005). Alternative simplifications to the differential mass balance equation include assuming that there is no accumulation (NA) of solute in the SCF phase, or neglecting the accumulation or first term on the right of (17.1) (Sovová 1994; Papamichail et al. 2000; Reverchon and Sesti Osséo 1994a); assuming a uniform extraction (UA) along the bed, or replacing the second term on the right of (17.1) by an expression reflecting a linear variation in solute concentration in SCF with the axial position along the bed, which is equivalent to assuming a “differential” bed (Papamichail et al. 2000; Reverchon and Sesti Osséo 1994a); and assuming a plug flow (PF), and/or neglecting the axial dispersion in the SCF phase or the third term on the on the right of (17.1). As summarized in Table 17.1, assuming the axially dispersed plug flow (ADPF) pattern (Reverchon and Marrone 1997; Goodarznia and Eikani 1998; Reis-Vasco et al. 2000; Spricigo et al. 2001; Ruetsch et al. 2003; Daghero et al. 2004; Zizovic et al. 2005, 2007b, c; Machmudah et al. 2006; Steffani et al. 2006; Salimi et al. 2008; Stamenić et al. 2008) that is implicit in the differential mass balance equation (17.1) presented in Sect. 2.1 is more the exception than the norm. Some authors (Reverchon et al. 1993a; Reverchon 1996; Kim and Hong 2002; Gaspar et al. 2003; Campos et al. 2005; Kotnik et al. 2007) circumvent the differential mass balance (17.1) treating the packed bed as a vessel with perfect mixing (PM), and others (Esquivel et al. 1996; Reverchon 1996; Sovová 2005) treating it as perfectly mixed multistages (PMMS) or a series of perfectly agitated mixing vessels. The perfectly mixed vessel or “hot-ball”-type model, so called because of the similitude in the mass transfer process with the cooling of a hot ball of a solid material in a fluid (Reverchon 1997), or Crank model, so called to honor the author of an influential book on diffusion in solids (Crank 1975), fail to account for the effect of the increase in solute concentration in the SCF phase along the bed in decreasing the rate of mass transfer. Models assuming several (n) perfectly mixed vessels in series approach plug flow as the value of n increases, with the n being an indirect measurement of the axial dispersion along the packed bed; the treatment of a packed bed as a series of discrete stages does not comply with the physical situation but is commonly applied in other separation processes in packed beds such as chromatography (Martin and Synge 1941).

Besides or instead of the differential mass balance equation (17.1), some models listed in Table 17.1 simplify the so-called source-and-transfer J term (17.2) that describes the rate of transfer of essential oil between the herb or spice and the high-pressure CO2. The linear driving force (LDF) approximation for mass transfer from the substrate to the SCF (see examples of this type of simplifying assumption in Table 17.1), which is valid when the residual solute concentration profile in the partially extracted solid substrate, Cs(r), is approximately parabolic, uses a global driving force and a single global mass transfer coefficient. The global driving force for mass transfer equals the difference between the average residual concentration of solute in the solid, corrected by the equilibrium-partition coefficient \( \left( {{{\bar{C}}_{\rm {s}}}{/}K} \right) \) and the concentration of solute in the SCF (Cf). The global mass transfer coefficient (kg, (17.5), Goto et al. 1993), on the other hand, accounts for both the internal resistance to mass transfer (related to an internal mass transfer coefficient, ki) and external resistance to mass transfer (related to the external mass transfer coefficient, kf):
$$ {k_{\rm g}} = \frac{{{k_{\rm {f}}}}}{{1 + \frac{{Bi}}{\xi }}} $$
(17.5)
where ξ, a particle-geometry parameter, equals 10 for a sphere and equals 6 for a thin slab (for which the characteristic dimension dp corresponds to its thickness); Bi is the dimensionless Biot number (17.6):
$$ Bi = \frac{{{k_{\rm {f}}}{d_{\rm {p}}}}}{{{D_{\rm {e}}}}} $$
(17.6)

When both the inner resistance to mass transfer in the plant material and the external resistance in the SCF film surrounding the particles can be neglected, it is unnecessary to include the so-called source and transfer J term in the mass balance and rate equations (17.1–17.4) because under these conditions Cf and \( {\bar{C}_{\rm {s}}} \) are related by equilibrium. Reis-Vasco et al. (2000) applied this simplifying assumption to the initial stages of the high-pressure CO2 extraction of pennyroyal essential oil.

The most simple models in Table 17.1 correspond to simple steady-state approximations that assume the rate of extraction is defined by a single mass transfer controlling resistance, which switches from external control (Ferreira et al. 1999; Kotnik et al. 2007) to internal control (Kotnik et al. 2007) in a given transition time. An alternative way to account for the transition from external control to internal control in a single model is to use a concentration-dependent global mass transfer coefficient when using the linear driving force approximation to mass transfer, as done by Coelho et al. (1997). It is important to point out that some models in Table 17.1 refer to authors who adopted them for SCFE of plant essential oils instead of the original authors who applied them for alternative SCFE applications. Specifically, these models are the Diff-Sph/IC model of Crank (1975), the EMTC model of Brunner (1984), the IMTC model of Hong et al. (1990), the LDF/PF/CDIC model of Cygnarowicz-Provost (1996), the LDF-Sph/PF model of Catchpole et al. (1994), Sovová’s (1994) model, and the LDF-D3-Sph/DB model of Skerget and Knez (2001).

Selected models that are highlighted in Table 17.1 are widely used because they have relatively simple analytical solutions and are used to best-fit model parameters with ease. The solution of the so-called Reverchon–Sesti Ossèo (R-SO) model was applied by Reverchon and Sesti Osséo (1994a), Reverchon et al. (1995a), Papamichail et al. (2000), Zekovic et al. (2001), Louli et al. (2004), Pfaf-Šovljanski et al. (2005), and Vargas et al. (2006). On the other hand, the solution of Sovová’s (1994) model was applied by Mira et al. (1996, 1999), Papamichail et al. (2000), Povh et al. (2001), Ferreira and Meireles (2002), Sousa et al. (2002, 2005), Martínez et al. (2003, 2007), Rodrigues et al. (2003), Louli et al. (2004), Campos et al. (2005), Perakis et al. (2005), Vargas et al. (2006), and Bensebia et al. (2009). Sovová’s model (1994) considers SCFE as a two-stage process, where the mass transfer coefficient in the first (convection-controlled) stage is kf, whereas the mass transfer coefficient in the second (internal-diffusion-controlled) stage decreases proportionally to the difference between the solubility of the essential oil in high-pressure CO2 and its actual concentration in the SCF phase in the bed. Povh et al. (2001) described a procedure to estimate the parameters of Sovova’s model based on the fitting of an integral extraction plot of solute yield versus specific solvent consumption (Fig. 17.2) to a spline with three straight lines representing successively the constant, falling, and diffusion-controlled extraction rate periods. Sovová et al. (1994a) applied an improved version of Sovová’s model (model ICB/ADPF in Table 17.1) in two aspects: they did not neglect the accumulation of essential oil in the SCF phase and they considered that the extraction was limited by a decreasing solubility (LDS) or that the saturation solubility of the essential oil in high-pressure CO2 decreased during extraction due to the progressive enrichment of the oil remaining in the partially extracted substrate in less volatile compounds. Authors using other models include Louli et al. (2004) (LDF/UENA model of Papamichail et al. 2000), Sousa et al. (2005) (LDF-D3-Slab/DB model of Goto et al. 1993), Campos et al. (2005) (Diff-Slab/IC model of Gaspar et al. 2003), Zizovic et al. (2007c) (μS/SGl model of Zizovic et al. 2005; μS/SCav model of Zizovic et al. 2007a; μS/SDuct model of Zizovic et al. 2007b), Stamenić et al. (2008) (μS/SCav model of Zizovic et al. 2007a; μS/SDuct model of Zizovic et al. 2007b), Langa et al. (2009) (IBC/PF/PCPR model of Sovová 2005), and Uquiche et al. (submitted) (Diff/PF model of Araus et al. 2009).

Although most authors of models in Table 17.1 applied the models to their own data, there are some exceptions. Goodarznia and Eikani (1998) modeled the data of Reverchon et al. (1993a) on SCFE of essential oils from basil, marjoram, and rosemary, as well as the data of Sovová et al. (1994a) on SCFE of caraway essential oil. Germain et al. (2005) also modeled the data of Sovová et al. (1994a) on SCFE of caraway essential oils. Zizovic et al. (2007b) modeled data of Coelho et al. (2003) on SCFE of fennel fruit oil. Zizovic et al. (2007c) modeled literature data on SCFE of essential oils from orange peel (Mira et al. 1996), ginger rhizome (Roy et al. 1996), clove bud (Reverchon and Marrone 1997), and eucalyptus leaf (Della Porta et al. 1999). Stamenić et al. (2008) modeled the data of Machmudah et al. (2006) on SCFE of nutmeg essential oil. Finally, Araus et al. (2009) modeled literature data on SCFE of essential oils from sage (Reverchon 1996), lavender (Akgun et al. 2000), oregano (Gaspar 2002), pennyroyal (Reis-Vasco et al. 2000), and chamomile (Povh et al. 2001).

17.3 Kinetic Parameters of CO2 Extraction of Essential Oils

Table 17.2 summarizes the conditions for the experimental studies on kinetics of mass transfer during SCFE of essential oils from herbs and spices reviewed in this chapter. Although most authors in Table 17.2 modeled the results of their own high-pressure CO2 extraction work, there are some exceptions, including the data of Roy et al. (1996) on extraction of ginger essential oils at 313 K and 10.8 MPa, the data of Della Porta et al. (1999) on extraction of eucalyptus essential oil at 323 K and 9 MPa, the data of Coelho et al. (2003) on extraction of fennel essential oil at 313 K and 9 MPa, and the data of Gaspar (2002) on extraction of oregano essential oil under selected conditions (310 K and 8 MPa or 320 K and 20 MPa).
Table 17.2

Summary of extraction conditions of selected mass transfer studies on high-pressure CO2 extraction of plant essential oils in packed beds

Substrate

Particle diameter (dp, mm)

Temperature (T, K)

Pressure (P, MPa)

Superficial velocity (U, mm/s)

Extractor volume (V, cm3)

L/D ratio of extractor (–)

Alecrim pimenta (Sousa et al. 2002)

0.38

298

6.7

0.12

220

27.8

Aniseed (Rodrigues et al. 2003)

0.50

303

8, 10, 14, 18

0.014–0.025

418

2.03

Basil (Reverchon et al. 1993a)

0.17

313

10

0.23

400

3.06

Black pepper (Ferreira et al. 1999; Ferreira and Meireles 2002)

0.080, 0.11

303, 313, 323

15, 20

0.018–0.20

26

29.1

Black pepper (Perakis et al. 2005)

0.18

313, 323

9, 10, 15

0.20–0.59

751

5.45

Boldo (Uquiche et al. submitted)

0.39, 0.40, 2.36

313

10

0.123

5

2.32

Caraway (Sovová et al. 1994a)

0.38

296, 313

9, 10

0.028–0.048

150

5.30

Carqueja (Vargas et al. 2006)

0.50

313, 323, 333, 343

9

0.35

4

4.09

Celery (Papamichail et al. 2000)

0.21, 0.49

318, 328

10, 15

0.167, 0.456

400

2.90

Chamomile (Povh et al. 2001)

0.30

303, 313

10, 12, 16, 20

0.030–0.087

204

4.18

Chamomile (Kotnik et al. 2007)

0.11

303, 313

10, 15

0.17–0.19

55

4.18

Cinnamon of cunha (Sousa et al. 2005)

0.52

288

6.7

0.065, 0.068

222

27.7

Clove (Reverchon and Marrone 1997)

0.37

323

9

0.244–0.488

400

3.06

Clove (Ruetsch et al. 2003)

0.79

323

9, 12

0.38, 0.76

1,500

2.62

Clove (Daghero et al. 2004)

0.79

323

9, 12

0.38, 1.52

1,500

2.62

Clove (Martínez et al. 2007)

0.86

308

10.0

0.039, 0.11

6, 133, 280

0.98, 1.05, 2.20

Eucalyptus (Della Porta et al. 1999)

0.37

323

9.0

0.514

400

6.00

Fennel (Reverchon et al. 1999)

0.37

323

9

0.20–0.61

400

3.06

Ginger (Roy et al. 1996)

0.35

313

11

0.74

2.2

6.67

Ginger (Martínez et al. 2003)

1.02

293, 303, 313

15, 20

0.091–0.12

150

13.3

Hop (Pfaf-Šovljanski et al. 2005)

0.488

313

15

0.050

200

3.98

Ho-sho (Steffani et al. 2006)

0.37, 0.50, 1.00

313, 323, 333

8, 9, 10

0.18–0.71

8

7.31

Lavender (Reverchon et al. 1995a)

1.67

321

9

0.31

400

3.06

Lavender (Akgun et al. 2000)

1.20

308, 313, 323

8, 10, 12, 14

0.44–1.4

39

50.0

Marigold (Campos et al. 2005)

0.62

313

12, 15

0.068, 0.202

139

19.1

Marjoram (Reverchon et al. 1993a)

0.15

313

10.0

0.23

400

3.06

Nutmeg (Spricigo et al. 2001)

0.30, 0.68, 1.45

296

9

0.032–0.053

35

4.76

Nutmeg (Machmudah et al. 2006)

0.56, 0.69, 2.12

313, 318, 323

1.0, 1.5

0.011, 0.068

500

1.86

Orange (Mira et al. (1996)

0.30, 0.50, 1.50, 7.50

323

15

0.084, 0.585

300

2.30

Orange (Mira et al. 1999)

0.30, 0.50, 1.50, 7.50

323

15

0.084, 0.585

300

2.30

Oregano (Esquivel et al. 1996)

1.10

298, 313

7, 10, 15

0.50–0.63

30

3.99

Oregano (Gaspar 2002)

0.36

310, 320

8, 20

0.22, 0.088

196

2.00

Oregano (Gaspar et al. 2003)

0.33, 0.36, 0.70, 1.55

300, 310, 320

7, 8, 10, 15, 20

0.017–0.058

319

0.47

Oregano (Uquiche et al. submitted)

0.35, 0.36, 2.36

313

10

0.123

5

2.32

Parsley (Louli et al. 2004)

0.29, 0.50

308, 318

10, 15

0.16–0.45

185, 209

1.34, 1.52

Pennyroyal (Reis-Vasco et al. 2000)

0.30, 0.50, 0.70

323

10

0.48–0.97

247–379

3.28–5.02

Peppermint (Goto et al. 1993)

0.12

313, 333, 353

8,8, 14.7, 19.6

0.099–0.43

21

2.17

Rosemary (Reverchon et al. 1993a)

0.23

313

10

0.23

400

3.06

Rosemary (Coelho et al. 1997)

0.72, 1.33

308, 313

10, 12.5, 20

0.11–0.43

5

12.9

Rosemary (Bensebia et al. (2009)

0.44

308, 313

10, 12, 15, 18

0.25–0.69

125

13.4

Sage (Catchpole et al. 1996b)

0.50–1.53

291

7

0.19–0.48

2,959

2.41

Sage (Reverchon 1996)

0.25–3.10

323

9

0.85–1.51

400

5.94

Sage (Langa et al. 2009)

0.3, 0.5, 0.8

313, 323

9, 10

0.15–0.34

1,000

6.00

Spearmint (Kim and Hong 2002)

0.30

312, 322

6.9, 8.5, 10.3

0.017–0.068

46

3.54

Thyme (Zekovic et al. 2001)

3.32, 1.46, 0.70

313

10

0.063

200

3.98

Valerian (Zizovic et al. 2007a)

0.40, 0.65, 0.90

313, 323

10, 15

0.072, 0.147

150

2.35

Valerian (Salimi et al. 2008)

0.59

310

17

0.233

10

12.9

Vetiver (Martínez et al. 2007)

0.12

313

20

0.054, 0.150

9, 187

1.45, 1.47

Wild thyme (Stamenić et al. 2008)

0.700

323

10

0.147

150

2.35

In this work, analysis required the estimation of the physical properties of the loaded CO2 phase produced during the extraction of essential oils. For that purpose, the authors neglected the changes in physical properties associated with the dissolution of essential oils in the solvent under the assayed conditions, and estimated the density (ρ) and viscosity (μ) of the loaded high-pressure CO2 as a function of the extraction temperature and pressure using the NIST (2000) database for pure CO2 (del Valle and de la Fuente 2006). On the other hand, D12 was estimated using the equation of Catchpole and King (1994), which requires reduced temperature (Tr = T/Tc) and reduced density (ρr = ρ/ρc, where ρc = 467.6 kg/m3 is the critical density of CO2) of the SCF, and the molecular weight (MW2) and critical volume (Vc2) of the pseudo-solute. As informed in Sect. 17.2.2, for the purpose of estimating MW2 and Vc2, representative compounds in families of compounds were selected, such as monoterpene (MT) hydrocarbons, oxygenated monoterpene (OMT) compounds, sesquiterpene (ST) hydrocarbons, oxygenated sesquiterpene (OST) compounds, waxes, and some plant-specific compounds; properties of representative compounds to whole families were assigned; and extracts were considered as pseudo-solutes whose properties were estimated using Kay’s rule as the weighted average of the properties of the representative compounds in each family (Poling et al. 2000). The composition of the essential oils was taken from the literature and was typically determined by gas chromatography analysis of the steam distillate, hydro-distillate, or CO2-extract of the herb or spice. For calculations in this current work, only those families representing more than 1% of the whole essential oil were considered, and the most concentrated four families in those cases where five or more were represented in excess of 1% each. Table 17.3 summarizes representative compounds of up to four families for essential oils in Table 17.2. As an example, the lavender essential oil of Reverchon et al. (1995a) has 3.33% MTs (main component, myrcene, representing 35.7% of all MTs), 87.9% OMTs (main component, linalyl acetate, representing 39.4% of all OMTs), 6.14% STs (main component, β-farnesene, representing 36.3 of all STs), and 2.63% OSTs (main component, bisabolol, representing 79.5% of all MTs). The values of Vc were estimated for the representative compounds in the various families using Joback’s modification of the Lydersen’s group-contribution method (Poling et al. 2000).

