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Separation Science and Technology

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Supercritical carbon dioxide extraction ofastaxanthin from Paracoccus NBRC 101723:Mathematical modelling study

Jyoti A. Chougle, Sandip B. Bankar, Prakash V. Chavan, Vandana B. Patravale& Rekha S. Singhal

To cite this article: Jyoti A. Chougle, Sandip B. Bankar, Prakash V. Chavan, Vandana B. Patravale& Rekha S. Singhal (2016): Supercritical carbon dioxide extraction of astaxanthin fromParacoccus NBRC 101723: Mathematical modelling study, Separation Science and Technology,DOI: 10.1080/01496395.2016.1178288

To link to this article: http://dx.doi.org/10.1080/01496395.2016.1178288

Accepted author version posted online: 27Apr 2016.Published online: 27 Apr 2016.

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Supercritical carbon dioxide extraction of astaxanthin from Paracoccus NBRC101723: Mathematical modelling studyJyoti A. Chouglea, Sandip B. Bankara,b, Prakash V. Chavanb, Vandana B. Patravalec, and Rekha S. Singhala

aFood Engineering and Technology Department, Institute of Chemical Technology, Nathalal Parekh Marg, Matunga, Mumbai, India;bDepartment of Chemical Engineering, College of Engineering, Bharati Vidyapeeth University, Dhankawadi, Pune, India; cDepartment ofPharmaceutical Sciences and Technology, Institute of Chemical Technology, Nathalal Parekh Marg, Matunga, Mumbai, India

ABSTRACTAstaxanthin (AX) is a secondary metabolite that accumulates inside the cell during Paracoccusfermentation. The fermentation biomass was extracted using supercritical carbon dioxide (SC-CO2).The solubility parameter of AX, CO2 and entrainer solvents was calculated and validated withexperimental results. The pressure and particle size of the biomass had a significant effect on theextraction of AX. A maximum recovery of 963.33 μg/g of AX was obtained after SC-CO2 extraction at40ºC, 350 bar and a run time of 60 min with ethanol (20% v/w) as an entrainer. Further, theexperimental data has been modelled using non-linear regression analysis method.

ARTICLE HISTORYReceived 21 September 2015Accepted 11 April 2016

KEYWORDSAstaxanthin; entrainer;mathematical modelling;solubility parameter;supercritical extraction

Introduction

Carotenoids are naturally occurring pigments havingyellow, orange or red colour. They are one of themost complex classes of natural colours with morethan 750 molecules isolated and structurally character-ized till date. Carotenoids exhibit antioxidant proper-ties, which enables them to prevent the accumulation ofharmful reactive oxygen species (ROS) generated dur-ing cellular metabolism[1] as well as chaotrope-inducedand other stresses.[2–4] They are naturally synthesized ashydrocarbons (carotenes) and their oxygenated deriva-tives as xanthophylls.[5] Xanthophylls contain variousoxygenated functional groups, making them structu-rally and functionally diverse carotenoid pigments.[6]

Astaxanthin (3,3′-Dihydroxy-β,β-carotene-4,4′-dione) is a subclass of xanthophylls, commonlyknown as ketocarotenoid. Astaxanthin (AX) impartshigher antioxidant activity and is comparatively morepolar than other carotenoids.[7] The complex nature ofAX molecule poses difficulty in its chemical synthesis,which yields a mixture of configurationally differentisomers.[8] AX production has been exclusivelyrestricted to the few microorganisms where it is presentas a secondary carotenoid. Microbial pigments playmultifarious roles in the natural ecophysiology of theproducing species and, indeed, in terms of biotechno-logical application.[1,9] A number of algae, yeast and afew bacterial sources producing AX have been isolated

and studied.[10] At present, the emphasis is mainly onalgal and yeast sources. However, their commercialproduction requires a higher incubation time alongwith cumbersome and expensive downstreamprocessing.[11] Hence, bacterial sources such asParacoccus species offer an advantage due to lowerfermentation time. Besides, Paracoccus MBIC 01143increased the accumulation of AX to almost two-foldwhen compared with other strains.[10]