Table 17.4 summarizes the estimations of the molecular weight (MW2) and critical volume (Vc2) of the pseudo-solutes representing the essential oils of the different herbs and spices reported in Table 17.3. It is clear that the properties of the pseudo-solutes vary between substrates, as expected, but also for a single substrate because of differences in the substrates or extracts. Indeed, the essential oils exhibit differences due to typical variations in biological samples associated with genetic and processing (e.g., harvest time, drying treatment, and storage condition) factors (Zetzl et al. 2003). In addition, steam distillates, hydrodistillates, and CO2 extracts from the same substrate exhibit differences due to thermal and/or oxidative degradation of labile components during distillation, or solubilization of additional compounds in CO2 with increased solvent power (Moyler 1993; Reverchon 1997). Figure 17.3 shows that the composition of sage essential oils extracted with high-pressure CO2 at 313 K and 9 MPa, or 323 K and 10 MPa, changes depending on process conditions and extraction time.
Fig. 17.3

Effect of process time and conditions on the composition of sage essential oils extracted with high-pressure CO2: Open image in new window monoterpenes, Open image in new window oxygenated monoterpenes, Open image in new window sesquiterpenes, Open image in new window oxygenated sesquiterpenes, and Open image in new window total essential oil components extracted at 313 K and 9 MPa; and Open image in new window monoterpenes, Open image in new window oxygenated monoterpenes, Open image in new window sesquiterpenes, Open image in new window oxygenated sesquiterpenes, and Open image in new window total essential oil components extracted at 323 K and 10 MPa (Adapted from Langa et al. 2009)

17.3.1 Axial Dispersion Coefficient

Authors del Valle and de la Fuente (2006) showed consistency in the reported literature values of axial dispersion coefficients for flow of high-pressure CO2 in a packed bed, when presenting the experimental values in a dimensionless plot of Dax/D12 versus Pep where Pep is the Peclet number for the particle (17.7), which in turn corresponds to the product of the dimensionless numbers of Reynolds (Re, 17.8) and Schmidt (Sc, 17.9).
$$ P{e_{\rm {p}}}\ ( = Re \cdot Sc) = \frac{{U\;{d_{\rm {p}}}}}{{{D_{12}}}} $$
(17.7)
$$ Re = \frac{{\rm rho \;U\;{d_{\rm {p}}}}}{\rm mu} $$
(17.8)
$$ Sc = \frac{\rm mu }{{\rm rho \;{D_{12}}}} $$
(17.9)
In a related work, del Valle and Catchpole (2005) correlated literature data for the axial dispersion of high-pressure CO2 in packed beds (Tan and Liou 1989; Catchpole et al. 1996a; Funazukuri et al. 1998; Yu 1998; Ghoreishi and Akgerman 2004). Typical measurements in these studies were conducted by injecting a pulse of solute (gaseous methane, volatile acetone or hexachlorobenzene, or low-volatility benzoic acid, oleic acid, or squalene) into the high-pressure CO2 stream before a bed (0.4 ≤ D ≤ 50.8 mm) packed with different materials (sand particles, glass beads, or steel beads ranging in size from dp = 0.05 to dp = 3.18 mm), and evaluating the dispersion (concentration profile) of the solute in the stream leaving the bed. Different flow directions (horizontal, upward, downward) and regimes (from molecular-transport-controlled, Ped ~ 9.1 × 10−3, to convection-controlled flow conditions, Ped ~ 1.2 × 103) were assayed in these studies.
Table 17.3

Summary of compositions of plant essential oils from high-pressure CO2 extraction studies in Table 17.2. Besides the name of the main component, for each of the up to 4 fractions the compound type,* percent of fraction, and percent of the main component in the fraction are indicated within parenthesis

Plant material

Fraction 1

Fraction 2

Fraction 3

Fraction 4

Basil (Reverchon and Sesti Osséo 1994b)

Estragole (OMT/89/54)

α-trans Bergamotene (ST/9.0/46)

T Cadinol (ST/2.2/47)

Lavender I (Reverchon et al. 1995a)

Myrcene (MT/3.33/35.7)

Linalyl acetate (OMT/87.9/39.4)

cis-β-Farnesene (ST/6.14/36.3)

α-Bisabolol (ST/2.63/79.5)

Lavender II (Akgün et al. 2000)

Camphor (OMT/56.9)

Fenchone (OMT/43.1)

Marjoram (Jimenez-Carmona et al. 1999)

Sabinene (MT/17.7/42.3)

cis-Sabinene hydrate (OMT/78.9/78.6)

β-Caryophyllene (ST/3.46/100)

Oregano (Gaspar 2002)

γ-Terpinene (MT/6.78/79.7)

Thymol (OMT/85.8/42.4)

β-Caryophyllene (ST/7.47/100)

Pennyroyal (Aghel et al. 2004)

Limonene (MT/14.6/100)

Pulegone (OMT/85.4/60.9)

Peppermint (Roy et al. 1996)

Limonene (MT/2.86/45.0)

Menthol (OMT/92.8/74.5)

Germacrene (ST/4.35/57.2)

Rosemary (Coelho et al. 1997)

Limonene (MT/26.0/47.6)

Camphor (OMT/65.1/57.6)

α-Humulene (ST/7.23/44.1)

Caryophyllene oxide (OST/1.60/100)

Sage I (Reverchon et al. 1995b)

β-Pinene (MT/11.6/21.1)

1,8-Cineole (OMT/70.8/76.8)

β-Caryophyllene (ST/14.5/48.8)

Manool (OST/3.19/56.1)

Sage II (Langa et al. 2009) (313 K/9 MPa)

Myrcene (MT/9.08/35.9)

Camphor (OMT/80.4/62.5)

β-Caryophyllene (ST/6.19/29.2)

Viridoflorol (OST/4.35/39.8)

Sage 2 (Langa et al. 2009) (323 K/10 MPa)

Myrcene (MT/11.4/39.1)

Camphor (OMT/79.9/69.0)

β-Caryophyllene (ST/5.79/30.4)

Caryophyllene oxide (OST/2.88/15.5)

Spearmint (Özer et al. 1996)

Limonene (MT/6.42/81.9)

Carvone (OMT/90.6/89.5)

β-Bourbonene (ST/2.95/78.6)

Thyme (Zekovic et al. 2001)

Thymol (OMT/19.6/4.9)

β-Caryophyllene (ST/2.25/100)

Tetradecane (HC/78.2/67.1)

Wild thyme (Sefidkon et al. 2004) Before flowering

γ-Terpinene (MT/52.2/42.8)

Thymol (OMT/32.9/58.1)

β-Caryophyllene (ST/14.6/42)

Spathulenol (OST/0.31/33.3)

Wild thyme (Sefidkon et al. 2004) After flowering

γ-Terpinene (MT/60.20/42.7)

Thymol (OMT/32.09/66.1)

Germacrene-D (ST/6.80/85.0)

Caryophyllene oxide (OST/0.91/87.5)

Anise (Rodrígues et al. 2003) (303 K/8 MPa)

Anethole (OMT/92.0/97.7)

γ-Himachalene (ST/2.27/100)

Isoeugenyl 2-methyl-butyrate (OST/5.76/100)

 

Anise (Rodrígues et al. 2003) (303 K/10 MPa)

Anethole (OMT/92.2/98.3)

γ-Himachalene (ST/2.72/100)

Isoeugenyl 2-methyl-butyrate (ST/2.72/100)

 

Anise (Rodrígues et al. 2003) (303 K/14 MPa)

Anethole (OMT/91.6/98.2)

γ-Himachalene (ST/2.91/100)

Isoeugenyl 2-methyl-butyrate (OST/5.50/100)

 

Caraway (Sovová et al. 1994a)

Limonene (MT/39.8)

Carvone (OMT/60.2)

Celery (Mišić et al. 2008)

Limonene (MT/28.9/91.7)

Sedanenolide (OMT/64.0/77.7)

β-Selinene (ST/4.89/73.5)

Carotol (OST/2.22/78.3)

Fennel (Simandi et al. 1999)

Limonene (MT/9.37/39.6)

Anethole (OMT/90.6/72.2)

Parsley (Louli et al. 2004) (10 MPa)

α-Pinene (MT/6.59/49.1)

Myristicin (PhPro/93.4/57.4)

Parsley (Louli et al. 2004) (15 MPa)

α-Pinene (MT/2.40/55.8)

Myristicin (MT/2.40/55.8)

Carqueja (Simões-Pires et al. 2005)

β-Pinene (MT/3.42/75.0)

Carquejyl acetate (OMT/42.7/90.7)

Ledol (OST/53.9/38.6)

Chamomile I (Povh et al. 2001)

β-Farnesene (ST/39.6/86.3)

α-Bisabolol (OST/60.4/47.0)

Chamomile II (Kotnik et al. 2007) (303 K/10 MPa)

Matricine (OST/100)

Chamomile II (Kotnik et al. 2007) (303 K/15 MPa)

Matricine (OST/96.5)

Chamomile II (Kotnik et al. 2007) (313 K/10 MPa)

Matricine (OST/97.3)

Chamomile II (Kotnik et al. 2007) (313 K/15 MPa)

Matricine (OST/96.4)

Marigold (Danielski et al. 2007) (313 K/12 MPa)

Tetradecanoic acid (LOHC/2.46/100)

Octacosane (HC/94.6/94.6)

Cholest-4-en-3-one-14-methyl (HOHC/2.94/40.7)

Marigold (Danielski et al. 2007) (313 K/15 MPa)

Octacosane (HC/98.7/43.1)

Taraxasterol (H-OHC/1.35/34.2)

Alecrim pimenta (Sousa et al. 2002)

p-Cymene (MT/3.22/45.0)

Thymol (OMT/74.8/67.9)

β-Caryophyllene (ST/20.0/72.2)

Caryophyllene oxide (OST/1.97/100)

Black pepper I (Ferreira et al. 1999)

Limonene (MT/66.2/30.1)

β-Caryophyllene (ST/33.8/21.8)

Black pepper II (Ferreira et al. 1999)

Limonene (MT/1.00/57.8)

β-Caryophyllene (ST/99.0/70.9)

Black pepper III (Perakis et al. 2005)

Limonene (MT/31.2/29.8)

Linalool (OMT/1.57/51.3)

β-Caryophyllene (ST/34.2/35.5)

Caryophyllene oxide (OST/33.0/51.5)

Boldo (Miraldi et al. 1996)

p-Cymene (MT/9.28/94.7)

Ascaridole (OMT/81.75/26.5)

Guaizulene (ST/8.96/100)

Cinnamon of Cunha (Sousa et al. 2005)

Anethole (OMT/96.5/95.8)

Germacrene

(ST/3.51/35.7)

Clove (Della Porta et al. 1998)

Eugenol (OMT/86.3/77.5)

β-Caryophyllene (ST/13.7/82.2)

Eucalyptus (Della Porta et al. 1999)

α-Pinene (MT/12.2/86.1)

1,8-Cineole (OMT/67.1/93.3)

Aromadendrene (ST/12.3/65.3)

Guaiol (OST/8.40/50.0)

Ginger (Martínez et al. 2003)

Zingiberene (OMT/9.77/56.7)

α-Zingiberene (ST/45.6/35.6)

Farnesol (OST/3.73/30.3)

6-Gingerol (Ging/40.9/28.9)

Hop (Pfaf-Šovljanski et al. 2005)

α-Humulene (ST/13.5/82.4)

Isohumulone (α-acid/13.0/100)

Lupulone (β-acid/73.5/53)

Ho-sho (Bakkali et al. 2005)

Sabinene (MT/21.7/35.5)

1,8-Cineole (OMT/75.0/80.0)

Viridiflorol (OST/3.29/100)

Nutmeg I (Spricigo et al. 1999)

Sabinene (MT/78.8/51.9)

Myristicin (OMT/21.2/36.8)

Nutmeg II (Machmudah et al. 2006)

3-Cyclohexene-1-ol (LOHC/15.7/26.4)

β-Phellandrene (MT/46.3/42.9)

Myristicin (OMT/36.2/89.9)

Copaene (ST/1.83/68.9)

Orange (Budich and Brunner 1999)

Limonene (MT/98.3/97.6)

Linalool (OMT/1.75/28.8)

Valerian I (Zizovic et al. 2007a) (313 K/10 MPa)

Borneol (OMT/15.9/36.8)

Valerena-4,7(11)-diene (ST/14.1/25.7)

Valerenal (OST/67.4/19.3)

(E)-Valerenyl isovalerate (H-OHC/2.68/70.0)

Valerian II (Zizovic et al. 2007a) (313 K/10 MPa)

Isovaleric acid (LOHC/6.01/100)

Bornyl acetate (OMT/13.9/59.3)

Valerena-4,7(11)-diene (ST/13.8/17.2)

Valerianol (OST/66.2/19.7)

Valerian II (Zizovic et al. 2007a) (313 K/15 MPa)

Isovaleric acid (LOHC/7.67/100)

Bornyl acetate (OMT/10.7/61.6)

β-Bisabolene (ST/13.2/17.7)

Valerianol (OST/68.4/16.6)

Valerian II (Zizovic et al. 2007a) (323 K/10 MPa)

Isovaleric acid (LOHC/4.37/100)

Bornyl acetate (OMT/12.1/58.9)

Valerena-4,7(11)-diene (ST/13.3/17.1)

Valerianol (OST/70.2/19.2)

Valerian II (Zizovic et al. 2007a) (323 K/15 MPa)

Isovaleric acid (LOHC/3.57/100)

Bornyl acetate (OMT/10.7/59.3)

Valerena-4,7(11)-diene (ST/13.3/17.1)

Valerianol (OST/72.7/20.0)

Valerian III (Zizovic et al. 2007a)

Isovaleric acid (LOHC/9.64/100)

Bornyl acetate (OMT/16.7/52.9)

δ-Elemene (ST/28.6/26.9)

Valerenal (OST/45.0/34.9)

*MT indicates a monoterpene hydrocarbon; OMT, an oxygenated monoterpene; ST, a sesquiterpene hydrocarbon; OST, an oxygenated sesquiterpene; HC, an hydrocarbon; LOHC, a light oxygenated hydrocarbon; HOHC, a heavy oxygenated hydrocarbon; PhPro, a phenyl propanoid; and Ging, a gingerol

Table 17.4

Summary of estimated molecular weights (MW) and critical volumes (Vc) of plant essential oils in Table 17.3

Plant material

Scientific name

Family

Identified compounds (%)

Molecular weight (MW, Da)

Critical volume (Vc, cm3/mol)

Basil

Ocimum basilicum

Lamiaceae

99.4

153.0

508.0

Lavender I

Lavandula angustifolia

Lamiaceae

100.1

194.5

682.6

Lavender II

Lavandula angustifolia

Lamiaceae

76.9

152.2

503.5

Marjoram

Origanum majorama

Lamiaceae

36.8

152.0

517.7

Oregano

Origanum vulgare

Lamiaceae

87.0

152.2

440.3

Pennyroyal

Mentha pulegium

Lamiaceae

100.0

149.7

504.1

Peppermint

Mentha × piperita

Lamiaceae

99.3

157.2

527.2

Rosemary

Rosmarinus officinalis

Lamiaceae

100.0

151.7

523.6

Sage I

Salvia officinalis

Lamiaceae

100.0

160.0

546.0

Sage II (313 K/9 MPa)

Salvia officinalis

Lamiaceae

81.4

155.2

519.8

Sage II (323 K/10 MPa)

Salvia officinalis

Lamiaceae

87.1

153.8

153.8

Spearmint

Mentha spicata

Lamiaceae

100.0

150.4

508.5

Thyme

Thymus vulgaris

Lamiaceae

11.9

186.8

719.0

Wild thyme, before flowering

Thymus serpyllum

Lamiaceae

98.0

148.1

506.6

Wild thyme, after flowering

Thymus serpyllum

Lamiaceae

88.2

144.3

500.4

Anise (303 K/8 MPa)

Pimpinella anisum

Apiaceae

99.2

152.7

500.0

Anise (303 K/10 MPa)

Pimpinella anisum

Apiaceae

97.7

152.5

499.6

Anise (303 K/14 MPa)

Pimpinella anisum

Apiaceae

97.0

152.8

500.7

Caraway

Carum carvi

Apiaceae

98.0

144.3

505.2

Celery

Apium graveolens

Apiaceae

99.8

172.7

585.9

Fennel

Foeniculum vulgare

Apiaceae

100.0

147.0

487.7

Parsley (10 MPa)

Petroselinum crispum

Apiaceae

83.4

187.1

533.1

Parsley (15 MPa)

Petroselinum crispum

Apiaceae

96.2

193.0

552.1

Carqueja

Baccharis trimera

Asteraceae

83.7

204.3

678.6

Chamomile I

Matricaria recutita

Asteraceae

44.4

214.9

790.6

Chamomile II (303 K/10 MPa)

Matricaria recutita

Asteraceae

7.56

306.4

886.5

Chamomile II (303 K/15 MPa)

Matricaria recutita

Asteraceae

8.42

306.4

886.5

Chamomile II (313 K/10 MPa)

Matricaria recutita

Asteraceae

9.74

306.4

886.5

Chamomile II (313 K/15 MPa)

Matricaria recutita

Asteraceae

9.65

306.4

886.5

Marigold (313 K/12 MPa)

Calendula officinalis

Asteraceae

30.9

387.9

1,565.1

Marigold (313 K/15 MPa)

Calendula officinalis

Asteraceae

28.2

395.2

1,601.4

Alecrim pimenta

Lippia sidoides

Verbenaceae

95.2

159.0

470.4

Black pepper I

Piper nigrum

Piperaceae

99.6

153.5

562.1

Black pepper II

Piper nigrum

Piperaceae

99.2

203.3

719.3

Black pepper III

Piper nigrum

Piperaceae

73.3

179.7

633.9

Boldo

Peumus boldus

Monimiaceae

98.2

166.6

525.1

Cinnamon of Cunha

Croton zehntneri

Euphorbiaceae

95.7

149.6

149.6

Clove

Syzygium aromaticum

Myrtaceae

98.5

168.8

454.7

Eucalyptus

Eucalyptus globules

Myrtaceae

100.0

155.0

528.6

Ginger

Zingiber officinale

Zingiberaceae

71.7

241.1

799.0

Hop

Humulus lupulus

Cannabaceae

93.3

364.5

1,224.8

Ho-sho

Cinnamomum camphora

Lauraceae

83.7

151.4

516.2

Nutmeg I

Myristica fragrans

Myristicaceae

89.6

145.2

498.9

Nutmeg II

Myristica fragrans

Myristicaceae

99.6

143.5

143.5

Orange

Citrus sinensis

Rutaceae

100

136.5

508.49

Valerian I (313 K/10 MPa)

Valeriana officinalis

Valerianaceae

83.5

204.6

712.1

Valerian II (313 K/10 MPa)

Valeriana officinalis

Valerianaceae

89.1

201.9

688.4

Valerian II (313 K/15 MPa)

Valeriana officinalis

Valerianaceae

86.2

199.2

683.0

Valerian II (323 K/10 MPa)

Valeriana officinalis

Valerianaceae

88.7

206.0

703.5

Valerian II (323 K/15 MPa)

Valeriana officinalis

Valerianaceae

86.4

208.3

711.8

Valerian III

Valeriana officinalis

Valerianaceae

82.7

190.2

662.7

Figure 17.4 summarizes the results of the correlation study of del Valle and Catchpole (2005). When dispersion is controlled by molecular transport (Ped ≤ 1) the ratio Dax/D12 has a nearly constant value (slightly below 1 in this particular case), as expected (Dullien 1992). On the other hand, under convention-controlled conditions (Ped > 1), the ratio Dax/D12 increases exponentially with Ped, which results in a nearly straight line having a slope between 1 and 2 when presenting the data in a log–log plot, as also expected (Dullien 1992). Data scattering for large values of Ped is partially explained by the scale of the measurements; data obtained using large vessels exhibited a larger axial dispersion coefficient than data obtained using small tubes (del Valle and Catchpole 2005). Dispersion typically increases as the length of the bed (L) increases due to the increase in the residence time in the packed bed (Han et al. 1985). Dispersion also increases as the diameter of the bed (DE) decreases because of the pronounced decrease in local porosity in the radial direction from the wall of the tube or vessel when the ratio DE/dp decreases, which increases concentration-gradient-driven radial diffusion and consequently increases axial dispersion of the solute (Fahien and Smith 1955). It is apparent for the results in Fig. 17.4 that the effect of an increase in L/dp predominates over the effect of an increase in D/dp, so that the axial dispersion is larger in large vessels than small tubes (for purposes here, L/dp ≤ 250 in small packed beds). Thus, del Valle and Catchpole (2005) selected Ped and the ratio L/dp as the independent variables in their correlation for Dax/D12 (17.10).
Fig. 17.4

Dimensionless plot of the axial dispersion coefficient (Dax) in a packed bed operating under a high-pressure CO2 and flow regime. The independent variable is the ratio Dax/D12 [where D12 is a binary diffusion coefficient of the solute (component 2) in CO2 (component 1)] and the dependent variable is the Peclet number for the particle (17.5)

$$ \frac{{{D_{\rm {ax}}}}}{{{D_{{12}}}}} = 0.540 + \frac{{0.530{{\left( {P{e_{\rm {p}}}} \right)}^2}}}{{1 + 42.8\left( {\frac{{P{e_{\rm {p}}}}}{{{L \mathord{\left/{\vphantom {L {{d_{\rm {p}}}}}} \right.} {{d_{\rm {p}}}}}}}} \right)}}. $$
(17.10)

Figure 17.4 reports experimental measurements of axial dispersion using closed circles for small packed beds (experimentally 89 ≤ L/dp ≤ 234) and open circles for large beds (295 ≤ L/dp ≤ 2,320), and includes the limit between the two regions predicted by (17.10) for L/dp = 250 in the form of a segmented line.

In this work, the authors believe that a precise estimation of the value of the axial dispersion coefficient is less important than determining whether axial dispersion phenomena affects SCFE of plant essential oils to such an extent that the term with Dax must be included in the differential mass balance equation (last term on the left of (17.1)). This determination is important because axial dispersion phenomena is typically neglected to simplify the fitting of model parameters. del Valle and de la Fuente (2006) analyzed the effect of dispersion in mass transfer for SCFE of oilseeds under typical industrial conditions based on the claim of Goto et al. (1996) that it can be disregarded in mass transfer models when the value of the Peclet number for the packed bed (PeL, 17.11) is above ca. 100.
$$ P{e_{\rm {L}}} = \frac{{U\;L}}{{{D_{\rm {ax}}}\varepsilon }} $$
(17.11)

Recommended conditions for SCFE of plant essential oils are 323 K and 9 MPa (Reverchon 1997), for which the following values of physical properties were estimated in this work: ρ = 285 kg/m3; μ = 2.47 × 10−5 Pa s; D12 ≅ 3.00 × 10−8 m2/s; and, Sc = 2.86. Conditions favoring axial dispersion in the extraction vessel include a large superficial solvent velocity (e.g., U = 5 mm/s) (Eggers 1996), a large particle size, a small bed voidage, and a tall vessel (see 17.10 and 17.11). Eggers (1996) mentioned that the aspect ratio (L/D) of a typical extraction vessel is between 4 and 6, while Reverchon (1997) specified that an industrial SCFE facility for plant essential oils (Essences, Salerno, Italy) used vessels of 0.3 m3, so in this work a packed bed L = 2.40 m tall and D = 40 cm wide was selected for calculations (L/D = 6, V = 0.3 m3). According to the analysis, dispersive effects can be neglected (PeL ≥ 100) for small particles of dp ≤ 0.71 mm, but for larger particles, it is necessary to reduce the bed voidage from ε ≤ 0.59 for dp = 1.0 mm to ε ≤ 0.34 for dp = 1.5 mm.

As shown in Table 17.1, most authors neglect the contribution of axial dispersion in their SCFE models for plant essential oils from solid substrates in packed beds. There are exceptions (studies where the axial dispersion coefficient is estimated using a literature correlation) including Ruetsch et al. (2003) and Daghero et al. (2004), who used the correlation of Wakao and Kaguei (1982); Goodarznia and Eikani (1998), Spricigo et al. (2001), Gaspar et al. (2003), Steffani et al. (2006), Zizovic at al. (2005, 2007a,b,c), Salimi et al. (2008), and Stamenić et al. (2008), who used the correlation of Tan and Liou (1989); and Machmudah et al. (2006), who used the correlation of Funazukuri et al. (1998). On the other hand, Reis-Vasco et al. (2000) used Dax as a fitting parameter for their experimental data, but their best-fit values decreased when the superficial solvent velocity of the CO2 increased (which was not as expected), and were 31–138 times larger than predicted using (17.10).

17.3.2 External Mass Transfer Coefficient

There are two values of kf (expressed in, e.g., m/s) and kfap (expressed in, e.g., s−1) reported in the literature as external mass transfer coefficients. Thus, in this work all values were recalculated first in similar units. To do this, the specific surface (ap), or total particle surface (Sp) per unit volume of the packed bed [(1 − ε) Vp], was estimated using (17.12):
$$ {a_{\rm {p}}} = \frac{{{\psi }}}{{\left( {1 - \varepsilon } \right)\;{d_{\rm {p}}}}}. $$
(17.12)

In (17.12), ψ is a factor that depends on the geometry of the particles: ψ tends to 2 for very thin slabs (approaching a so-called infinite slab geometry), for which dp is the thickness of the slab; and ψ = 6 for spheres. The void fraction in the packed bed (ε) in (17.12) ranged from 0.24 for milled black pepper (Ferreira et al. 1999) to 0.901 for rapidly decompressed oregano (Uquiche et al., submitted). We assumed a typical value ε = 0.6 in absence of a reported value (Mira et al. 1996; Papamichail et al. 2000; Louli et al. 2004; Zizovic et al. 2007a).

Figure 17.5 summarizes corrected values of kf from the literature in a dimensionless plot of Sh/Sc1/3 versus Re, where Sh is the dimensionless Sherwood number defined in (17.13):
Fig. 17.5

Dimensionless plot of Sh Sc−1/3 versus Re [where Sh, Sc, and Re are the dimensionless Sherwood (17.11), Schmidt (17.7), and Reynolds (17.6) numbers] for literature values of the external mass transfer coefficient (kf) in SCFE of plant essential oils as a function of the flow regime in the packed bed. Plotted values were estimated from best-fitting parameters reported by the identified authors using the following models (model names reported in Table 17.1): Open image in new window EMTC model applied by Ferreira et al. (1999) and Kotnik et al. (2007); Open image in new window R-SO model applied by Papamichail et al. (2000) and Louli et al. (2004); Open image in new window LDF/UENA model applied by Papamichail et al. (2000) and Louli et al. (2004); Open image in new window LDF/PF/CDIC model applied by Coelho et al. (1997); Open image in new window LDF-Sph/PF model applied by Esquivel et al. (1996); Open image in new window LDF/ADPF model applied by Reverchon and Marrone (1997); Open image in new window Sovova’s model applied by Mira et al. (1996, 1999), Papamichail et al. (2000), Povh et al. (2001), Ferreira and Meireles (2002), Sousa et al. (2002, 2005), Martínez et al. (2003, 2007), Rodrigues et al. (2003), Louli et al. (2004), Campos et al. (2005), Perakis et al. (2005), Vargas et al. (2006), and Bensebia et al. (2009); Open image in new window IBC/PF model applied by Louli et al. (2004); Open image in new window IBC/PFNA model applied by Sovová et al. (1994b); Open image in new window IBC/PF/PCPR model applied by Sovová (2005), Machmudah et al. (2006), and Langa et al. (2009); Open image in new window DDD/PM model applied by Kim and Hong (2002); Open image in new window SC/PF model applied by Germain et al. (2005); and Open image in new window SC/ADPF model applied by Steffani et al. (2006)

$$ Sh = \frac{{{k_{\rm {f}}}{d_{\rm {p}}}}}{{{D_{12}}}} $$
(17.13)
Figure 17.5 also includes reference lines corresponding to correlations in the literature for the external mass transfer coefficient in packed beds operating with liquids, gases, and SCFs. The correlations include the equation of Wakao and Kaguei (1982) for mass transfer in packed beds with low-pressure liquids and gases (17.14), which is valid for 3 < Re < 3,000 and 0.5 < Sc < 104, and the equation of Puiggené et al. (1997) for evaporation of 1,2-dichlorobenzene from glass beads into a high-pressure CO2 stream (17.15), which is valid for 10 < Re < 100 and Sc < 10.
$$ Sh = 2 + 1.1\;R{e^{0.6}}\;S{c^{0.33}} $$
(17.14)
$$ Sh = 0.206\;R{e^{0.8}}\;S{c^{0.33}} $$
(17.15)

The experimental values of Sc for the kinetic studies in Table 17.2 ranged from 2.05 to 17.0, and this result conditioned the selection of values for the two lines corresponding to the correlation of Wakao and Kaguei (1982) in Fig. 17.5. The values of mass transfer coefficients predicted by Wakao and Kaguei (1982) for liquids and gases (17.14) are above those predicted by the literature correlations for mass transfer in packed beds operating with SCFs under forced convection (del Valle and de la Fuente 2006). Among the specific correlations for mass transfer in packed beds operating with SCFs, the predictions made in the equation of King and Catchpole (1993) are above those made in the equation of Tan et al. (1988), which are in turn above those made in (17.15) (del Valle and de la Fuente 2006). Thus, the expected estimated values of Sh/Sc1/3 derived from the studies in Table 17.2 should be seen between the top and bottom lines in Fig. 17.5.

Figure 17.5 shows that experimental values of Sh/Sc1/3 for the SCFE of plant essential oils exhibit considerable scattering (a span covering 3 orders of magnitude was observed, e.g., with data of Kim and Hong 2002), and are generally smaller (up to several orders of magnitude) than those predicted by the literature correlations. Most best-fit values were below the predictions of (17.15) with the exception of values of Papamichail et al. (2000) and Martínez et al. (2007), and a single value of Mira et al. (1999) using Sovová’s model (Table 17.1), some values of Papamichail et al. (2000) and Louli et al. (2004) using model LDF/UENA, values of Machmudah et al. (2006) and Langa et al. (2009) using model IBC/PF/PCPR, and values of Steffani et al. (2006) using model SC/ADPF (who used (17.14) to get first guess values for kf). Smaller best-fit values than predictions of literature correlations are probably due to a combination of several factors, including underestimation of the contribution of internal (solid phase) mechanisms to the total resistance to mass transfer, overestimation of the mass transfer area, underestimation of solvent flow heterogeneity effects, and underestimation of natural convection effects.

Some kinetic models assume that the extraction rate is controlled by external resistances to mass transfer (Ferreira et al. 1999; Kotnik et al. 2007). If this is not the case, the best-fit value of kf would be smaller than in model systems without internal resistance to mass transfer, as those used to obtain the two correlations reported in Fig. 17.5, to compensate the contribution to the total resistance of the solid matrix (del Valle and de la Fuente 2006). This will also occur if the internal resistance to mass transfer is not neglected, but underestimated.

An overestimation of ap would also be compensated by an underestimation of the value of kf in cases where an overall mass transfer coefficient (kfap) is used as a fitting parameter for experimental data (del Valle and de la Fuente 2006). In the work presented in this chapter the assumption is that the solid particles were spherical ((17.12) for ψ = 6), and although spheres have the smallest surface-area-to-volume ratio among regular geometric shapes, not all of the external surface of the particles is fully available for extraction due to tight packing in low-porosity beds (Marrone et al. 1998) or agglomeration of solid particles (Štastová et al. 1996; Eggers et al. 2000; del Valle et al. 2008).

Other causes of a reduction in the extraction rate and an associated reduction in the best-fitting value of kf are irregularities in the packing of solid particles and other nonidealities that change the interstitial velocity of the high-pressure CO2 across the extraction vessel (del Valle et al. 2004). Indeed, it is possible to have high-velocity zones near the wall of an extraction vessel coexisting with low-velocity zones close to the axis of the vessel, with the end result of smaller extraction rates and smaller values of kf in the axis than near the wall of the vessel (Sovová et al. 1994b; del Valle et al. 2004). These changes in velocity can be explained by the radial variations in bed porosity that result when packing comparatively large particles in small-diameter vessels (i.e., when dp/D < 10 for mono-disperse particles) or radial variations in solvent viscosity when heating the packed-bed contents by conduction through the wall of the extraction vessel. Consequently with this hypothesis Brunner (1994) reported that the residual content of theobromine in ground cocoa seed shells increases when moving from the vessel wall toward the center of the extraction vessel in large-scale extraction experiments, and that these changes in residual solute content are more pronounced when the superficial velocity of high-pressure CO2 decreases from 3.5 to <1.7 mm/s. The global effect of these changes is a reduction in the average value of the external mass coefficient (del Valle et al. 2004).

The last explanation for the differences between experimental and correlated values of kf is neglecting the undesirable effects of natural convection on the external mass transfer. The natural convection phenomenon is important in experiments where high-pressure CO2 moves slowly upwards in a vertical extraction vessel and against the gradient in density (Δρ = ρsat − ρ) that develops when essential oils dissolve into the CO2 stream, a condition under which the loaded CO2 phase moves down under the influence of the force of gravity (Stüber et al. 1996; Puiggené et al. 1997; Germain et al. 2005). Thus, the extraction rate in a SCFE system using CO2 upflow conditions is smaller than in a system using downflow conditions due to the negative influence of natural convection on mass transfer opposed by gravity (Sovová et al. 1994a, b; Stüber et al. 1996; Germain et al. 2005). This is important to consider in SCFE of plant essential oils because of several factors favoring undesirable convection phenomena (Germain et al. 2005): (1) the preference of solvent upflow conditions in industrial practice to improve extraction by fluidization of small particles and avoidance of compaction of the packed bed; (2) the use of near-critical conditions for extraction (Table 17.2); (3) the large solubility of essential oil components in high-pressure CO2 under typical extraction conditions (Sect. 17.4); and (4) the use of a small superficial solvent velocity in experimental studies, as reported in the literature. Both correlations presented in Fig. 17.5 apply under forced convection conditions, but not when natural convection effects start to dominate as the ratio Gr/Re2 increases (>> 1), where Gr is the dimensionless Grashof number defined in (17.16):
$$ Gr = \frac{{g\;d_{\rm {p}}^3\;{\rm rho^2}\;\Delta \rm rho }}{{{c_{\rm {sat}}}\;{\rm mu^2}}}. $$
(17.16)

Germain et al. (2005) showed that for the extraction of caraway essential oils with high-pressure CO2 at 313 K and 9–10 MPa (Sc = 2.13), another correlation of Puiggené et al. (1997) that takes into account the effect of natural convection phenomena predicts smaller values of the external mass transfer coefficient when mass transfer is opposed by gravity (CO2 upflow conditions) than when it is aided by gravity (CO2 downflow conditions), whereas there are virtually no differences in Sh/Sc1/3 for a relatively large Re (e.g., Re ≥ 50). For a value of Re slightly below (Re ≈ 10) the value of Sh/Sc1/3 drops pronouncedly; this drop is only slightly dependent on the value of Gr (for 10 < Gr < 38,000), but shifts to smaller values of Re as the value of Sc decreases (e.g., Re ≈ 2.5 for Sc = 34.4). This helps to explain some of the experimental results reported in Fig. 17.5.

In selected cases, the value of kf was not fitted to a cumulative extraction plot, but instead adopted from a literature correlation for forced convection. Goto et al. (1993, 1998), Spricigo et al. (2001), and Steffani et al. (2006) used the equation of Wakao and Kaguei (1982). Several authors used the equation of Tan et al. (1988), including Reverchon et al. (1993a), Reverchon (1996), Goodarznia and Eikani (1998), Perakis et al. (2005), Zizovic et al. (2005, 2007a,b,c), Salimi et al. (2008), and Stamenić et al. (2008). Catchpole et al. (1996b), Gaspar et al. (2003), Ruetsch et al. (2003), Daghero et al. (2004), and Machmudah et al. (2006) used the equation of King and Catchpole (1993). Araus et al. (2009) and Uquiche et al. (submitted) used the equation of Puiggené et al. (1997). It is relevant to mention that in most of these studies, the selected equations were applied for values of Re below the limit where the natural convection effects must be taken into account. Two exceptions where natural convection phenomenon was accounted for are the works of Akgun et al. (2000), who used the equation of Lee and Holder (1995), and Germain et al. (2005), who use an equation of Puiggené et al. (1997).

17.3.3 Effective Diffusivity in the Solid Matrix

To compare the best-fit internal mass transfer parameters in the reviewed studies in this work, the value of a microstructural factor FM (17.17) that embodies all effects of the substrate and its pretreatment on inner mass transfer was estimated (Aguilera and Stanley 1999; del Valle and de la Fuente 2006; Araus et al. 2009; Uquiche et al. submitted):
$$ {F_{\rm {M}}} = \frac{{{D_{^{12}}}}}{{{D_e}}}. $$
(17.17)

The term FM gives the retarding effect of the solid matrix on the mass transfer rate by indicating how many times smaller the effective diffusivity of the essential oil is in the treated plant material than its binary diffusion coefficient in high-pressure CO2. It is convenient to use FM instead of De in modeling SCFE processes because it is independent of extraction temperature and pressure, interstitial solvent velocity, and substrate particle size (Araus et al. 2009).