AX is an intracellular pigment where it is naturallypresent and serves its various functions. Hence, thedisruption of the cell wall is an essential step towardsthe extraction of AX. The tough sporopollenin cell wallin the cysts of Haematococcus pluvialis and the thickcell wall of Phaffia hinder AX extraction.[12] A numberof physical processes such as sonication, homogeniza-tion, chemical processes involving solvents and acids,and biological processes like enzymatic cell wall disrup-tion using lytic enzymes have been used for extractionof AX.[13] Sonication can be a very efficient techniquesince it extracts both low molecular weight solutes[14]

and high molecular weight compounds such as AXusing chaotropic substances, solvents or supercriticalextraction. The nature and permeability of cell wallmajorly influence the method of extraction. Recently,the focus has shifted towards green technologies ofextraction due to which supercritical fluid extraction(SCFE) is gaining popularity.[15,16]

CONTACT Rekha S. Singhal rs.singhal@ictmumbai.edu.in; Sandip B. Bankar sandipbankar@gmail.com Food Engineering and TechnologyDepartment, Institute of Chemical Technology, Nathalal Parekh Marg, Matunga, Mumbai – 400 019, India.

SEPARATION SCIENCE AND TECHNOLOGYhttp://dx.doi.org/10.1080/01496395.2016.1178288

© 2016 Taylor & Francis

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Conventionally, the extraction of intracellular AX iscarried out using solvent extraction methods. Most ofthese solvents are not suitable for food and pharma-ceutical applications. Hence, the use of GRAS (gener-ally recognized as safe) solvents such as ethanol or theuse of solvent-free technologies such as SCFE is con-sidered to be superior over conventional techniques.SCFE uses carbon dioxide as a solvent in its super-critical state (SC-CO2) above 31.1°C and 74 bar, and isgenerally suitable for the extraction of thermally sen-sitive molecules that are non-polar.[17] The lower visc-osity and higher diffusivity of supercritical fluidfacilitate mass transfer, thereby decreasing the overallextraction time. The supercritical medium can beeasily separated from the extraction products, thuseliminating any additional steps of separation.Further, it does not generate any chemical waste,making it a green technology. Carbon dioxide (CO2)is not only readily available at high purity, but alsosafe to handle.[18] These features make it an apt sol-vent for supercritical extraction process.

The use of SCFE for the extraction of AX fromParacoccus is limited and its literature is scarce.Hence, the present work was undertaken to describethe supercritical extraction of AX from ParacoccusMBIC 01143. The operating parameters like pressure,temperature particle size and time of extraction havebeen optimized for higher extraction of AX. The effectof co-solvents on the extraction efficiency of AX wasalso studied using the Fedor solubility parameterapproach. The one-factor at-a-time studies have beenused effectively to optimize the production of biotech-nologically important substances.[19] However, due tothe interaction of process variables that typify biologicalcomplexity, modelling approaches can represent a moredirect and effective means to understand the system.[-20,21] Hence, an attempt has been made to model theexperimental data using non-linear regression analysiswithin an ambit of operating parameters.

Materials and methods

Materials

All the chemicals and solvents used in the presentstudy were of AR grade and purchased from S.D.Fine-Chem. Ltd, Mumbai, India. Methanol used forAX analysis was of HPLC grade (Merck, Canada). CO2

cylinders were supplied by Bombay Carbon Dioxide,Mumbai, India. Standard AX (98% w/w) was obtainedas a gift sample from DSM Nutritional Products Ltd.,Switzerland.

Bacterial strain and fermentation medium

Paracoccus sp. NBRC 101723 (formerly available as MBIC01143, also classified as Agrobacterium aurantiacum) wasprocured from Biological Resource Center (NBRC),National Institute of Technology and Evaluation(NITE), Chiba, Japan. The fermentation medium compo-sition used for maintenance and production containedglycerol (2 g/L), soy peptone (39.3 g/L) and NaCl (22.3g/L) at pH 7.5 ± 0.2. The batch fermentation was carriedout at 20 ± 2°C for 96 h on a rotary shaker at 180 rpm. Theexperiments were carried out in 250 ml Erlenmeyer flaskswith a 100 mL working volume.[10]

Conventional solvent extraction

The conventional extraction of AX was performed asper the previous study.[10] The harvested cells from thefermentation broth were dried and then suspended inacetone and vortexed. The mixture was centrifuged at10000 g for 5 min. The supernatant containingextracted AX was collected and the pellets were re-extracted with acetone. The supernatants were collectedfrom pellets after repeated cycles of extraction till thebiomass was colourless. The samples were pooled foranalysis of AX content by HPLC.