There are some problems in expressing the internal mass transfer parameters as reported in the literature in consistent units. For example, some contributions describe the best-fit value of an internal mass transfer coefficient ki (expressed in, e.g., m/s) (Reverchon et al. 1999; Reis-Vasco et al. 2000) or the product kiap (expressed in, e.g., s−1) (Sovová et al. 1994a; Esquivel et al. 1996; Mira et al. 1996, 1999; Coelho et al. 1997; Ferreira et al. 1999; Papamichail et al. 2000; Povh et al. 2001; Ferreira and Meireles 2002; Sousa et al. 2002, 2005; Martínez et al. 2003, 2007; Rodrigues et al. 2003; Louli et al. 2004; Campos et al. 2005; Perakis et al. 2005; Sovová 2005; Machmudah et al. 2006; Vargas et al. 2006; Bensebia et al. 2009; Langa et al. 2009), and in these cases the effective diffusivity was computed using the relationship between De and the reciprocal of kiap (or the so-called internal diffusion time ti, s) proposed by Villermaux (1987) and reported in (17.18):
$$ {D_{\rm {e}}} = \frac{{{k_{\rm {i}}}{d_{\rm {p}}}}}{{\left( {1 - \varepsilon } \right)\;\xi }} $$
(17.18)
where the particle-geometry parameter ξ was defined in connection with (17.5) in Sect. 2.3 (ξ = 10 for a sphere, ξ = 6 for a for thin slab).
When values of the effective diffusivity were reported, those cases were distinguished where they referred to the movement of the pseudo-solute in the solid (e.g., diffusion model), from those referring to movement in the fluid phase trapped in the solid (e.g., DDD models, SC models). Under the latter conditions, the values of De can be estimated according to (17.19) (del Valle and de la Fuente 2006):
$$ {D_{\rm {e}}} = {D/prime_e}K $$
(17.19)
where \( D_{\rm {e}}^/prime \)(the effective diffusivity of the pseudo-solute in the fluid trapped within the pores of the solid matrix) is the reported value, and K, the partition of the pseudo-solute between the SCF and the herb or spice which, in absence of a reported value (Sovová et al. 1994a; Mira et al. 1996, 1999; Coelho et al. 1997; Ferreira et al. 1999; Papamichail et al. 2000; Povh et al. 2001; Ferreira and Meireles 2002; Martínez et al. 2003, 2007; Rodrigues et al. 2003; Louli et al. 2004; Campos et al. 2005; Perakis et al. 2005; Vargas et al. 2006; Bensebia et al. 2009), is estimated using (17.20):
$$ K = \frac{{{C_{\rm {fo}}}}}{{{C_{\rm {so}}}}} $$
(17.20)
Table 17.4 is an example of computed values of FM in the case of SCFE of essential oils from oregano bracts, reporting the effect on FM of different independent variables such as extraction temperature, extraction pressure, superficial velocity of the CO2, sample pretreatment, and sample particle size. It is important to note that in those experiments where Esquivel et al. (1996), Gaspar (2002) (data modeled by Araus et al. 2009), and Gaspar et al. (2003) studied the effect of extraction temperature and/or extraction pressure, they also changed the superficial velocity of the CO2, because they kept the mass flow rate constant instead. Indeed, the superficial velocity of the CO2 (U) depends not only on its mass flow rate (Q), but also on its density (ρ) under process conditions, which is a strong function of the extraction temperature and pressure, especially under near-critical conditions, according to (17.21):
$$ U = \frac{{4\;Q}}{{\pi \;{{D}}_{\rm {E}}^2\;\rho }} $$
(17.21)
As proposed by Araus et al. (2009), it was expected that the values of FM are dependent on sample pretreatment, but independent of process temperature, process pressure, CO2 superficial velocity, and substrate particle size, but clearly this is not the case (Table 17.4). Some of the differences can be imputed to typical variations in biological materials associated with differences in genetic makeup, growing environment, and harvest time (Zetzl et al. 2003). Although some differences were expected between the samples assayed by Esquivel et al. (1996), Gaspar (2002), Gaspar et al. (2003), and Uquiche et al. (submitted), which explains why the differences were smaller between experiments in a single study than among the four studies, the percent differences in estimated values of FM between experiments in single studies were clearly still large. The very large difference in values of FM between the sample with dp = 1.55 mm (untreated sample) and all other samples in the study of Gaspar et al. (2003) can be explained by the positive effect of sample milling in reducing internal resistance to mass transfer. Uquiche et al. (submitted) also imputed the differences in values of FM between their samples to microstructural differences caused by conventional milling, low-temperature milling, and rapid decompression of oregano and provided microscopy evidence of these differences. In work presented in this chapter the composition of the essential oil sample of oregano reported by Gaspar (2002) was used as representative of the extracts obtained in all experiments (Table 17.5); however, this assumption may be erroneous because of the aforementioned variability exhibited by biologic materials, as well as the variability in extract composition with process temperature and process pressure (i.e., extracts obtained using higher density CO2 are expected to contain heavier and more polar compounds than the sample analyzed by Gaspar). As it will be analyzed later in this section, the errors introduced when not accounting for the actual composition are not as large as those observed in Table 17.5 and, in addition, differences were not expected in extract composition as used in experiments done by Gaspar et al. (2003) to assess the effect on extraction kinetics of the superficial solvent velocity, or the size of milled particles (Table 17.5). In this work, the authors believe mathematical models adopted and their ability to fit the physical picture of the actual extraction process explain the differences among estimated values of FM reported in Table 17.5 to a large extent. For example, in the work of Gaspar et al. (2003) average values of FM were 7.32 × 105 (range of value between 2.65 × 105 and 5.72 × 106) using model IBC-Diff (Table 17.5), 4.28 × 105 (range: 1.46 × 105 to 3.81 × 106) using model Diff-Slab/IC, and 4.19 × 105 (range: 1.38 × 105 to 3.81 × 106) using model Diff-Slab/PM. Furthermore, values of FM for a selected experiment of Gaspar et al. (2003) – dp = 0.360 mm/T = 300 K/P = 8 MPa/Q = 8.33 g CO2/min – differed by a factor of more than 10 depending on the model: 3.13 × 105 using model IBC-Diff (Gaspar et al. 2003) and 2.64 × 105 using model Diff-PF (Araus et al. 2009).
Table 17.5

Values of microstructural factor for high-pressure CO2 extraction of essential oils from oregano in selected studies from Tables 17.1 and 17.2 as a function of extraction conditions (system temperature and pressure, superficial velocity) and sample pretreatment and particle size

Studied effect

Independent variable

Microstructural factor (FM, –)

Reference

Process conditionsa

T = 298 K/P = 7 MPa

34,900

Esquivel et al. (1996)

T = 313 K/P = 10 MPa

3,600

T = 313 K/P = 15 MPa

1,880

Process pressureb

P = 7 MPa

409,000

Gaspar et al. (2003)

P = 8 MPa

313,000

P = 10 MPa

265,000

P = 15 MPa

277,000

Process temperaturec

T = 300 K

277,000

Gaspar et al. (2003)

T = 310 K

308,000

T = 320 K

390,000

Superficial solvent velocityd

U = 0.017 mm/s

593,000

Gaspar et al. (2003)

U = 0.029 mm/s

542,000

U = 0.040 mm/s

519,000

U = 0.052 mm/s

479,000

Sample particle sizee

dp = 0.330 mm

440,000

Gaspar et al. (2003)

dp = 0.360 mm

440,000

dp = 0.700 mm

477,000

dp = 1.550 mm

5,720,000

Sample pretreatmentf

Conventionally milled (dp = 0.354 mm)

2,650

Uquiche et al. (submitted)

Low-temperature-milled (dp = 0.339 mm)

2,540

Rapidly decompressed (dp = 0.844 mm)

1,000

ap = 1.10 mm/Q = 8.33 g CO2/min

bdp = 0.36 mm/T = 300 K/Q = 8.33 g CO2/min

cdp = 0.36 mm/P = 15 MPa/Q = 8.33 g CO2/min)

ddp = 0.36 mm/T = 310 K/P = 10 MPa

eT = 300 K/P = 7 MPa/U = 0.017 mm/s

fT = 313 K/P = 10 MPa/U = 1.234 mm/s

Table 17.6 supports the claim that mathematical models and their ability to fit the physical picture of the actual extraction process explain the differences among estimated values of FM to a great extent in the case of four different substrates. For basil, marjoram, and rosemary average values of FM were approximately 1.5 times larger using model Diff-Sph/PM (Reverchon et al. 1993a) than model Diff-ADPF (Goodarznia and Eikani 1998), and approximately 70 times larger using model Diff-ADPF than model μS/SGl (Zizovic et al. 2005). For caraway, values of FM were 20–110 times larger using model IBC/PFNA (Sovová et al. 1994a) than model Diff-ADPF (Goodarznia and Eikani 1998), and approximately 10 times larger using model Diff-ADPF than model SC/PF (Germain et al. 2005). Finally, for pennyroyal values of FM were 1.5–3.5 times larger using model Diff-PF (Araus et al. 2009) than model LDF/ADPF (Reis-Vasco et al. 2000), and for selected experiments 6.8 times larger using model IBC/PF/PCPR (Sovová 2005) or 10.7 times larger using model μS/SGl (Zizovic et al. 2005) than using model LDF/ADPF (Reis-Vasco et al. 2000).
Table 17.6

Values of microstructural factor for high-pressure CO2 extraction of plant essential oils in selected studies from Tables 17.1 and 17.2. All reported values for a single substrate and extraction condition were based on single experiments from an original publication, and fitted by individual authors to different models

Substrate

Original Study

Goodarznia and Eikani (1998)

Zizovic et al. (2005)

Sovová (2005)

Contribution of the authors

Basil (Reverchon et al. 1993a)

91,200

72,000

675

Marjoram (Reverchon et al. 1993a)

97,100

59,100

894

Rosemary (Reverchon et al. 1993a)

48,400

28,800

891

Caraway (Sovová et al. (1994a), extraction at 313 K and 9 MPa)

2,180,000

20,000

1,860 (Germain et al. 2005)

Caraway (Sovová et al. (1994a), extraction at 313 K and 10 MPa)

680,000

36,000

3,620 (Germain et al. 2005)

Pennyroyal (Reis-Vasco et al. (2000), dp = 0.3 mm)

280

436 (Araus et al. 2009)

Pennyroyal (Reis-Vasco et al. (2000), dp = 0.5 mm)

168

817

436 (Araus et al. 2009)

Pennyroyal (Reis-Vasco et al. (2000), dp = 0.7 mm)

120

1,278

436 (Araus et al. 2009)

Table 17.7 reports the interval of FM-values estimated for all mass transfer studies in Tables 17.1 and 17.2 that inform best-fit values of internal mass transfer parameters, with the exception of studies in Tables 17.5 and 17.6. The results of the single experiments were collated using the same material based on this chapter’s hypothesis that the values of FM depend on the sample and its pretreatment, but do not depend on the extraction temperature and pressure, CO2 superficial velocity, and particle diameter (del Valle and de la Fuente 2006; Araus et al. 2009; Uquiche et al. submitted). Explanations of the observed variations in the form of wide intervals for the values of FM were advanced in the previous paragraphs in explaining some differences in Tables 17.5 and 17.6.
Table 17.7

Summary of values of the microstructural factor for high-pressure CO2 extraction of plant essential oils in studies from Tables 17.1 and 17.2 that are not included in Tables 17.4 or 17.5

Substrate

Pretreatment

Model namea

Microstructural factor (FM, –)

Black pepper (Ferreira and Meireles 2002)

Milled

Sovová

(230–2.40) × 107

Black pepper (Perakis et al. 2005)

Milled

Sovová

(12.5–1.47) × 103

Valerian II (Zizovic et al. 2007a)

Milled

μS/SCav

(218–6.79) × 105

Valerian I (Zizovic et al. 2007a)

Milled

μS/SCav

(7.25–3.58) × 106

Valerian III (Zizovic et al. 2007a)

Milled

μS/SCav

(4.63–2.99) × 106

Spearmint (Kim and Hong 2002)

Milled

DDD/PM

(30.1–4.17) × 104

Marigold (Zizovic et al. 2007a)

Milled

Sovová

(68.2–4.06) × 103

Marigold (Zizovic et al. 2007a)

Milled

Diff-Slab/PM

(11.2–4.99) × 104

Sage (Reverchon 1996)

Milled

LDF-Slab/PMMS

5.54 × 104

Sage (Araus et al. (2009)

Milled

Diff/PF

(39.5–3.95) × 103

Sage (Catchpole et al. 1996b)

Chopped

LDF/IMTC

2.52 × 103

Sage (Langa et al. 2009)

Milled

IBC/PF/PCPR

49.9–3.75

Rosemary (Coelho et al. 1997)

Milled

LDF/PF/CDIC

(16.9–7.39) × 102

Rosemary (Bensebia et al. 2009)

Milled

Sovová

(4.34–1.26) × 102

Hop (Pfaf-Šovljanski et al. 2005)

Milled

R-SO

3.20 × 104

Aniseed (Rodrigues et al. 2003)

Milled

Sovová

(30.5–2.09) × 103

Eucalyptus (Zizovic et al. 2007c)

Milled

μS/SCav

1.58 × 104

Chamomile (Povh et al. 2001)

Milled

Sovová

(14.7–7.97) × 103

Chamomile (Araus et al. 2009)

Milled

Diff/PF

1.08 × 104

Chamomile (Kotnik et al. 2007)

Milled

EMTC

(6.65–3.53) × 103

Thyme (Zekovic et al. 2001)

Milled

R-SO

(13.9–1.2) × 103

Orange peel (Mira et al. 1996)

Milled

Sovová

(13.5–1.15) × 103

Orange peel (Mira et al. (1999)

Milled

Sovová

4290–7.29

Orange peel (Zizovic et al. 2007c)

Milled

μS/SCav

1.68 × 102

Ginger (Martínez et al. 2003)

Milled

Sovová

(11.1–2.21) × 103

Alecrim pimenta (Sousa et al. 2002)

Triturated

Sovová

1.03 × 104

Ho-sho (Steffani et al. 2006)

Milled

SC/ADPF

(83.1–4.44) × 102

Parsley (Louli et al. 2004)

Milled

Sovová

(7.53–2.23) × 103

Parsley (Louli et al. 2004)

Milled

Sovová

(7.5–2.54) × 103

Lavender (Reverchon et al. 1995a)

Milled

R-SO

6.41 × 103

Lavender (Akgun et al. 2000)

Manually crushed

SC/PF

(36.8–9.25) × 102

Lavender (Araus et al. 2009)[7]

Milled

Diff/PF

2.03 × 102

Cinnamon of cunha (Sousa et al. 2005)

Triturated

Sovová

(6.17–4.62) × 103

Boldo (Uquiche et al. submitted)

Rapidly decompressed

Diff/PF

5.66 × 103

Boldo (Uquiche et al. submitted)

Conventionally milled

Diff/PF

4.75 × 103

Boldo (Uquiche et al. submitted)

Low-temperature-milled

Diff/PF

4.18 × 103

Nutmeg (Spricigo et al. 2001)

Milled

SC/ADPF

(56.5–3.39) × 102

Nutmeg (Machmudah et al. 2006)

Milled

Fennel (Reverchon et al. 1999)

Milled

LDF/PF

(2.25–2.37) × 102

Celery (Papamichail et al. 2000)

Milled

Sovová

(15.1–2.04) × 102

Celery (Zizovic et al. 2005)

Milled

μS/SDuct

1.28 × 103

Carqueja (Vargas et al. 2006)

Milled

Sovová

(4.25–1.79) × 102

Carqueja (Vargas et al. 2006)

Milled

R-SO

(8.30–1.58) × 102

Clove (Martínez et al. 2007)

Milled

Sovová

84.2–69.6

aModel names are specified in Table 17.1

Table 17.8

Predicted binary diffusion coefficient D12 (m2/s × 108) of selected components in plant essential oils (component 2) in supercritical CO2 (component 1) as a function of system temperature and CO2 density

Solute

MW2 (Da)

Vc2 (cm3/mol)

ρ = 285.0 (kg/m3)

ρ = 682.6 (kg/m3)

313 K (8.1 MPa)

323 K (9.0 MPa)

333 K (9.9 MPa)

313 K (10.0 MPa)

323 K (12.8 MPa)

333 K (15.7 MPa)

Limonene

136.2

507.5

3.38

3.49

3.60

1.37

1.41

1.45

Linalool

154.3

565.5

3.22

3.32

3.42

1.30

1.34

1.38

Linalyl acetate

196.3

682.5

2.95

3.04

3.13

1.19

1.23

1.26

β- Caryophyllene

204.4

722.5

2.88

2.97

3.06

1.16

1.20

1.23

Farnesol

222.4

837.5

2.71

2.79

2.88

1.09

1.13

1.16

Farnesyl acetate

264.4

954.5

2.55

2.63

2.71

1.03

1.061

1.09

n-Octacosane

394.8

1,603.5

2.04

2.11

2.17

0.824

0.850

0.877

Triolein

885.5

3,233.5

1.49

1.54

1.59

0.603

0.622

0.642

According to (17.17), the validity of reported values of the microstructural correction factor in Tables 17.517.7 depends partially on the values of the binary diffusion coefficient (D12) estimated in this chapter using the equation of Catchpole and King (1994). This equation was developed with a large database that did not include typical components in plant essential oils. Table 17.8 displays estimated variations in the D12 of typical components in plant essential oil extracts in high-pressure CO2 as a function of CO2 density and system temperature. Values of D12 decrease when decreasing the temperature (a 6.4% decrease from 333 to 313 K), or increasing the density of the CO2 (a 60% decrease from 285 to 683 kg/m3), or increasing the size of the solute. However, changing D12 to a considerable extent demands extreme changes in extract composition; the reduction is limited to 25% between the heaviest OST (the 17-C farnesyl acetate) and lightest MT (the 10-C limonene), 40% between the wax (the 28-C n-octacosane) and limonene, and 56% between the triglyceride (the 57-C triolein) and limonene. According to this analysis, the discrepancies in D12 associated with the use of the equation of Catchpole and King (1994) and the adoption of an erroneous pseudo-solute could result in discrepancies that are substantially smaller than discrepancies in values of FM reported in Tables 17.517.7.