SC-CO2 extraction of AX

The SCFE was carried out using laboratory-scale super-critical equipment (Thar SFE-500) of Thar Technologies,Inc. PA, USA. High-pressure extraction vessel (SS 316insulated) was packed with a cotton plug at the bottom,followed by a layer of SPEED matrix (a hydromatrix anddispersing agent) to eliminate the dead volume of theextraction vessel. A known amount of dried biomasslayer was placed in the vessel and covered with a cottonplug. The vessel was packed firmly to ensure that CO2

diffused uniformly through the sample matrix. The ves-sel was kept in place and a thermocouple was connectedto the vessel body. The system was equipped with anautomated back-pressure regulator, which maintainedthe pressure at the desired level. A pressure-tight cyclonecollector (made of SS 316) was used to collect the extractfrom CO2. The operating conditions of SC-CO2 extrac-tion were optimized as described next.

Effect of pressure

Optimization of the pressure for maximum extraction ofAX was done by varying the pressure from 150 to 350bar. The flow rate of SC-CO2, temperature of extraction

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and time of extraction were kept constant at 15 g/min,35ºC and 60 min, respectively. The SC-CO2 extracts soobtained were estimated for AX by HPLC.

Effect of temperature

To evaluate the effect of temperature, AX extractionwas carried out under the optimized pressure estab-lished from the prior set of experiments. The tempera-ture was varied from 35°C to 65°C with a flow rate of15g/min for 60 min. The SC-CO2 extracts were thenestimated for its AX content.

Effect of particle size of biomass

The particle size of the dried biomass was optimized forhigher AX extraction. The size of the dried biomass wasvaried by grinding it and passing through the sieves. Theground biomass was sieved to obtain coarse (3 mm) andfinely ground powder (0.1 mm). A control experimentwas performed without any grinding of the dried biomass.

Effect of time

The extraction time required for higher AX release wasestimated by carrying out extraction for different timeintervals (30–120 min). The flow rate of SC-CO2 waskept constant at 15 g/min. Other experimental para-meters like pressure, temperature and particle size werekept at their optimum. The extract obtained after SC-CO2 extraction was further analysed by HPLC.

Effect of entrainer

Supercritical CO2 is highly non-polar in nature. When apolar solvent (entrainer) is mixed with SC-CO2, the polar-ity of the supercritical CO2 is altered, which in turnincreases the solubility of polar compounds. Hence thedried biomass of AX was dampened with entrainers,which are chaotropic alcohols such as methanol, ethanoland isopropanol at 10% and 20% v/w and extracted usingSC-CO2 under previously optimized conditions. The SC-CO2 extracts thus obtained were then estimated for thecontent of AX by HPLC. The control experiments withconventional solvent (acetone) extraction were also per-formed to compare the extraction efficiency of SC-CO2.

[13]

Analysis of AX by HPLC

The extracted AX was dissolved in acetone and ana-lysed by HPLC (Jasco, Tokyo, Japan) using WatersSpherisorb C18 reverse-phase column (4.6 × 250 mm,5 μm). The HPLC method reported by Asker et al.[22]

was used for the quantification of AX with slight mod-ifications. The mobile phase used was a mixture ofmethanol and water (95: 5 v/v) with a flow rate of 1mL/min. AX was detected by measuring the absorbanceat 476 nm. A standard curve of absorbance vs. concen-tration of pure AX was plotted using a concentrationrange of 10–100 µg/mL (R2 = 0.9986), which was usedto estimate the AX in the SCFE extracts.

Estimation of solubility parameters

One of the ways to have a detailed insight into thesolubility of a solute in supercritical fluid is the estima-tion of its solubility parameters. Solubility parameter isvery helpful to predict the solubility of a solute in super-critical fluids.[23] The estimation of solubility parameterprovides a semi-quantitative evaluation of experimentalconditions to be selected for optimized extraction condi-tions. The solubility parameter (δ) of a supercritical fluidcan be estimated by using the following equation:[24,25]