Another factor that is partially responsible for errors in the estimation of FM, according to (17.19), is the erroneous estimation of the partition K of the pseudo-solute between the solid and the fluid. A discussion of errors in the estimation of K can be found in Sect. 4.4.

There are some reports on the estimation of De for a porous solid as a function of D12 and the inner porosity (εp) of the solid substrate (Goto et al. 1993; Ruetsch et al. 2003; Daghero et al. 2004; Perakis et al. 2005). According to the equation of Wakao and Smith (1962), (17.22), FM can be estimated as follows:
$$ {F_{\rm {M}}} = \frac{1}{{\varepsilon_{\rm {p}}^2}} $$
(17.22)
Considering that in these studies, inner porosity values for the substrates ranged from εp = 0.487 for black pepper (Perakis et al. 2005) to εp = 0.537 for peppermint (Goto et al. 1993), the values of FM estimated using (17.22) ranged from 4.0 to 4.2. Thus, (17.22) produces smaller values of FM than those reported in Tables 17.517.7. Ruetsch et al. (2003) and Daghero et al. (2004) did not measure εp, but assumed a value εp = 0.5. On the other hand, Perakis et al. (2005) estimated the porosity from experimental values of the true density (ρp) of ground particles of black pepper, and the bulk density (ρp) of a packed of the particles according to (17.23):
$$ \varepsilon = 1 - \frac{{{\rm rho_{\rm b}}}}{{{\rm rho_{\rm p}}}} $$
(17.23)
The problem with using (17.21) to estimate the inner porosity of the substrate is that ε is the total porosity of the bed instead of εp, which is smaller. (17.24) relates the inner porosity of the substrate (εp) with the total porosity (ε) and the interparticle porosity of the particles in the packed bed (εb):
$$ {\rm varepsilon_{\rm {p}}} = \frac{{\rm varepsilon - {\rm varepsilon_{\rm {b}}}}}{{{1} - {\rm varepsilon_{\rm {b}}}}} $$
(17.24)

Considering that randomly packed spherical particles in a dense bed have a large ratio, D/dp, for which the expected value of interparticle porosity is εb = 0.36 (Carman 1937), it can be estimated using (17.24) that εp = 0.198 for ε = 0.487, and then using (17.22) that FM = 25.4, which is still small but closer to the experimental values reported in Tables 17.517.7.

This chapter’s analysis of the inner mass transfer within the solid substrate up to this point has implicitly considered that the substrate is a homogeneous material. Tables 17.517.7 include examples of materials being considered as being composed of broken superficial cells and intact inner cells, and total mass transfer in these heterogeneous materials considers separate extraction of the two fractions according to different controlling mechanisms, respectively external resistance to mass transfer, and internal (diffusive) resistance to mass transfer. These models usually use the ratio of broken to intact cells or the fraction of free solute (α) in the pretreated substrate as a fitting parameter; however, this ratio has to agree with the microstructure of the biological substrate, particularly of the specialized secretory structures where plant essential oils are encapsulated. For a spherical particle obtained by milling of a parenquimatous tissue, α is given by (17.25):
$$ \alpha = 1 - {\left( {1 - \frac{{{d_{\rm {c}}}}}{{{d_{\rm {p}}}}}} \right)^3} $$
(17.25)
where the thickness of a superficial layer of ruptured cells is closely related to the diameter (dc) of the specialized secretory structure, and dp is the diameter of the milled particle.
Figure 17.6 shows the effect of the ratio between cell diameter and particle diameter (dc/dp) on the best-fit values of fractions of broken cells (α) in milled herbs or spices containing superficial glands, including oregano bracts (Gaspar et al. 2003), pennyroyal leaves (Sovová 2005), rosemary leaves (Bensebia et al. 2009), and sage leaves (Langa et al. 2009); secretary ducts, including caraway fruits (Sovová et al. 1994a), celery seeds (Papamichail et al. 2000), chamomile flowers (Povh et al. 2001), aniseed fruits (Rodrigues et al. 2003), parsley seeds (Louli et al. 2004), and marigold flowers (Campos et al. 2005); or secretory cavities, such as orange peels (Mira et al. 1996, 1999). For calculations, the cell diameters (dc) estimated from microphotographs in the literature were as follows: for oregano, dc = 78 μm (Svoboda and Svoboda 2000); for pennyroyal, dc = 52.5 μm (Zizovic et al. 2007c); for rosemary, dc = 85 μm (Svoboda and Svoboda 2000); for sage, dc = 52 μm (Serrato-Valenti et al. 1997); for caraway, dc = 123 μm (Svoboda and Svoboda 2000); for celery, dc = 35 μm (Stamenić et al. 2008); for chamomile, dc = 140 μm (Zizovic et al. 2007c); for aniseed, dc = 108 μm (Zizovic et al. 2007c); for parsley, dc = 50 μm (Podlaski et al. 2003); for marigold, dc = 120 μm (Zizovic et al. 2007c); and for orange peels, dc = 500 μm (Svoboda and Svoboda 2000). The line in Fig. 17.6 corresponds to (17.25) which is only valid for size reduction relying on impact or attrition mechanisms that fracture surface cells only. Figure 17.6 shows that (17.25) only partially explains the best-fit values of broken cells reported in the literature, possibly because of differences between the assumed and actual particle shape, microstructure, and fracturing mechanism of the specialized secretory structures in the plant materials.
Fig. 17.6

Effect of particle diameter on the best-fit values of the fraction of broken cells in milled herbs or spices. Calculations were made from data of Open image in new window caraway (Sovová et al. 1994a), Open image in new window orange peel (Mira et al. 1996), Open image in new window orange peel (Mira et al. 1999), Open image in new window celery (Papamichail et al. 2000), Open image in new window chamomile (Povh et al. 2001), Open image in new window oregano (Gaspar et al. 2003), Open image in new window aniseed (Rodrigues et al. 2003), Open image in new window marigold (Campos et al. 2005), Open image in new window pennyroyal (Sovová 2005), Open image in new window parsley (Louli et al. 2004), Open image in new window rosemary (Bensebia et al. 2009), and Open image in new window sage (Langa et al. 2009)

Zizovic et al. (2005, 2007a, b, c) have contributed a series of studies on the mathematical modeling of SCFE of plant essential oils at the micro-scale that demonstrate the need to include a description of the encapsulating secretory structures in plant tissue to improve the predictive capacity of the model. These structures (glandular trichomes or glands, large or small secretory cavities, and secretory ducts) (Sect. 17.1.1), are not equally affected by pre-treatment, nor by the extraction process. For example, milling causes partial destruction of glandular trichomes or glands in the surface of leaves, terminal shoots, and flowers of Laminaceae herbs, and subsequent SCFE causes partial destruction of the remaining glands by a mechanism involving diffusion of CO2 through the gland wall, its dissolution into the essential oil, and swelling the CO2-saturated mixture to the extent of rupturing the gland. Zizovic et al. (2005) obtained microscopical evidence of the rupture of a fraction φ ~ 0.35 of the glands during milling of dried mentha leaves to a final particle diameter of 0.5–1 mm, as well as of the rupture of about ϕ ~ 0.39 of the glands after contacting unmilled leaves with high-pressure CO2 at 313 K and 10 MPa for 1 h. Zizovic et al. (2005) hypothesized that all glands cracked during the process as a result of swelling of the gland contents, become disrupted upon saturation of the essential oil with the CO2 at a single time that is determined by diffusion of CO2 through the gland wall, but later Stamenić et al. (2008) proposed a cracking time distribution based on microscopical evidence gathered by exposing wild thyme leaves to high-pressure CO2 at 313 K and 10 MPa different times between 20 min and 100 min. These models were applied to basil, rosemary, marjoram, and pennyroyal by Zizovic et al. (2005) and to wild thyme by Stamenić et al. (2008).

Unlike superficial glands that can rupture upon swelling of the gland contents by dissolution of CO2 into the essential oil, inner secretory cavities in plant tissue are ruptured only as a result of a size-reduction pretreatment, with the probability of rupture being dependent on the relative sizes of secretory cavities and milled particles. Since the physical picture for the extraction of essential oil from secretory cavities at the microscale is similar to that of intact and broken cells proposed by Sovová (1994) (Sect. 17.2.3), the mathematical model in this particular case considered simultaneous extraction of essential oils from disrupted cavities controlled by an external mass transfer coefficient, and of essential oils from nondisrupted cavities controlled by a best-fit internal mass transfer coefficient. Zizovic et al. (2007a) estimated the fraction of disrupted cavities in milled valerian roots as the ratio between the cavity diameter (determined by microscopy) and the particle diameter (determined by sieving). Zizovic et al. (2007a) estimated the mean diffusion pathway in nondisrupted cells as half the difference between the particle diameter and cavity diameter, but they did not explain the basis for this assumption. This model was applied to valerian roots by Zizovic et al. (2007a), and to clove buds, ginger rhizomes, and eucalyptus leaves by Zizovic et al. (2007c). Consequently, Zizovic et al. (2007c) developed a separate model for SCFE of plant materials with large secretory cavities, such as citrus peels, where most cavities are cracked.

In the case of plant material with secretory ducts, the size-reduction pretreatment opens each duct on two opposite sides of the particle. The essential oil in the duct becomes saturated with CO2 during extraction and the swelling of the mixture results in a superficial layer of oil embedding the whole particle. SCFE can be pictured as a two-stage process. In the first stage, when the mass transfer area is the external surface of the particle, the extraction of essential oil is defined by convection of the superficial oil to the CO2 (mass transfer coefficient from a literature correlation). In the second stage, when the mass transfer area diminishes to that fraction of the external surface of the particle covered with openings of secretory ducts, the essential oil moves from a receding boundary in the pore to the pore opening by unimpeded diffusion (defined by the binary diffusion coefficient of the oil in CO2), and then by convection (the same mass transfer coefficient from the first stage) from the pore opening to the bulk of the high-pressure CO2 phase; the diffusion path for the essential oil in this second stage is half the particle diameter. Zizovic et al. (2007b) proposed a fully predictive mathematical model for SCFE plant material with secretory ducts, which used the diameter of the secretory ducts and their superficial density (number of ducts per unit surface area) as microstructural parameters. The model was applied for fruits of celery (Stamenić et al. 2008), and fruits of fennel, and flowers of chamomile and marigold (Zizovic et al. 2007b).

17.4 Phase Equilibrium Effects in Essential Oil Extraction, Fractionation, and Recovery

In this section, the effect of phase equilibrium on the extraction, fractionation, and recovery of plant essential oils using high-pressure CO2 is discussed. Firstly, the variations in the solubility of essential oil components in high-pressure CO2 are discussed as a function of system temperature and pressure (Sect. 17.4.1). Secondly, there is discussion of the selective removal of high-solubility MTs from the remaining OMTs so as to produce citrus essential oils with an improved functionality (more intense aroma, less off-flavors, increased solubility in water) based on high-pressure phase equilibrium data for ternary CO2 + MT + OMT and more complex systems (Sect. 17.4.2). Next, the thermodynamic solubility in CO2 of complex essential oil mixtures is compared with the “operational” solubility of the CO2 extract of the corresponding herb or spice under comparable temperature and pressure (Sect. 17.4.3). Finally, the effect of sorption phenomena on the aforementioned “operational” solubility (Sect. 17.4.4) is discussed.
Table 17.9

Summary of high-pressure equilibrium CO2 + plant essential oil component binary systems. The essential oil components were classified as monoterpene hydrocarbons, oxygenated monoterpenes, sesquiterpene hydrocarbons and oxygenated sesquiterpenes, and waxy compounds

Solute

Data points

Temperature(s) or temperature range (K)

Pressure(s) or pressure range (MPa)

Solubility range (mg solute/g CO2)

Monoterpenes

p-Cymene (Wagner and Pavlicek 1993)

16

313–323

3.855–9.829

6.73–41.7

Limonene (di Giacomo et al. 1989)

26

308, 315, 323

3.0–10.0

0.681–142

Limonene (Matos et al. 1989)

14

318, 323

8.6–9.8

12.4–106

Limonene (Marteau et al. 1995)

29

310, 320, 323

6.96–9.85

5.58–73.2

Limonene (Iwai et al. 1996)

15

313, 323, 333

3.94–10.26

3.41–24.3

Limonene (Akgun et al. 1999)

22

313, 323, 333

7.04–11–20

1.24–54.8

Limonene (Chang and Chen 1999)

28

314, 323, 333

0.83–11.00

1.55–47.2

Limonene (Vieira de Melo et al. 1999)

16

323, 333, 343

7.00–10.55

4.96–88.2

Limonene (Kim and Hong 1999)

11

312, 322

6.2–9.3

3.10–79.4

Limonene (Berna et al. 2000)

8

318

6.9–10.5

5.27–1,202

Limonene (Gamse and Marr 2000)

42

304, 314, 324

3.1–8.4

2.79–65.4

Limonene (Benvenuti and Gironi 2001)

8

315

3.05–8.50

5.89–18.4

Limonene (Leeke et al. 2001)

15

318, 323

7.32–10.05

2.79–81.3

Limonene (Francisco and Sivik 2002)

8

313, 333

8–25

12.4–89.2

Limonene (Fonseca et al. 2003)

4

323

8.3–9.5

130–244

α-Pinene (Pavlicek and Richter 1993)

72

313, 323, 328

3.25–9.75

3.60–54.3

α-Pinene (Richter and Sovová 1993)

24

296–335

6.14, 7.65

4.15–102

α-Pinene (Akgun et al. 1999)

19

313, 323, 333

7.15–10.93

5.27–53.5

α-Pinene (Francisco and Sivik 2002)

8

313, 333

8–25

9.32–82.7

Oxygenated monoterpenes

p-Anisaldehyde (Mukhopadhyay and De 1995)

13

323, 373

5.5–13.7

0.619–43.9

Camphor (Akgun et al. 1999)

39

313, 323, 333

7.51–12.61

2.98–139

Camphor (Carvalho et al. 2006)

15

314, 324, 334, 354

8.65–15.71

32.5–275

Carvacrol (Leeke et al. 2001)

49

313, 323

7.70–30.85

9.59–740

Carvone (Kim and Hong 1999)

13

312, 322

6.2–9.6

0.307–59.0

Carvone (Gamse and Marr 2000)

31

304, 314, 324

2.0–10.0

0.683–50.9

1,8-Cineole (Matos et al. 1989)

15

318, 323

7.75–9.80

14.1–82.5

1,8-Cineole (Francisco and Sivik 2002)

8

313, 333

8.0–25.0

10.5–86.2

Citral (di Giacomo et al. 1989)

29

308, 315, 323

3.0–11.0

0.104–78.9

Citral (Marteau et al. 1995)

26

310, 320, 330

7.94–11.93

2.42–4.85

Citral (Benvenuti and Gironi 2001)

10

315

4.70–9.58

0.692–36.0

Citral (Fonseca et al. 2003)

4

323

8.7–10.3

32.5–143

β-Citronellol (Tufeu et al. 1993)

15

309, 316, 321

8.46–15.70

25.8–160

Eugenol (Cheng et al. 2000)

21

308, 318, 328

1.480–12.512

4.48–61.8

Fenchone (Akgun et al. 1999)

21

313, 323, 333

7.04–11.50

1.04–1.04

Geraniol (Tufeu et al. 1993)

9

309, 316, 321

10.82–16.27

37.9–120

Linalool (Chang and Chen 1999)

29

313, 323, 333

0.81–11.06

1.05–35.4

Linalool (Vieira de Melo et al. 1999)

3

323

7.49–8.37

1.75–4.56

Linalool (Berna et al. 2000)

13

318, 328

7.1–11.1

2.39–1,381

Linalool (Fonseca et al. 2003)

3

323

8.6–9.4

132–196

Linalool (Iwai et al. 1994)

14

313, 323, 333

4.00, 10.96

1.05–27.9

Linalool (Raeissi and Peters 2005)

12

319–348

9.355–13.705

71.5

Menthol (Carvalho et al. 2006)

12

323, 343

6.5–13.5

0.256–218

Menthol (Sovová and Jež 1994)

40

308, 313, 318, 323, 328

6.52–11.56

0.782–47.1

Menthol (Sovová et al. 2007)

47

303, 313, 323, 333

6.64–14.37

1.24–147

Thymol (Carvalho et al. 2006)

12

323, 343

6.5–13.5

19.6–497

Verbenol (Richter and Sovová 1993)

73

313, 323, 328

5.09–13.78

0.208–194

Sesquiterpenes and oxygenated sesquiterpenes

β-Caryophyllene (Michielin et al. 2009)

86

303, 313, 323, 333, 343

4.5–19.2

18.7–522

Artemisinin (Xing et al. 2003)

36

310, 318, 328, 338

10.0–27.0

0.628–17.1

Farnesol (Núñez et al. 2010)

58

313, 323, 333

9.7–26

0.657–9.67

α-Humulene (Michielin et al. 2009)

77

303, 313, 323, 333, 343

4.7–19.2

18.7–521

Patchoulol (Hybertson 2007)

8

313, 323

10.0–25.0

2.17–48.0

Typical wax component

Octacosane (Reverchon et al. 1993b)

28

308, 313, 318

8.0–27.5

0.110–3.50

Octacosane (Stassi and Schiraldi 1994)

3

308–318

25

0.610–3.36

Octacosane (Chandler et al. 1996)

14

308, 318

10.0–24.0

0.170–4.22

17.4.1 Solubility in CO2 of Essential Oil Components in Model (Binary) Systems

There are many experimental studies about the solubility of selected essential oil components in CO2 as a function of system temperature and pressure, as shown in Table 17.9. The data include four different solute families and CO2 conditions that span from subcooled liquid, to superheated vapor, and to SCF (equilibrium temperatures of 296–373 K, and equilibrium pressures of 0.81–30.9 MPa). There is abundant information in the literature about the solubility of limonene in high-pressure CO2, but virtually none about other 10-carbon MT compounds, the only exceptions being p-cymene and α-pinene (Table 17.9). On the other hand, there is extensive information on the solubility of OMT compounds in high-pressure CO2, including anisaldehyde, camphor, carvacrol, carvone, 1,8-cineole (eucalyptol), citral, β-citronellol, eugenol, fenchone, geraniol, linalool, menthol, thymol, and verbenol (Table 17.9). There is less solubility information about the 15-carbon terpene compounds, which is limited to artemisinin (OST), β-caryophyllene (ST), farnesol (OST), α-humulene (ST), and patchoulol (OST). Finally, although there is extensive information in the literature on the solubility of waxy compounds in high-pressure CO2, Table 17.9 is limited to experimental works with octacosane. Literature on the solubility of waxy compounds includes n-alkanes having 9–36 carbon atoms under typical CO2 extraction conditions, as well as long-chain n-alkanes under typical gas-processing conditions (Stassi and Schiraldi 1994; Chandler et al. 1996; Reverchon et al. 1993b). Stahl et al. (1988) conducted a systematic study on the solubility of essential oil components in high-pressure CO2 including data for limonene, anethole (OMT), carvone, eugenol, β-caryophyllene, and valeranone (OST). This chapter does not include the results of Stahl et al. (1988) in Table 17.9 since they reported trend lines instead of actual experimental data, so their results are of less value for quantitative comparison purposes.