δcalcm3

� �1=2¼ 1:25 Pcð Þ1=2 ρr;SF

ρr;L¼ 0:47ρr;SF Pcð Þ1=2

(1)

where Pc is the critical pressure (bar), ρr,SF is thereduced density of the supercritical fluid (g/cm3) andρr,L is the reduced density of liquid state (g/cm3). Thisequation reflects the variation of the solvent power ofthe supercritical fluid as a function of density. Solubilityparameter (δ) of a given solute can be estimated byusing the Fedors group contribution method when thesolute molecular structure is known.[26] Table 1 showsthe estimation of the solubility parameter of AX byusing the Fedors method.[26] The solubility parametersof AX were calculated using the following equation:

δcalcm3

� �1=2¼

PΔEvð ÞiPΔVð Þi

� �1=2(2)

where

Table 1. Solubility parameter of AX using Fedors groupcontribution.Group No. Δei ΔTi Δ vi ΔE (e X v)

CH3 10 1125 17.9 335 11250>CH2 2 1180 2.68 32.2 2360>C=O 2 4150 10.72 21.6 8300≡CH 2 820 3.58 -2 1640>C= 8 1030 7.12 -44 8240>C< 2 350 -0.44 -38.4 700CH= 14 1030 19.6 189 144206-membered ring 2 250 5.36 32 500Conjugated double bonds 13 400 1.69 1.69 5200Total Ʃ 10335 68.21 527.09 52610

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PΔEvð Þi is summation of all cohesive energy

(cal/mol)PΔVð Þi is summation of all molar volume

(cm3/mol)Using the above equation, δ for AX at 25°C was

found to be 9.9 (cal/cm3)1/2 or 20.43 MPa1/2.The δ values for AX at other temperatures are shown in

Table 2. The critical temperature of AX was calculatedusing the equation: Tc = 535log

PΔTi, where ΔTi is the

summation of the critical temperatures of the contributinggroups. The Fedors method was found to be useful forestimating the extraction potential of carotenoids usingsupercritical fluids.[27,28] The solubility of solute in SC-CO2 as a function of temperature can be described asfollows[29]:

δcalcm3

� �1=2¼

PΔEvð ÞiPΔVð Þi

� �1=2¼δ1

V1

V2

� �1:13

¼δ1ρ1ρ2

� �1:13

¼ δ1Tc�T2

Tc�T1

� �0:33

(3)

where V is the molar volumeδ1 is the solubility parameter of solute at tempera-

ture T1 (cal/cm3)1/2

δ2 is the solubility parameter of solute at tempera-ture T2 (cal/cm

3)1/2

Hildebrand[30] proposed the square root of the cohe-sive energy density as a numerical value, indicating thesolvency behaviour of a specific solvent. The solubilityparameter of the entrainer solvent, δ, at different tem-peratures and pressures was calculated using the fol-lowing equation:

δcalcm3

� �1=2¼ ΔEvap

V

� �1=2¼ ΔHvap�RT

V

� �1=2(4)

whereΔEvap = summation of all cohesive energy, (cal/mol)ΔHvap = heat of vaporization of solvent, (cal/mol)R = gas constant, 1.987 cal/mol KV = molar volume, (cm3/mol)

The compressibility factor for entrainer solvent atvarying pressure and temperature conditions obtainedfrom Reid and Sherwood[31] was used to calculateΔHvap under different conditions.

Results and discussion

Estimation of solubility parameters

The solubility parameter was evaluated to select appro-priate experimental conditions for optimization of theSC-CO2 protocol. The solubility parameter theory qua-litatively explains the effects of temperature and density(or pressure) on solubility in supercritical fluids.According to this theory, a higher solubility is achievedwhen the solubility parameters of the solute and solventare closer to each other.[32] Hence the solubility para-meters were calculated to understand the solubility ofAX in the SC-CO2 with respect to pressure and tem-perature. Figure 1 shows the dependence of solubilityparameters of AX and SC-CO2 as a function of tem-perature and pressure. It can be seen that the solubilityparameter of AX remains fairly constant as a functionof temperature. A similar trend is followed by thesolubility parameter of SC-CO2 at higher pressure(300–400 bar). However, it is evident that the solubilityparameter of SC-CO2 is a strong function of pressure.The value of solubility parameter is 12.4 MPa1/2 and16.35 MPa1/2 at 35ºC for 100 and 300 bar, respectively.An increase in the pressure shows the value of solubilityparameter of SC-CO2 close to the solubility parameterof AX, which results in the enhancement of extractionefficiency. Thus, according to the solubility parameterapproach, the favourable condition for extraction of AX

Table 2. Solubility parameters of AX at different temperatures.Temperature (°C) Solubility parameter δ(Mpa1/2)

35 20.3340 20.2945 20.2450 20.1955 20.1460 20.0865 20.0370 19.9875 19.93

0

5

10

15

20

25

35 45 55 65 75 85

Solu

bilty

par

amet

er (

MPa

1/2)

Temp (°C)

Figure 1. Solubility parameter of AX and SC-CO2 as a function oftemperature and pressure. Filled rectangle, Astaxanthin; filledtriangle, CO2 100 bar; empty triangle, CO2 150 bar; filled circle,CO2 300 bar; open circle, CO2 350 bar; filled square, CO2 400 bar.

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would be at 350 bar and 35°C. The practical feasibilityof AX extraction with initial conditions (temperature35ºC, pressure 350 bar and run time of 60 min) wasvalidated with the experimental data.

Supercritical fluid extraction of AX

The selection of the operating conditions depends onthe compound to be extracted, in particular its mole-cular weight and polarity, which influence the extrac-tion process. Factors such as pressure and temperatureneed to be optimized during SC-CO2 extraction.

Effect of pressure on SC-CO2 extraction

The extraction pressure is the most significant processparameter of SC-CO2 extraction and is used to adjustthe selectivity of the supercritical fluids (SCF). In gen-eral, an increase in the pressure enhances the solventpower and decreases extraction selectivity.[17] Hence,the effect of extraction pressure was evaluated at aconstant temperature of 35ºC for 60 min, using SC-CO2 at a flow rate of 15 g/min. Experimental runs atdifferent pressures were conducted to study the effectand select the optimum extraction pressure (Fig. 2a).The extraction efficiency was found to increase with anincrease in pressure up to 300 bar. The maximum AX

recovery at 300 bar was found to be 730 μg/g. The AXextraction remained unaltered beyond 300 bar. Theseresults are in accordance with Sajilata et al.[27] whoreported an increase in zeaxanthin recovery up to 300bar and beyond which it decreased with an increase inthe pressure of the system. At higher pressure, CO2

becomes highly compressed and solvophilic interac-tions are overcome by solvophobic interactionsbetween the solute and the solvent, which result inrepulsing solute–solvent interactions. This incidentallyinduces complex extraction and minimizes the extrac-tion efficiency of the solute.[33]

Effect of temperature on SC-CO2 extraction ofAX

The selected temperature range for extraction should bein the vicinity of the critical point and as low as possi-ble to avoid degradation in case of thermolabile mole-cules. An increase in temperature reduces the density ofSC-CO2 (for a fixed pressure), thus reducing the sol-vent power of the supercritical solvent; however, itincreases the vapour pressure of the compounds to beextracted. Therefore, the tendency of these compoundsto get extracted in the fluid phase is increased.[17] Theeffect of temperature (35–55ºC) at 300 bar on AXrecovery was investigated using SC-CO2 (Fig. 2b). A

(a)(b)

0

100

200

300

400

500

600

700

800

150 200 250 300 350

Ast

axan

thin

(µg/

g)

Pressure (bar)

0

200

400

600

800

35 40 45 50 55

Ast

axan

thin

(µg

/g)

Temperature (°C)(c) (d)

0100200300400500600700800900

1000

30 60 90 120

AX

(µg

/g)

Extraction time (h)

Figure 2. Effect of pressures (a), temperature (b), particle size (c) and extraction time (d) on supercritical fluid extraction of AX.

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very small increase in the recovery of AX was achievedat 40°C (769 µg/g). The AX extraction remained unal-tered after 40°C. The optimum conditions for theextraction vary from one source to another and there-fore have to be optimized separately. Nobre et al.[34]

reported the use of SC-CO2 extraction for the recoveryof AX from Haematoccoccus pluvialisto to result in 92%w/w carotenoid recovery at 300 bar/60°C. On the con-trary, Lim et al.[15] achieved maximum yield of bothcarotenoids and AX from Phaffia rhodozyma to be 84and 90% w/w, respectively, at 40°C and 500 bar.