Solubility values of selected essential oil components in high-pressure CO2 vary widely, as exemplified in Fig. 17.7 for the solubility of limonene in high-pressure CO2 at approximately 313 K (310–318 K) and as a function of system pressure, due to the inherent limitations of methodologies applied to assess phase equilibrium (Raal and Mühlbauer 1998). Limonene is the most abundant MT in plant essential oils, representing >90% (w/w) of some of them, because it acts typically as a carrier of other compounds (mainly OMTs) that impact more definitely on plant aroma. The experimental methods can be broadly classified as analytic (if one or both phases in equilibrium are sampled and analyzed to determine composition) or synthetic (if the global composition of the system is predetermined, and the conditions of the system are changed so as to reach a phase boundary). These broad classes, in turn, can be implemented in static or dynamic equilibrium cells, depending on agitation. In dynamic cells, the time to reach equilibrium is shortened by agitation of the cell contents, or recirculation of one or the two phases in the cell (the so-called multi-pass dynamic systems, where sampling is done in recirculation loops). Measurements using all methods are susceptible to error if true equilibrium conditions are not reached, and no single method is more questionable in this regard than the one-pass dynamic method (di Giacomo et al. 1989; Kim and Hong 1999; Gamse and Marr 2000; Benvenuti and Gironi 2001; Fonseca et al. 2003). Observation of the cell contents through a window-cell helps to ascertain the quality of stirring and the number and nature of phases in the system. In the case of analytical methods, where system temperature and pressure are kept constant, sampling and analysis of one phase as a function of equilibration time can help to ascertain whether equilibrium conditions have been reached. Another problem with analytic methods occurs when an incomplete picture of the equilibrium is achieved when only the CO2-rich phase is sampled, and when CO2 transfers to the solute-rich phase (Matos et al. 1989; Berna et al. 2000). A final problem when using an analytic system is the disturbance of system conditions and the associated shift in equilibrium during sampling, which causes a drop in pressure (Iwai et al. 1996; Vieira de Melo et al. 1999). Since these disturbances are unavoidable, users of analytical methodologies try to minimize the negative effects of sampling by using large cells (Akgun et al. 1999; Leeke et al. 2001), or by reducing the size of the sampled aliquot by coupling the cell with a high-sensitivity instrument such as an infrared absorption device (Marteau et al. 1995), a densitometer (Chang and Chen 1999), or a chromatograph (Francisco and Sivik 2002).
Fig. 17.7

Solubility of limonene in supercritical CO2 as a function of system pressure (approximately between 1 MPa and 10 MPa) as reported by Open image in new window di Giacomo et al. (1989) at 313 K, Open image in new window Matos et al. (1989) at 318 K, Open image in new window Marteau et al. (1995) at 310 K, Open image in new window Iwai et al. (1996) at 313 K, Open image in new window Akgun et al. (1999) at 313 K, Open image in new window Chang and Chen (1999) at 314 K, Open image in new window Kim and Hong (1999) at 312 K, Open image in new window Berna et al. (2000) at 318 K, Open image in new window Gamse and Marr (2000) at 314 K, Open image in new window Benvenuti and Gironi (2001) at 315 K, Open image in new window Leeke et al. (2001) at 318 K, and Open image in new window Francisco and Sivik (2002) at 313 K. Lines represent the solubility isotherms at Open image in new window 311 and Open image in new window 318 K predicted using the Peng-Robinson-Mathias-Copeman equation of state with the modified Huron-Vidal (MHV1) – UNIFAC mixing rules and model parameters in database of PE 2000 (Pfohl et al. 2000), a shareware software for modeling high-pressure phase equilibria

The sampling problem inherent in analytic methods can be avoided by using synthetic methods. Synthetic systems use a variable volume cell to change system pressure while keeping the temperature and global composition constant. Raising the pressure (reducing the inner volume of the cell) to make the CO2-rich phase collapse to a single bubble (as is the case when the composition of the liquid phase equals the global composition of the system) determines the bubble pressure at the test temperature. Alternatively, decreasing the pressure (increasing the inner volume of the cell) to cause the solute-rich phase collapse to a single drop (as is the case when the composition of the vapor phase equals the global composition of the system) determines the dew point at the test temperature. A problem of the synthetic method is the inherent difficulty in reaching and determining both bubble and dew point conditions for binary and more complex systems (Marteau et al. 1995).

The solubility of limonene in supercritical CO2 at 313 K increases steadily with system pressure at low pressures (P < 8 MPa) and then increases sharply at high pressures (P > 8 MPa), with the transition between steady and sharp increase occurring close to the critical point of the mixture (Fig. 17.7). The reported critical point of CO2 + limonene mixtures at 313 K is 8.3 MPa (Matos et al. 1989) or 8.5 MPa (Tufeu et al. 1993), and under these conditions the composition of the liquid phase coincides with that of the SCF phase (35.1 g limonene/kg CO2). The binary CO2 + limonene system exhibits a temperature crossover at ~8 MPa (Akgun et al. 1999; Berna et al. 2000). Thus, as the temperature increases isobarically, solubility of limonene in CO2 decreases at P < 8 MPa due to reduction in the density and solvent power of CO2, whereas solubility increases at P > 8 MPa due to the rise in vapor pressure and volatility of limonene. There is a general consistency between experimental solubility data for <8.5 MPa and for <80 g limonene/kg CO2, but the data of Chang and Chen (1999) and Gamse and Marr (2000) are ~3 times and ~10 times, respectively, above the general trend. The results of Francisco and Sivik (2002) are questionable because they report limited solubility of limonene in CO2 under conditions where the two components are mutually miscible (at 313 K and well above the critical pressure of the CO2 + limonene mixture). The data are more diverse at pressures >8.5 MPa due to experimental difficulties in measuring solubilities under conditions near the critical point of a mixture.

Figure 17.7 also includes the solubility isotherms at 310 and 318 K of limonene in high-pressure CO2 predicted using the computer program PE 2000 (Pfohl et al. 2000). PE 2000 models liquid–vapor equilibrium by searching the phase transition corresponding to the bubble-point curve of the CO2 + limonene system. Phase equilibrium was modeled using the modification of Mathias-Copeman of the Peng-Robinson (PR) equation of state (EoS), or the so-called PR-Mathias-Copeman EoS (Poling et al. 2000), and the first modification (or Modification 1, M1) of the Huron-Vidal (HV) mixing rules with the activity coefficients estimated using UNIFAC, or the so-called MHV1-UNIFAC mixing rules (Poling et al. 2000). The database of PE 2000 included all model parameters for the CO2 + limonene system. Figure 17.7 shows a reasonable agreement between the predictions of the model and the experimental measurements, including the temperature cross-over at ~8 MPa. This finding is important because the selected model is of a predictive nature, in that the model parameters for the binary system are not estimated using phase equilibrium data; this chapter will expand on the implications of this feature when comparing the solubilities in high-pressure CO2 of other compounds in Table 17.9.
Table 17.10

Solubilities of selected plant essential oil components in high-pressure CO2 at 313 K and relatively low (approximately 8 MPa) or relatively high pressure (8.6–10 MPa). Essential oil component included representative monoterpene hydrocarbons (limonene and α-pinene) and oxygenated monoterpenes (citral, linalool, and menthol), a sesquiterpene hydrocarbon (β-caryophyllene), an oxygenated sesquiterpene (farnesol), and a hydrocarbon (octacosane)

Compound

Molecular weight (MW, Da)

Vapor pressure (Pv, Pa)

Low-pressure

High-pressure

Pressure (P, MPa)

CO2 density (ρ, kg/m3)

Solubility (Csat, mg/g CO2)

Pressure (P, MPa)

CO2 density (ρ, kg/m3)

Solubility (Csat, mg/g CO2)

Limonene (Benvenuti and Gironi 2001)a

136.2

515 (Espinosa-Díaz et al. 1999)

8.13

295.6

7.04

9.0

408.4

CMc

α-Pinene (Richter and Sovová 1993)

136.2

1,440 (Richter and Sovová 1993)

7.74

252.7

60.1

9.0

408.4

CM

α-Pinene (Akgun et al. 1999)

136.2

1,440 (Richter and Sovová 1993)

7.74

252.7

60.1

Camphor (Akgun et al. 1999)

152.2

133 (Espinosa-Díaz et al. 1999)b

7.97

276.1

3.60

8.8

436.1

98.9

Citral (Benvenuti and Gironi 2001) a

152.2

30 (Stull 1947)

8.00

261.3

1.30

9.0

408.4

7.66

Linalool (Iwai et al. 1994)

154.2

95 (Espinosa-Díaz et al. 1999)

7.99

278.3

5.27

Menthol (Sovová and Jež 1994)

156.3

<133 (Stull 1947)b

7.86

264.3

3.31

9.02

497.9

50.8

β-Caryophyllene (Michielin et al. 2009)

204.4

0.018 (The Good Scents Company 2009a)

8.6

375.9

18.65

Farnesol (Núñez et al. 2010)

222.4

0.192 (The Good Scents Company 2009b)

9.73

609.3

4.29

Octacosane (Chandler et al. 1996)

394.3

~7 × 10–6 (Chandler et al. (1996)

10.0

631.7

0.170

aAt 315 K

bSublimation pressure

cCompletely miscible

Table 17.10 compares the solubilities in high-pressure CO2 of selected solutes from each component family in Table 17.9 to those of limonene, under selected system conditions (313 K and 8 or 9–10 MPa). The density of the CO2 under the selected system conditions bracket the interval proposed by Reverchon (1997) for SCFE of plant essential oils (250–500 kg/m3). At the lower end of recommended CO2 density, ~260 kg/m3 (at 313 K and 8 MPa), the solubility of limonene in high-pressure CO2 is approximately 6 g/kg, which is about 50% lower than the solubility of α-pinene reported by Akgun et al. (1999), probably because of the increased volatility (larger vapor pressure) of α-pinene as compared to limonene at 313 K (Table 17.10). The oxygen-bearing functional groups in OMTs increase their molecular weight and polarity, and decrease their vapor pressure as compared to MTs, which causes the solubility of OMTs in high-pressure CO2 at 313 K and 8 MPa to be about 50% of that of limonene. At the upper end of recommended CO2 density, ~410 kg/m3 (at 313 K and 9 MPa), the binary systems of MTs and CO2 are above their critical points, thus MTs are fully miscible with CO2. Tufeu et al. (1993) reported the critical points at 314 K of the binary CO2 + citral (8.76 MPa, 36.4 g citral/kg CO2) and CO2 + linalool (8.66 MPa, 11.5 g linalool/kg CO2) systems, and these critical point values bring into question the limited solubility of citral in high-pressure CO2 at 313 K and 9 MPa as reported by Benvenuti and Gironi (2001) (Table 17.10). The solubilities in high-pressure CO2 at 313 K and ~9 MPa of the two OMTs in Table 17.10 (camphor and menthol) are approximately 1 order of magnitude larger than the corresponding solubilities of the ST (β-caryophyllene) and OSTs (artemisinin, farnesol, patchoulol), also included in Table 17.10, which are in turn approximately 2 orders of magnitude above the corresponding solubility of a typical wax (n-octacosane), 0.015 g/kg CO2, which is as expected because of the differences in molecular weight (increasing) between OMT compounds, ST/OST compounds, and waxes.

Figure 17.8 expands the results in Table 17.10 to show solubility isotherms of selected compounds in a wider pressure range, together with the estimates of the predictive model in this chapter. In order to use the PR-Mathias-Copeman EoS in PE 2000, an adjustment was made of the so-called model parameters c1, c2, and c3, to vapor pressure data for α-pinene (Daubert and Danner 1989), citral (Hall 2001), linalool (Espinosa-Díaz et al. 1999), β-caryophyllene (Helmig et al. 2003; The Good Scents Company 2009a), farnesol (Helmig et al. 2003; The Good Scents Company 2009b), and n-octacosane (Daubert and Danner 1989; Chandler et al. 1996). Other parameters required were the normal boiling point, critical temperature, critical pressure, and acentric factor for the pure compounds. In those cases where no reliable values for these properties were available, values were estimated using group contribution methods. The normal boiling point of n-octacosane was estimated using Joback’s method (Poling et al. 2000). On the other hand, the critical temperature and critical pressure of citral, linalool, β-caryophyllene, farnesol, and n-octacosane were also estimated using Joback’s method (Poling et al. 2000), whereas the acentric factor of these same solutes was estimated using the method of Lee-Kesler (Poling et al. 2000). PE 2000 includes all of these group-contribution algorithms for the estimation of physical properties. Figure 17.8 shows that the predictive model implemented in PE 2000 gives values of solubility for typical essential components in high-pressure CO2 under typical extraction conditions for herbs and spices that are only qualitatively correct; thus, it can be only moderately appropriate for the purpose of discussing equilibrium effects on mass transfer kinetics as attempted in this chapter. An advantage of the method is that it is fully predictive if a group contribution method is applied to estimate the effect of temperature on the vapor or sublimation pressure of the solutes. Obviously, the predictive capabilities of the model improve when including experimental instead of estimated values of relevant physical properties, as suggested by the better fit of the model to experimental solubility data for limonene (Fig. 17.7) than higher molecular solutes such as STs, OSTs, and waxes (Fig. 17.8 compares the experimental data and predicted solubility isotherms for β-caryophyllene, farnesol, and n-octacosane).
Fig. 17.8

Solubilities of selected plant essential oil components in supercritical CO2 as a function of system pressure (approximately between 1 MPa and 12 MPa), including Open image in new window limonene at 315.7 K; α-pinene at 313 K, data of Open image in new window Richter and Sovová (1993) and Open image in new window Akgun et al. (1999); Open image in new window citral at 315 K, data of Benvenuti and Gironi (2001); linalool at 313 K, data of Open image in new window Iwai et al. (1994) or Open image in new window Chang and Chen (1999); Open image in new window caryophyllene at 313 K, data of Michielin et al. (2009); Open image in new window farnesol at 313 K, data of Núñez et al. (2010); and Open image in new window octacosane at 313 K, data of Chandler et al. (1996). Lines represent the solubility isotherms at corresponding temperatures predicted by the Peng-Robinson-Mathias-Copeman equation of state with the modified Huron-Vidal (MHV1) – UNIFAC mixing rules using PE 2000 (Pfohl et al. 2000). The solubility isotherm for Open image in new window limonene in supercritical CO2 at 315.7 K predicted by PE 2000 is included as a reference

Differences in solubility between solutes using data for binary CO2 + solute systems suggest the possibility of selectively recovering a single solute or mixture of solutes in a complex essential oil sample. A general application of this type of fractionation process is the deterpenation of essential oils, which consists of the selective elimination of oxidation-prone and water-immiscible MTs that mask the characteristic aroma of OMTs in an herb or spice, and cause a haze in aqueous essential oil solutions (Stahl et al. 1988; Temelli et al. 1990; Reverchon 1997). Mukhopadhyay and De (1995) proposed the selective recovery of menthol from peppermint oil based on the solubility isotherms at 323 and 343 K of the binary CO2 + menthol (component 2) and CO2 + thymol (component 3) systems at pressures ranging from 6.5 to 13.5 MPa. They computed the values of the separation factor between menthol and thymol, R23 (17.26), as a function of system temperature and pressure,
$$ {R_{23}} = \frac{{{y_2}}}{{{y_3}}}, $$
(17.26)
and found that 3.37 ≤ R23 ≤ 6.12, which suggests that it is possible to enrich menthol in the high-pressure CO2 phase. Mukhopadhyay and De (1995) neglected the molecular interactions between menthol and thymol, which may affect the separation factor, as exemplified next for the separation of limonene and linalool using high-pressure CO2. It is also important to mention that using the separation factor to draw conclusions about the selective recovery of a component in a binary or multicomponent mixture has limitations in that the analysis should be made by comparing of concentration ratios between the two components in two phases (liquid, SCF) in equilibrium; if these concentration ratios coincide in the two phases, then it is not possible to selectively recover one of the components using high-pressure CO2 as the separating agent. Thus, the selectivity of the separation between menthol and thymol, α23 (17.27), instead of the separation factor R23 should be computed, where:
$$ {\rm alpha_{23}} = \frac{{{{{y_2}} \mathord{\left/{\vphantom {{{y_2}} {{y_3}}}} \right.} {{y_3}}}}}{{{{{x_2}} \mathord{\left/{\vphantom {{{x_2}} {{x_3}}}} \right.} {{x_3}}}}} $$
(17.27)

Chafer et al. (2001) used composition information from the vapor phase for the ternary CO2 (1) + limonene (2) + linalool (3) system to estimate the separation factor R23 so as to evaluate the possibility of recovering a linalool-enriched fraction. They concluded that the deterpenation of linalool was possible based on R23 values of ~2 for mixtures of limonene and linalool containing about 90–95% (mol/mol) of limonene, but also observed that the values of R23 were approximately four times higher when estimated on the basis of binary equilibrium data, which reveals a loss of information when solute–solute interactions in the more complex systems are not accounted for. Because of the requirement of ternary data to assess the fractionating capabilities of high-pressure CO2, this subject is discussed next.

17.4.2 Essential Oil Fractionation in Model (Ternary) Systems and Complex Mixtures

Two CO2-containing tertiary systems of practical importance that have been extensively analyzed in the literature are CO2 + limonene + citral and CO2 + limonene + linalool, because limonene and citral (a mixture of two isomers, geranial and neral) are the key MT and OMT, respectively, in lemon essential oil (Gironi and Maschietti 2008), and linalool replaces citral as the key OMT in orange essential oil (Budich and Brunner 1999). High-pressure CO2 fractionation allows deterpenation of citrus oils so as to improve their shelf life, solubility in water, and aroma (Stahl et al. 1988; Temelli et al. 1990; Reverchon 1997), and the designing of these two deterpenation processes demands phase equilibria data for the aforementioned model systems (Budich et al. 1999; Gironi and Maschietti 2008).