Effect of particle size and time of extraction

Apart from pressure and temperature, the particle sizeof matrix and time of extraction are important processparameters to be considered for SCFE processoptimization.[17] Since carotenoids are intracellular,pretreatments such as crushing, freeze drying and enzy-matic cell degradation aid in the extraction process. Inthe present study, two particle sizes were used forextraction, viz. coarsely ground (0.3mm) and finelyground (0.1 mm), which were compared with the intactbiomass. The biomass was finely ground just beforeloading it into the extraction vessel to avoid degrada-tion. The extraction increased from 749 µg/g (using0.3 mm) to 844 µg/g (0.1 mm) for the finely groundparticles (Fig. 2c).

The effect of extraction time was also evaluated at aconstant temperature of 40 ºC and pressure of 300 barusing SC-CO2 at a constant flow rate of 15 g/min. Amaximum recovery of 844.67 μg/g of AX was obtainedafter 60 min of extraction (Fig. 2d), beyond which nosignificant increase in recovery was observed. Thus, anextraction time of 60 min was found to be suitable toextract AX under the tested conditions.

Effect of co-solvents

The non-polar nature of pure SC-CO2 is unsuitable forthe extraction of slightly polar solutes due to low solutesolubility. The polarity of pure SC-CO2 can be increasedby use of polar co-solvents, which enhance the solutesolubility in SC-CO2.

[35] Thus in order to improve theyield under the optimized conditions of pressure andtemperature, the effect of addition of co-solvents to SC-CO2 on AX extraction yields was studied. In the presentstudy, the solvents evaluated were methanol, ethanol andisopropyl alcohol. The correlation between solubilityparameters of AX, CO2 (300 bar) and entrainers (metha-nol, ethanol and 2-propanol) (300 bar) as a function oftemperature is shown in Fig. 3. Ethanol at 20% v/wresulted in the highest AX recovery (963.33 μg/g) as

compared to the other solvents. Ethanol at 20% v/wbehaves as a potent chaotrope that can readily lyse allthe cells of the ethanol-tolerant strain of Saccharomycescerevisiae.[3] The presence of entrainers along with SC-CO2 reduces the difference between SC-CO2 (with entrai-ner) and AX. This enhances the solubility of AX in SC-CO2, leading to increased extraction. The control studywith conventional extraction of AX[13] without SC-CO2

resulted in the extraction to be 317μg/g. Hence, the SC-CO2 extraction under optimized conditions was found tobe 203% higher than the conventional solvent extractionmethod.

Kagliwal et al.[25] reported the use of 2-propanol asan entrainer at 30% v/w for the extraction of carote-noids from dried sea buckthorn seed powder. Thisenhanced the recovery of tocopherols and carotenes to91.1% and 69.6% w/w, respectively. All the co-solventsexcept methanol at 10 and 20% v/w increased theextraction of AX (Fig. 4). The addition of co-solventsat 20% v/w increased the extraction of AX marginallyfrom 834 to 860 µg/g. Ethanol is popularly recom-mended to be used as an effective co-solvent for AXextraction during SC-CO2 extraction. The GRAS statusof ethanol further makes it favourable for foodapplications.[36] The increase in co-solvent concentra-tion beyond 20% v/w did not have any additional effecton the extraction of AX.

SCFE has been used to extract carotenoids by var-ious researchers.[15,16,27,28] The solubility of targetedcarotenoids in supercritical fluids depends not only onphysical and chemical properties but also on the oper-ating conditions such as temperature, pressure, density

0

5

10

15

20

25

30

40 45 50 55 60 65 70 75

Solu

bilit

y pa

ram

eter

MPa

1/2

Temperature (°C)

Figure 3. Solubility parameters of AX, CO2 and entrainer(methanol, ethanol and 2-propanol) at 300 bar. Filled rectangle,Astaxanthin; filled square, methanol; filled triangle, ethanol;empty triangle, 2-propanol; filled square, CO2.

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of solvent and solvent flow rate in the supercriticalregion.[37] The use of co-solvent (methanol and etha-nol) for extraction is also known to significantlyincrease the extraction yield. Mezzomo et al.[16] com-pared the effect of hexane: isopropanol solution, 50:50,and sunflower oil as co-solvents at concentrations of 2and 5% v/w to extract AX from pink shrimp (Penaeusbrasiliensis and Penaeus paulensis) processing waste.Sunflower oil showed a lower yield of carotenoidextraction but made the process selective for carotenoidextraction, while 2% hexane:isopropanol significantlyincreased the extraction yield.

Mathematical modelling of AX extraction

The supercritical extraction of AX can be expressed as afunction of pressure, temperature, particle size andentrainer (solvent) properties. The effect of solventproperties on the extraction efficiency of AX can beconsidered in terms of its solubility parameter. Thesolvents that exhibit greater affinity with AX areexpected to have close solubility parameter values andvice versa.

SE ¼ fðP; T; dp; δÞ (5)

where SE indicates supercritical extraction of AX in µg/g of solid while P, T, dp and δ are pressure, tempera-ture, particle diameter and solubility parameter, respec-tively. The above equation can be transformed to thedimensionless form as follows:

SE ¼ KPPc

� �a TTc

� �b dpdpintact

� �c δ

δCO2

� �d

(6)

where SE is the supercritical extraction of AX withrespect to initial content of AX. Pc, Tc, dpintact andδCO2 are CO2 critical pressure, CO2 critical tempera-ture, intact particle diameter and solubility parameterof CO2, respectively. The method of non-linear regres-sion has been applied to evaluate the coefficient andexponents of each dimensionless term.[38]

Figure 5 shows the parity plot. The statistical analy-sis of the data was also performed and statistical para-meters such as correlation coefficient (R2), Chi-square(χ2) and the root mean square error (RMSE) wereestimated to assess the goodness of fit of the mathema-tical model to the experimental data. Generally, thehigher R2 and the lower χ2 and RMSE values give bettermodel fitting. The Chi-square (χ2) and RMSE werecalculated as follows:

χ2¼PNi

SEexp;i�SEpred;i� �

N� n(7)

RMSE ¼ 1N

XNi

SEexp;i�SEpred;i� �2" #0:5

(8)

where SEexp;i and SEpred;i are the ith experimental andpredicted supercritical extraction ratio, respectively. N isthe number of observations and n is the number ofparameters

Table 3 shows the estimated values of model para-meters, R2, χ2 and RMSE. The R2, χ2 and RMSE valuesindicate that mathematical model fits well to the experi-mental data. The proposed model, therefore, could beused to predict the extent of supercritical extraction ofAX within the range of operating parameters studied inthe present investigation.

600

700

800

900

1000

AX

(µg

/g)

Co solvent

Figure 4. Effect of co-solvent on the extraction of AX. Emptybar, 10% v/w co-solvent; gradient fill bar, 20% v/w co-solvent.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Pred

icte

d va

lues

Experimental values

Figure 5. Parity plot with standard deviation (±8%).

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The correlation obtained is as follows:

SE ¼ 0:015PPc

� �2:75 TTc

� �0:005 dpdpintact

� ��0:1 δ

δCO2

� �0:2

(9)

Eq. (9) shows that operating pressure, particle sizeand solvent property have a significant effect on theextraction of AX while temperature has a negligibleeffect. Besides, the operating pressure has a positiveeffect on the extraction of AX while the reverse is truefor particle size.

Conclusions

The solubility parameter approach gives an insight intothe extraction behaviour of AX from Paracoccus MBIC01143 as a function of pressure, temperature, particlesize and extraction time. The operating conditions wereoptimized as a temperature of 40°C, pressure of 300 barand extraction time of 60 min. Use of 2-propanol andethanol as an entrainer at 20% v/w of dried biomassunder the optimized conditions enhanced the extrac-tion of AX. An increased recovery of 203% of AX wasobtained after SC-CO2 extraction in comparison withthe conventional solvent extraction. Based on theexperimental results, a correlation that satisfactorilyfitted the experimental data could be developed.Additional scale-up trials at pilot plants would berequired to use it effectively and efficiently at the indus-trial level.

Nomenclature

dp particle diameter, (mm)E cohesive energy, (cal/mol)H enthalpy, (cal/mol)K coefficient defined in Eq. (6), (-)n number of parametersN number of observationsP pressure, (bar)

R universal gas constant, (cal/mol. K)SE supercritical extraction of AX, (µg/g)SE supercritical extraction of AX with respect to

initial content of AX, (-)T temperature, (°C)V molar volume, (cm3/mol)

Greek words

ρ density, (gm/cm3)χ2 Chi-square: statistical analysis parameter

Subscript

c critical conditioni specyL liquid stater reduced conditionSF supercritical fluidvap vaporization

Funding

The authors gratefully acknowledge the UGC-SAP,Government of India, for their financial assistance duringthe course of this investigation.

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