The phase equilibria of the ternary CO2 (1) + limonene (2) + citral (3) system was studied by Benvenuti and Gironi (2001) at 315 K and 8.4 or 9.0 MPa, and by Fonseca et al. (2003) at 323 K and 9.5, 9.7, or 10.3 MPa. Fonseca et al. (2003) reported that the selectivity α23 for the separation between limonene and citral varied between 1.72 and 2.00, which indicates that the vapor (or CO2-rich) phase is enriched in limonene, whereas citral remains in the liquid (or essential oil-rich) phase. This agrees with the vapor pressure ratio between limonene and citral, P2Sat/P3Sat = 17 (Benvenuti and Gironi 2001), which defines separation under low-solubility (relatively small pressure) conditions. The selectivity α23 did not depend on system pressure (9.5–10.3 MPa), nor the composition of the essential oil model mixture (49–73% w/w limonene) (Fonseca et al. 2003). On the other hand, values of α23 estimated by Benvenuti and Gironi (2001) at 315 K ranged from 1 to 62 depending on the limonene content in the CO2-rich phase and the system pressure (limonene content in a CO2-free basis ranged 36–90% mol/mol at 8.4 MPa, and 26–74% mol/mol at 9 MPa).

The vapor–liquid equilibria of the CO2 (1) + limonene (2) + linalool (3) ternary system has been studied by Morotomi et al. (1999) at 313 K and 6.9 MPa, 333 K and 6.9 MPa, or 333 K and 10.0 MPa, by Vieira de Melo et al. (1999) at 323 K and 7.54, 8.08, 8.76, or 8.90 MPa, and by Chafer et al. (2001) at 318 or 328 K, pressures between 7 and 11 MPa, and mixtures having 40% or 60% (w/w) limonene in a CO2-free basis. The selectivity for the separation between limonene and linalool is α23 > 1.2 (Morotomi et al. 1999), which suggests the possibility of enriching limonene in the vapor phase, thus making the isolation of linalool in the liquid phase feasible, particularly in essential oil mixtures enriched in oxygenated compounds. Vieira de Melo et al. (1999) reported that α23 decreases from 3.75 to 2.14 as the pressure increases from 7.54 to 8.90 MPa, probably as a result of the increase in the solvent power of high-pressure CO2 for OMTs. The apparent selectivity at 323 K and 8 MPa based on binary data (α23 = 4.6) was larger than the true selectivity based on ternary data (α23 = 3.6), thus confirming the need for ternary equilibrium data for the design of deterpenation process (Vieira de Melo et al. 1999). Chafer et al. (2001) reported the composition of the vapor phase only; thus, it was not possible to estimate values of selectivity for the separation of limonene and linalool based on their data.

The use of model systems with a limited number of components is appropriate only as a rough estimate of the behavior of more complex natural mixtures. Because of that, Budich and Brunner (1999) and Budich et al. (1999) recommended the estimation of separation factors and other design parameters for the high-pressure CO2 deterpenation process by using actual essential oil mixtures. Cold-pressed orange oil is constituted by about 200 components, mainly MTs (~95% w/w) and OMTs. Temelli et al. (1990) measured the solubility in CO2 of this oil at 313, 323, 333, and 343 K and 8.3, 9.7, 11.0, and 12.4 MPa using a one-pass dynamic method. Experimental results confirmed that CO2 preferably solubilizes MTs so that the selectivity α23 for the separation between limonene (2) and linalool (3), the key components in the MT and OMT fractions, respectively, ranged from 1.10 to 2.83 within the experimental region. Under isothermal conditions, α23 reached a maximum at 9.7 MPa and then decreased to a minimum at 12.4 MPa. Temelli et al. (1990) also reported an unusual increment in solubility at 313 K and 12.4 MPa, which they attributed to the formation of a liquid phase, a common occurrence in systems of high-pressure CO2 and complex liquid mixtures.

Budich and Brunner (1999) studied the equilibrium of CO2 + orange peel oil at 323, 333, or 343 K and 8–13 MPa. For data analysis they assumed orange peel oil as a binary mixture of 98.25% (w/w) terpenes (T, 96.7% w/w limonene) and 1.75% (w/w) oxygenated aroma compounds (A, 28.8% w/w linalool). The solubility of the essential oil in high-pressure CO2 was similar to that of pure limonene, probably because of the elevated content of limonene in orange peel oil. The selectivity αTA ranged from 1.3 to 3.2, which suggests the possibility of removing the MT fraction using high-pressure CO2. Under isothermal conditions, αTA decreases as the pressure increases. For low-solubility values (<10 g extract/kg CO2) αTA decreases with temperature under isobaric conditions because of a more limited increase in the vapor pressure of the OMTs than MTs; for high-solubility values (>50 g extract/kg CO2) αTA increases with temperature due to the reduction in the density and solvent power of the CO2; in the intermediate range (10–50 g extract/kg CO2) there is not a definite trend for the variations in αTA with temperature.

Figure 17.9 compares the values of selectivity measured by Budich et al. (1999) for the multicomponent CO2 + orange peel oil system at 323 and 333 K with those reported for the CO2 + limonene + citral or CO2 + limonene + linalool model systems. For all temperature-solubility pairs, α23 < αTA, e.g., at 323 K the values of α23 reported by de Vieira de Melo et al. (1999) are 25% of the values of αTA, whereas the values of α23 reported by de Fonseca et al. (2003) are ~40% of the values of αTA, and at 333 K Morotomi et al. (1999) report values of α23 ranging from 16% to 51% of corresponding values of αTA at 333 K. Budich et al. (1999) reported that values of αTA at 333 K and 10 MPa decreased pronouncedly as the content of terpenes in the liquid phase increased, or when replacing the real OMT fraction (αTA ~ 2.2 for a 98.3% w/w MT content in the liquid phase) by pure linalool (αTA ~ 1.2). This result is consistent with the value α23 ~ 1.1 reported by Morotomi et al. (1999) for the model limonene + linalool system containing 85% w/w MT in the liquid phase. Based on data in Fig. 17.9, Budich et al. (1999) recommended deterpenation of orange oil at ≥ 333 K, where both αTA (=1.5) and the solubility of the oil in high-pressure CO2 are high enough to make the process economical.
Fig. 17.9

Separation factors between terpenes and aroma (oxygenated) compounds in model and real systems as a function of essential oil concentration in the CO2 phase: α23 for the separation at 323 K of limonene and linalool in a ternary CO2 + limonene + linalool system reported by Open image in new window Vieira de Melo et al. (1999) and Open image in new window Morotomi et al. (1999); Open image in new window α23 for the separation at 333 K of limonene and citral in a ternary CO2 + limonene + citral system (Fonseca et al. 2003); and αTA for the separation at Open image in new window 323 K or Open image in new window 333 K between terpene and aroma (oxygenated) compounds in orange peel oil (Budich et al. 1999)

17.4.3 Thermodynamic and Operational Solubility in the CO2 Extraction of Essential Oils

There have been few publications on high-pressure phase equilibria between CO2 and complex mixtures other than those of Temelli et al. (1990) with cold-pressed orange oil, and those of Budich and Brunner (1999) with orange peel oil. Reported equilibrium isotherms include those of clove bud oil at 303, 308, 313, 318, and 328 K for 5.8–10.8 MPa (Souza et al. 2004); of fennel seed oil at 303, 313, 323, and 333 K for 4.74–21.0 MPa (Moura et al. 2005); of vetiver (Vetiveria zizanioides) root oil at 303, 318, and 333 K for 5–30 MPa (Takeuchi et al. 2008); of candeia (Eremanthus erythropappus) bark oil at 313, 323, and 333 K for 6.27–25.2 MPa (Teixeira de Souza et al. 2008); and of priprioca (Cyperus articulatus) rhizome oil at 313, 323, and 333 K and 4.42–29.9 MPa (Moura et al. 2005). These measurements are usually performed using synthetic methods (Sect. 17.4.1), and are difficult to set up, in that bubble and dew or cloud points are not easily visually identified for complex mixtures of CO2 and natural extracts. With the exception of vetiver root and priprioca rhizome, these studies complement other studies on SCFE (Table 17.1). Furthermore, besides assisting the analysis of the extraction process, the results of these studies can help to optimize the condition of the separation step of the entire SCFE process. Indeed, the high-pressure phase equilibrium for complex CO2 + essential oil systems under typical separation conditions in a SCFE plant (e.g., 273–288 K and 2–9 MPa, Reverchon and De Marco 2008) determines the residual solute content in a recycled CO2 stream, which affects the extraction rate (del Valle et al. 2004), as well as the residual content of CO2 in the extract, which affected solvent losses during the process (Takeuchi et al. 2008).
Table 17.11

Comparison of estimated thermodynamic solubility and operational solubility for selected studies on high-pressure CO2 extraction of plant essential oils

Extract

Temperature (T, K)

Pressure (P, MPa)

Solubility (Csat, mg solute/g CO2)

Orange peel oil

Limonene (Iwai et al. (1994)

313

7.17

6.2

Linalool (Iwai et al. 1994)

313

7.17

2.1

Model oil mixturea

313

7.17

6.0

Actual essential oil (Budich and Brunner 1999)

313

7.17

5.1

Actual essential oil (Budich and Brunner 1999)

313

15

CM*

Ibid. in the presence of substrate (Mira et al. 1996, 1999)

313

15

13.2–19.3

Clove oil

Eugenol (Cheng et al. 2000)

313

8.06

5.6

β-Caryophyllene (Stahl et al. 1988)

313

8.06

2.3

Model oil mixtureb

313

8.06

5.0

Actual essential oil (Souza et al. 2004)

313

8.06

11

Ibid. in the presence of substrate (Martínez et al. 2007)

308

10

230

Fennel oil

Limonene (Iwai et al. 1994)

313

8.02

9.6

Anethole (Stahl et al. 1988)

313

8.02

6

Model oil mixturec

313

8.02

5

Actual essential oil (Moura et al. 2005)

313

8.02

26

Ibid. in the presence of substrate (Reverchon et al. 1999)

313

9

2

Candeia oil

Actual essential oil (Teixeira de Souza et al. 2008)

313

6.17

111

Ibid. in the presence of substrate (Teixeira de Souza et al. 2008)

313

10

4.5

aIdeal solubility estimated neglecting interactions between solutes and assuming orange peel oil as a mixture of 98% (w/w) limonene and 2% (w/w) linalool

bIdeal solubility estimated neglecting interactions between solutes and assuming clove oil as a mixture of 86% (w/w) eugenol and 14% (w/w) β-caryophyllene

cIdeal solubility estimated neglecting interactions between solutes and assuming fennel oil as a mixture of 9% w/w limonene and 91% w/w anethole

*Complete miscibility between the essential oil and high-pressure CO2

Table 17.11 presents the solubilities of essential oil extracts of orange peel, clove bud, fennel seed, and candeia bark under selected temperature and pressure conditions, as taken from the publications of Budich and Brunner (1999), Souza et al. (2004), Moura et al. (2005), and Teixeira de Souza et al. (2008), respectively. Specifically referred to are the values from the P-y branch of isotherms in equilibrium diagrams under the conditions where only two phases (a CO2-rich vapor phase and an essential oil-rich liquid phase) were at equilibrium, which forced the neglect of many data points under conditions where the authors reported partial liquid miscibility. Liquid immiscibility conditions in complex systems result from interactions between minor components in the essential oil mixture, and those interactions have large effects on the actual equilibrium. One such effect is a limited dependence on temperature of the equilibrium concentration of the essential oil in the high-pressure CO2-rich phase. Another effect is unusual variations in essential oil solubility as a function of system temperature and pressure, such as the increase in solubility of cold-pressed orange oil in high-pressure CO2, as reported by Temelli et al. (1990) at 313 K and 12.4 MPa. Taking further advantage of equilibrium data of essential oils in high-pressure CO2 collected up to now demands more detailed experimental evidence.

The thermodynamic solubility values reported in Table 17.11 are different from those expected based on measurements for model binary systems of CO2 and the main MT, OMT, and ST/OST in the actual essential oils. The belief here is that this finding is due to the effect of minor components in the essential oils which, as mentioned before, interact with each other and the major components in the mixture, thus strongly affecting the equilibrium, as exemplified in the following paragraph.

In general, the solubility of a particular substance in high-pressure CO2, such as MT or OMT, may be affected by the presence of other substances in the natural product, such as a wax or a triglyceride, which may exhibit a higher or lower solubility in the CO2. The example of a major MT and a wax is relevant in the particular case of essential oils because, as previously mentioned, they are usually encapsulated within specialized wax-made structures that serve a protective function in herbs (Gaspar et al. 2001). Sovová et al. (2001) reported high-pressure phase equilibria data for a ternary CO2 + limonene + blackcurrant oil system at 313 K and 8–12 MPa, and showed that the solubility of limonene in high-pressure CO2 decreased in the presence of triglycerides for pressures up to 20% higher than the critical pressure of the CO2 + limonene binary mixture (Pcm = 8.44 MPa).

17.4.4 Operational Solubility and Sorption Phenomena in the CO2 Extraction of Essential Oils

Figure 17.1b defines the “operational” solubility of plant essential oils as the concentration of the essential oil in high-pressure CO2 at the outlet of the extraction vessel, provided that CO2 and the herb or spice reach equilibrium conditions as the CO2 travels along the vessel, and there is some free solute in the substrate. The initial slope of the cumulative plot of solute yield versus specific CO2 consumption may represent the actual “operational” solubility only if extraction is preceded by an initial static period to achieve steady temperature and pressure conditions and equilibration between the substrate and the high-pressure CO2. Table 17.11 shows that the operational solubility (in the presence of the solid substrate) of selected essential oils in high-pressure CO2 is smaller than the thermodynamic solubility (in the absence of the solid substrate) under equivalent conditions, probably due to binding of the essential oils to the solid matrix or an insufficient amount of essential oils in the herb or spice to saturate the CO2 (del Valle et al. 2005; Sovová 2005).

Figure 17.10 shows selected values of operational solubility Cfo as a function of the ratio between Cso and ρ, together with trend lines that can be explained on the basis of either limited availability of the essential oil in the solid matrix or a sufficient amount to saturate the high-pressure CO2 phase in a case where the essential oil is not bound to the solid matrix. If the porosity of an extraction vessel with an inner volume V packed with a milled herb or spice of inner porosity εp is ε, the vessel will contain V [ε + (1 − ε) εp] ρ of high-pressure CO2 at system temperature and pressure (at those conditions the density of the CO2 is ρ). If the substrate loaded in the extraction vessel (a total weight V (1 − ε) εp ρs, where ρs is the true density of the solid matrix) initially contains a concentration Cso of essential oil in a solute-free basis, in a situation where there is not enough solute to saturate the CO2 following a static extraction period, (17.28) defines the operational solubility:
$$ {C_{\rm {fo}}} = \frac{1}{{\frac{1}{{{\rm varepsilon_{\rm {p}}}}}\left( {\frac{\rm varepsilon }{{1 - \rm varepsilon }}} \right) + 1}}\frac{{{\rm rho_{\rm {s}}}}}{\rm rho }{C_{\rm {so}}} $$
(17.28)
where the term ε/(1 − ε) represents the ratio of interparticle void volume to apparent particle volume. Equation 17.28 suggests that a plot of Cfo versus (Cso/ρ) (Fig. 17.10) will result in a straight line with a slope m (17.29):
Fig. 17.10

Best-fit values of operational solubility of essential oils in high-pressure CO2 as a function of the initial essential oil content in the herb or spice. Plotted values include substrates with light essential oils (vc ≤ 550 cm3/mol) extracted with low-density (ρ ≤ 650 kg/m3) CO2Open image in new window caraway (Sovová et al. 2004), Open image in new window nutmeg (Machmudah et al. 2006), and Open image in new window sage (Langa et al. 2009) – or high-density (ρ > 650 kg/m3) CO2 – orange peel (Mira et al. 1996, 1999), Open image in new window nutmeg (Spricigo et al. 2001; Machmudah et al. 2006), Open image in new window alecrim pimenta (Sousa et al. 2002), and Open image in new window aniseed (Rodrigues et al. 2003), as well as substrates with heavy essential oils (vc > 550 cm3/mol) extracted with low-density (ρ ≤ 650 kg/m3) CO2Open image in new window chamomile (Povh et al. 2001), Open image in new window carqueja (Vargas et al. 2006), and Open image in new window valerian (Zizovic et al. 2007a) or high-density (ρ > 650 kg/m3) CO2Open image in new window chamomile (Povh et al. 2001), Open image in new window ginger (Martínez et al. 2003), Open image in new window marigold (Campos et al. 2005), and Open image in new window valerian (Zizovic et al. 2007a)

$$ m = \frac{{{\rm rho_{\rm {s}}}}}{{\frac{1}{{{\rm varepsilon_{\rm {p}}}}}\left( {\frac{\rm varepsilon }{{1 - \rm varepsilon }}} \right) + 1}} $$
(17.29)

On the other hand, if there is enough solute to saturate the CO2 phase (Cso/ρ large), Cfo will reach an asymptotic value Csat (the thermodynamic solubility of the complex essential oil mixture in the CO2 under process conditions). It is difficult to compute the slope m in the absence of precise measurements of the bed porosity (ε), the interparticle porosity (εp), and the true density of the matrix (ρs), which may vary depending on the substrate and its pretreatment, but the data in Fig. 17.10 were plotted under the simplifying assumption that m changes little between substrates. Regarding the horizontal asymptote, it is important to stress that Csat is a strong function of the essential oil mixture and the system conditions characterized by the temperature and density of the CO2 (Chrastil 1982).

Figure 17.10 presents selected data that follow the trend suggested by the hypothesis of limited solute in a noninteracting solid matrix. A log–log plot was made to allow a wide range of experimental values in a single plot, and under those conditions a linear relationship such as (17.28) (power relationship with an exponent one) follows a straight line with a unitary slope (such as the trend line included in Fig. 17.10 for values of Cso/ρ below 0.05 g dm3). Fig. 17.10 includes essential oils with relatively low values of critical volume (Vc ≤ 550 cm3/mol) enriched in monoterpene hydrocarbons, oxygenated monoterpenes, and related compounds such as those of aniseed, caraway, alecrim pimenta, nutmeg, orange peel, and sage, and extracts with larger values of critical volume (Vc > 550 cm3/mol) that are instead enriched in heavier sesquiterpenes, waxes, and related compounds, such as the extracts of carqueja, chamomile, ginger, marigold, and valerian. Apparently, heavy extracts and essential oils behave the same for low solute contents (Cso/ρ ≤ 0.05 g dm3) in the solid matrix, as expected; only for high solute contents (Cso/ρ > 0.05 g dm3) do the values for heavy extracts level off to an apparent solubility of Csat ~ 10 g/kg. Another trend that is apparent in Fig. 17.10 is that the values of Cfo for low CO2 density (ρ ≤ 650 kg/m3) tend to be below the values Cfo for higher CO2 densities (ρ > 650 kg/m3), particularly in the upper end of values of Cso/ρ, as expected for an increase in solubility with the solvent power of CO2.
Table 17.12

Summary of operation solubility values in high-pressure CO2 extraction of plant essential oils studies from Tables 17.1 and 17.2, as a function of the extraction conditions and the initial solute content of the substrates

Substrate

Temperature (T, K)

CO2 density (ρ, kg/m3)

Initial solute content (Cso, mg solute/g solute-free)

Operational solubility (Cfo, mg solute/g CO2)

Clove (Martínez et al. 2007)

306

713

157

230

Clove (Ruetsch et al. 2003)

323

581

212

34.0

Clove (Ruetsch et al. 2003)

323

288

212

2.50

Orange peel (Mira et al. 1996)

323

700

100.0

95.0

Orange peel (Mira et al. 1996)

323

700

45.0

8.00

Black pepper (Ferreira and Meireles 2002)

313

780

35.8

93.2

Black pepper (Ferreira et al. 1999)

303, 323

698, 847

35.8

89.0–85.8

Black pepper (Ferreira et al. 1999)

303–323

698–847

14.7

35.3–24.2

Black pepper (Perakis et al. 2005)

313, 323

384–780

92.0–155

3.80–2.50

Caraway (Sovová et al. 1994a)

313

623

28.8

80.9

Caraway (Sovová et al. 1994a)

313

484

28.8

18.2

Nutmeg (Spricigo et al. 2001)

296

819

18.0–69.0

67.5

Nutmeg (Machmudah et al. 2006)

313–323

629–780

58.0

24.0–9.00

Parsley (Louli et al. 2004)

318

742

650

33.0

Parsley (Louli et al. 2004)

308, 318

498, 713

120

8.302.80

Cinnamon of Cunhã (Sousa et al. 2005)

288

851

38.5

28.3

Aniseed (Rodrigues et al. 2003)

313

700–836

31.3–105

27.7–11.0

Alecrim pimenta (Sousa et al. 2002)

283–298

728–891

22.4–34.0

22.7–13.2

Carqueja (Vargas et al. 2006)

313–343

208–486

17.5–24.0

19.1–6.60

Celery (Papamichail et al. 2000)

348, 328

498–742

500

8.31–2.12

Celery (Papamichail et al. 2000)

318

498

62.0

2.12

Ginger (Martínez et al. 2003)

293–313

847–905

20.0–25.0

6.41–5.15

Chamomile (Povh et al. 2001)

303, 313

623–809

22.4–34.2

3.71–1.15

Valerian (Zizovic et al. 2007a)

313, 323

384–780

6.14–12.6

3.22–0.511

Marigold (Campos et al. 2005)

313

718, 780

14.2

2.80

Fennel (Reverchon et al. 1999)

323

288

18.3

2.00

Rosemary (Coelho et al. 1997)

308, 313

629–777

7.05

1.98–1.65

Rosemary (Bensebia et al. 2009)

313, 333

290–780

32.0

0.356–0.238

Boldo (Uquiche et al. submitted)

313

632

13.1

1.75

Pennyroyal (Reis-Vasco et al. 2000)

323

384

25.3

1.16

Sage (Langa et al. 2009)

313, 323

384, 486

12.9–19.2

0.800–0.600

Lavender (Akgun et al. 2000)

323

220–670

15.3

0.418–0.234

Oregano (Uquiche et al. submitted)

313

632

6.02

0.390

Table 17.12 complements Fig. 17.10, providing values of operational solubility (Cfo) reported from studies in Table 17.2 reviewed in this chapter. The data in Fig. 17.10 exhibit scattering because of variations in substrates and their pretreatments, extraction temperatures, and CO2 densities that are not fully accounted for in the plot, and some additional values in Table 17.12 are not fully consistent with the aforementioned trends. Of all single-measurement Cfo values reported in Table 17.12 (boldo, cinnamon of Cunha, fennel, oregano, and pennyroyal), only the one for pennyroyal does not follow the general trends in Fig. 17.10. In the case of rosemary, the data of Coelho et al. (1997) and Bensebia et al. (2009) are inconsistent, and only the Cfo values of Coelho et al. (1997), higher, follow the trend lines in Fig. 17.10. The data on clove by Ruetsch et al. (2003) and Martínez et al. (2007) are outside (above and/or to the right) the upper limits selected for Fig. 17.10 and are inconsistent; only the Cfo values of Martínez et al. (2007) follow the general trends in Fig. 17.10. The data of Perakis et al. (2005) on black pepper, to the right of the upper limit of Cso/ρ (> 0.05 g m3) in Fig. 17.10, are only slightly below the top solubility Csat ~ 10 g/kg for heavy extracts. Finally, the data of operational solubility Cfo of Ferreira et al. (1999) and Ferreira and Meireles (2002) for black pepper are irregularly high, whereas the data of initial solute content Cso of Papamichail et al. (2000) for celery and of Louli et al. (2004) for parsley are too high, considering the typical amount of extractible compounds in those substrates (Moyler 1993).

Goto et al. (1998) showed that the operational solubility of menthol (the main component in the essential oil of mint leaves) is smaller than its thermodynamic solubility in high-pressure CO2 at 313 K and 13.6 MPa, and suggested that the transfer of menthol to the CO2 phase was limited by strong interactions between the essential oil and solid matrix. They also claimed weaker interactions between n-triacontane (the main component in the cuticular waxes of mint leaves) with the solid matrix than between menthol and the solid matrix because the operational solubility of n-triacontane was closer to its thermodynamic solubility than the operational solubility of menthol. As shown in Sect. 17.4.3, solute–solute interactions between the components of the mint leaf extract may be partially responsible for a reduction in the apparent solubilities of menthol and n-triacontane in CO2 when they are a part of a complex essential oil mixture as compared with their corresponding thermodynamic solubilities in the binary CO2 + menthol or CO2 + n-triacontane systems, but this does not negate the possibility of a reduction in their apparent solubility due to some additional interactions between the solutes and the solid matrix.

The effect of solute binding by the solid matrix, which affects solute availability in SCFE, can be accounted for by an equilibrium sorption isotherm that relates the concentration of solute in the high-pressure CO2 phase with the residual content of solute in the solid phase (the pretreated herb or spice) under equilibrium conditions. Some authors hypothesize that the operational solubility Cfo depends on the substrate and extraction conditions, but does not depend on the solute content in the substrate, as reported in Table 17.12. Other authors hypothesize a constant partition coefficient K (17.20) for essential oils between the high-pressure CO2 phase and the solid phase, which may correspond to a linear sorption isotherm (17.30a), derived from (17.20) or the initial slope of another sorption isotherm model for a low essential oil content in the pretreated herb or spice, such as the Freundlich (17.30b), Langmuir (17.30c), or Brunauer-Emmett-Teller (BET, (17.30d) models. Finally, selected authors combine the possibility of a constant Csat for large concentrations of essential oil in the solid matrix (Cso > Clim) and a constant partition coefficient for smaller values of Cso (≤ Clim) using the so-called isotherm of Perrut et al. (1997). Table 17.13 summarizes the values of the linear partition coefficient K (or equivalent partition coefficient, (17.31)), as reported in studies from Table 17.2 reviewed in this chapter.
Table 17.13

Summary of values of solute partition coefficients in high-pressure CO2 extraction of plant essential oils in studies from Tables 17.1 and 17.2, as a function of the extraction conditions and the initial solute content of the substrates

Substrate

Temperature (T, K)

CO2 density (ρ, kg/m3)

Initial solute content (Cso, mg solute/g solute-free)

Solute partition coefficient (K, –)

Cinnamon of Cunhã (Sousa et al. 2005)

288

851

38.5

2.38–2.00

Carqueja (Vargas et al. 2006)

313

486

20.4

0.813

Carqueja (Vargas et al. 2006)

323

285

17.5

0.694

Carqueja (Vargas et al. 2006)

333

235

21.7

0.104

Carqueja (Vargas et al. 2006)

343

208

24.0

0.067

Clove (Ruetsch et al. 2003)

323

288, 581

212.1

0.314

Clove (Daghero et al. 2004)

323

288, 581

212.1

0.022–0.008

Nutmeg (Machmudah et al. 2006)

313

780

58.0

0.300–0.150

Nutmeg (Machmudah et al. 2006)

323

700, 780

58.0

0.300–0.100

Nutmeg (Machmudah et al. 2006)

318

742

58.0

0.200

Boldo (Uquiche et al. submitted)

313

632

13.1

0.134

Parsley (Louli et al. (2004)

308

713

120

0.067a

Parsley (Louli et al. (2004)

318

498, 742

650, 120

0.051–0.023a

Parsley (Louli et al. (2004)

308

713

63

0.0099b

Parsley (Louli et al. (2004)

318

498, 742

63, 450

0.0076–0.0038b

Celery (Papamichail et al. 2000)

328

654

500

0.0605a

Celery (Papamichail et al. 2000)

318

498, 742

63, 270

0.0585–0.0471a

Celery (Papamichail et al. 2000)

328

654

417

0.0046b

Celery (Papamichail et al. 2000)

318

498, 742

417, 476

0.0041–0.00001b

Oregano (Uquiche et al. submitted)

313

632

6.02

0.0647

Peppermint (Goto et al. 1993)

313

445, 777

0.0506–0.0202

Peppermint (Goto et al. 1993)

333

228, 594

0.0331–0.0113

Peppermint (Goto et al. 1993)

353

184, 415

0.0248–0.0066

Sage (Langa et al. 2009)

313

486

17.3–19.2

0.047–0.042

Sage (Langa et al. 2009)

323

384

12.9

0.033

Black pepper (Perakis et al. 2005)

313

486, 629

93.0, 134.0

0.0090–0.0025

Black pepper (Perakis et al. 2005)

323

384

84.0

0.0063

Pennyroyal (Sovová 2005)

323

384

25.3

0.063

aSovová’s model, model R-SO

bModel LDF-UENA

The mathematical models for the linear, Freundlich, Langmuir, and BET’s sorption isotherms are, respectively, as follows:
$$ {\bar{C}_{\rm {s}}} = \frac{{{C_{\rm {f}}}}}{K} $$
(17.30a)
$$ {\bar{C}_{\rm {s}}} = \frac{{{{\left( {{C_{\rm {f}}}} \right)}^n}}}{k} $$
(17.30b)
$${\bar{C}_{\rm {s}}} = \frac{{k\;{C_{\rm m}}{C_{\rm f}}}}{{1 + k\;{C_{\rm f}}}} $$
(17.30c)
$$ {\bar{C}_s} = \frac{{k\;{C_{\rm m}}{C_{\rm f}}}}{{\left( {{C_{\rm {sat}}} - {C_{\rm {f}}}} \right)\left[ {{C_{\rm {sat}}} + \left( {k - 1} \right){C_{\rm {f}}}} \right]}}$$
(17.30d)
where k and n are empirical sorption energy parameters, and Cm (the so-called monolayer coverage of the solid surface) is the maximal amount of essential oil that can hold the solid matrix. Ruetsch et al. (2003) and Daghero et al. (2004) arbitrarily assumed that the monolayer coverage corresponded to the initial solute content (Cm = Cso) in clove. The sorption isotherm models (17.30a–17.30d) are written with Cs instead of Cf as the independent variable because they are adapted from the literature on adsorptive separations. In adsorptive separation processes, where the solute in a fluid phase transfers to a solid phase, there is no upper limit to solute concentration in the fluid phase (for all practical purposes, solute and mobile or fluid phases are mutually miscible), and eventual saturation of the solid matrix imposes an upper limit on the concentration of the solute in the solid for high concentration in the fluid under equilibrium conditions. Depending on the herb or spice and its pretreatment, this upper limit in concentration of solute in the solid substrate is not reached when the concentration of the essential oil in the CO2 is limited by its solubility under process conditions. Because of that, Ruetsch et al. (2003), Daghero et al. (2004), and Salimi et al. (2008) imposed an upper limit (Cf ≤ Csat) to the value of solute concentration in the CO2 phase for high concentrations of solute in the solid phase (Fig. 17.11). Equation 17.31 defines the limit value of K for small value of Cs (Cs → 0) for both Langmuir’s and BET’s sorption isotherm models (Frendlich’s isotherm model predicts limit values, K = 0 for n > 1 and K → ∞ for n < 1):
Fig. 17.11

Sorption isotherm models for equilibrium partition of essential oil between high-pressure CO2 and an herb or a spice as a function of the solute content in the substrate under equilibrium conditions at constant system temperature and pressure

$$ K = \frac{1}{{k\;{C_{\rm m}}}} $$
(17.31)

Observation did not reveal special trends in values of the linear partition coefficients (Table 17.13) as a function of the substrate and its essential oil content, the temperature of the system, or the density of the CO2 (plots not shown). Based on (17.28) for a noninteracting solid matrix, for a packed bed with porosity ε = 0.6, a solid substrate with true density ρs = 1,000 kg/m3, an inner porosity εp = 0.1, and high-pressure CO2 at 323 K and 9 MPa (ρ = 287.5 kg/m3), the expected value of the partition coefficient in a situation of limited essential oil content in the plant material would be K = 0.222, which is between upper and lower limit values reported in Table 17.13. No evidence was found that K increases as the initial essential oil content in the herb or spice increases. Also, no evidence was found that K decreases as the density of the CO2 increases, as expected (a comparison of (17.28), (17.29), and (17.30a) suggests that K = m/ρ for a situation where the essential oil does not interact with the solid matrix).

17.5 Concluding Remarks

This chapter reviewed mass transfer and phase equilibrium parameters that can be used to design industrial SCFE processes for plant essential oils. Relevant mass transfer parameters include an axial dispersion coefficient (Dax) for the migration of the solute in the SCF along the bed; an external mass transfer coefficient (kf) for its movement through the stationary SCF film surrounding the solid particles; and an effective diffusivity (De) for its movement through the solid matrix, which were computed in the form of a so-called microstructural factor (FM). This review suggests neglecting axial dispersion effects to simplify the mass transfer models.

Based on this review, it is recommended that SCFE experiments be carried out under forced convection conditions, and that the external mass transfer coefficient (kf) be estimated using a literature-based correlation between dimensionless variables valid for mass transfer in packed beds operating with SCFs. Best-fitting usually provides underestimations of kf because of the underestimation of internal resistances to mass transfer, overestimation of the specific surface of the solid substrate, neglecting of solvent flow heterogeneity effects when using a small D/dp ratio, and/or neglecting of natural convention effects when using low-Re flow conditions.

The values of the microstructural factor for inner mass transfer in the herb or spice estimated in this chapter ranged from FM = 102 to FM = 105, which suggested pronounced limitations to mass transfer within the solid matrix in the high-pressure CO2 extraction of plant essential oils. The estimated values of FM, unlike those expected, depended on the system (temperature, pressure) conditions, the superficial velocity of the CO2, and/or the particle size of the substrate. Furthermore, for equivalent experiments, the best-fit values of FM changed dramatically depending on the applied mathematical model, which raised questions about the validity of some of the hypotheses of these mass transfer models. To improve the modeling of high-pressure CO2 extraction of plant essential oils, extraction experiments should be complemented by measurements using microscopy and allied/complementary techniques to fully characterize the pretreated solid matrix at a relevant scale (Aguilera and Stanley 1999; Zizovic et al. 2005, 2007a, b, c; Stamenić et al. 2008). Such measurements would result in microstructure–extractability relationships, which could be taken advantage of to optimize the pretreatment of the herb or spice samples prior to SCFE.

Regarding phase equilibrium data for designing industrial SCFE processes for plant essential oils, the conclusion here is that their “operational” solubility in high-pressure CO2 depends markedly on the availability of the solute (the complex essential oil mixture) and its partition between the solid matrix (the herb or spice) and the SCF. The reviewed literature included several phase equilibrium studies using binary systems CO2 + pure essential oil (mainly MT and OMT) component, few studies using ternary CO2 + limonene + citral/linalool systems, and limited studies using CO2 and complex essential oil mixtures (low-pressure CO2 extracts of herbs or spices). Further advancements in this field will require additional fluid phase equilibrium measurements using binary mixtures of CO2 and ST or OST compounds, CO2 + MT + OMT model ternary mixtures representing plant essential oils other than citrus oils, or CO2 + complex essential oil mixtures. Furthermore, given that the “operational” solubility of essential oils in high-pressure CO2 does not depend solely on thermodynamic solubility, quantifying the effect of the availability and binding of the solute to the herb or spice demands additional measurements of the solid-SCF phase equilibrium in addition to the aforementioned fluid phase equilibrium data. Because there is no real evidence in the literature that the solute partition between the solid substrate and the SCF is constant, sorption isotherms should be experimentally measured instead of assuming a sorption pattern and achieving best-fit model parameters as part of the data analysis process.

Notes

Acknowledgments

The present work was funded by the Chilean agency Fondecyt (Regular project 105–0675 and International Cooperation project 703–0033). We are indebted to Verónica Glatzel (PUC) for recalculating from the literature some of the values of external mass transfer coefficient (kf), and effective diffusivities (De) that we report in Sect. 17.3.2 and 17.3.3, respectively; and to Gustavo Lozano (TUHH) for simulating the solubility isotherms for selected essential oil components included in Figs. 17.7 and 17.8 using the predictive methodology described in Sect. 17.4.1 in PE 2000.

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Copyright information

© Springer New York 2010

Authors and Affiliations

  • José M. del Valle
    • 1
  • Juan C. de la Fuente
    • 2
  • Edgar Uquiche
    • 3
  • Carsten Zetzl
    • 4
  • Gerd Brunner
    • 4
  1. 1.Departamento de Ingeniería Química y BioprocesosPontificia Universidad Católica (PUC) de ChileSantiagoChile
  2. 2.Departamento de Procesos Químicos, Biotecnológicos y AmbientalesUniversidad Técnica Federico Santa MaríaValparaísoChile
  3. 3.Departamento de Ingeniería QuímicaUniversidad de La FronteraTemucoChile
  4. 4.Thermische VerfahrenstechnikTechnische Universität Hamburg-Harburg (TUHH)HarburgGermany

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