Bioresource Technology 102 (2011) 7280–7288

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Bioresource Technology

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Multiple response optimization of vegetable oils fatty acid composition to improvebiodiesel physical properties

S. Pinzi a, D. Leiva a, G. Arzamendi b, L.M. Gandia b, M.P. Dorado a,⇑a Dept. of Physical Chemistry and Applied Thermodynamics, EPS, Edificio Leonardo da Vinci, Campus de Rabanales, Universidad de Cordoba, 14071 Cordoba, Spainb Dept. of Applied Chemistry, Edificio de los Acebos, Universidad Pública de Navarra, Campus de Arrosadía s/n, E-31006 Pamplona, Spain

a r t i c l e i n f o a b s t r a c t

Article history:Received 19 March 2011Received in revised form 30 April 2011Accepted 2 May 2011Available online 7 May 2011

Keywords:Unsaturation degreeChain lengthStatistical modelDesirabilityFatty acid methyl ester

0960-8524/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.biortech.2011.05.005

⇑ Corresponding author. Tel.: +34 957 218332; fax:E-mail addresses: pilar.dorado@uco.es, mpdorado@

The effect of fatty acids chain length (LC) and its interaction with unsaturation degree (UD) on importantbiodiesel quality parameters was studied. Low calorific value, kinematic viscosity, flash point, cetanenumber and cold filter plugging point of biodiesel blends covering a wide range of fatty acids were ana-lyzed. Analytical results were processed with statistical regression to obtain a prediction model for eachproperty, combining LC and UD. Due to the antagonistic effects of the chemical composition over qualityproperties, the Derringer desirability function was proposed to allow the most suitable fatty acid compo-sition. This target was achieved considering an average of 1.26 double bounds and 17 carbon atoms. A setof combinations of LC and UD values that provides a biodiesel that fits the European standard EN 14214was proposed. It was found that a reduction of FAME LC allows a lower UD while keeping biodiesel spec-ifications under the standard limits.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Biodiesel is a renewable resource that is gaining interest in thescientific community and may become a competitive alternative topetrodiesel fuel. It is commonly produced by transesterification oftriglycerides with an alcohol (usually methanol, CH3OH) in thepresence of a basic or acid catalyst (Dorado et al., 2004). The usualraw materials to produce biodiesel consist of vegetable oils, animalfats and other sources with a considerable content of triglycerides(Luque et al., 2008).

Fuel properties depend on fatty acid composition of raw mate-rials (oils or fats) because the fatty acid profile of biodiesel is iden-tical to that of the parent oil or fat. In turn, the properties of fattyacid esters are determined by the chemical structure of the fattyacids; between the most significant features are the chain length(LC) and the degree of unsaturation (UD) (Pinzi et al., 2009).

Progresses on molecular biology research (Durrett et al., 2008)may help to improve the fatty acid profile of vegetable oils, thusenhancing fuel properties of biodiesel. Genetic modification offatty acid composition offers a method to address most fuel prop-erty issues simultaneously. For example, the presence of somemetabolites (e.g., methyl caprate and methyl oleate) or the contentof polyunsaturated methyl esters could be increased or reduced,respectively (Lu and Kang, 2007). For these reasons, to improvebiodiesel quality, thus facilitating the acceptance of biodiesel by

ll rights reserved.

+34 957 218417.ujaen.es (M.P. Dorado).

both customers and vehicle manufactures, it is extremely impor-tant to find out the optimal fatty acid composition of the raw mate-rial used in biodiesel production.

The influence of the chemical structure of fatty acids composi-tion on biodiesel physical and chemical properties has beendemonstrated (Canakci and Sanli, 2008; Harrington, 1986; Knothe,2008; Ramos et al., 2009). Several studies have shown that heatingvalue, cetane number and oxidation stability increase with chainlength and decrease with unsaturation of the fatty acids (Freedmanand Bagby, 1989; Knothe, 2007; Knothe et al., 2003; Lapuerta et al.,2009; Mehta and Anand, 2009). However, low temperature flowcharacteristics and viscosity of the fuel improve with shorter andpolyunsaturated methyl ester fatty acid chains (Knothe andSteidley, 2005; Sarin et al., 2010). For this reason there is no fattyacid profile that provides a fuel for which all these parametersare optimal (Durrett et al., 2008; Knothe, 2008).

Recently, it has been discussed that esters of saturated mediumchain acids, especially esters of decanoic (capric) acid, may beespecially suitable as major components of optimal biodiesel. Thisis because they show reasonable cold flow properties with highmelting points and excellent oxidative stability due to absence ofdouble bounds and are an alternative to the long-chain saturatedfatty esters (Knothe, 2008; Knothe et al., 2009).

The aim of this work is to predict the effect of the chain lengthant its interaction with the degree of unsaturation on the mostimportant quality parameters of biodiesel. Also, an optimized fattyacid profile to improve different quality parameters will beproposed. Provided that the same fatty acid profile may depict

S. Pinzi et al. / Bioresource Technology 102 (2011) 7280–7288 7281

antagonistic effects over different quality properties, a compromisebetween the optimal values of all properties is needed. To solvethis conflict, a desirability function is used (Derringer and Suich,1980; Pinzi et al., 2010). For this purpose, a multiple response opti-mization of five quality parameters of biodiesel, i.e. low calorificvalue (LCV), kinematic viscosity (l), flash point (FP), cetane num-ber (CN) and cold filter plugging point (CFPP) will be carried out.Unsaturation degree (UD) and length of chain (LC) of fatty acidsmethyl esters from analyzed biodiesel are considered independentfactors. To achieve a suitable statistical variability between LC andUD, 18 blends of a wide range of fatty acid content, including con-ventional fatty acid methyl esters (FAME) and short chain fattyacid methyl esters (for example, coconut methyl esters, CME) areanalyzed.

2. Methods

2.1. Raw materials and sample preparation

Sunflower oil, maize oil and olive-pomace oil were acquiredfrom KOIPE (SOS Cuétara, Madrid, Spain), linseed oil and coconutoil were purchased from Guinama (Valencia, Spain) and palm oilwas purchased from Quimics Dalmau (Barcelona, Spain).

Methyl esters (biodiesel) of sunflower oil (SFME), olive-pomaceoil (OPME), maize oil (MME), linseed oil (LME), coconut oil (CME)and palm oil (PME) were produced by alkaline transesterificationthat was optimized for each feedstock in previous works (Pinziet al., 2011a,b).

To obtain a high statistical variability on fatty acid composition(LC and UD), a total of 18 samples prepared by blending SFME,OPME, MME, LME, CME and PME in different volume ratios wereused. The volume ratio of the blends and their detailed FAME com-position are shown in Table 1 and Fig. 1. A high number of blendsincluding CME were provided to increase the variability of sampleswith short chains of fatty acids.

2.2. Reagents

KOH pellets [85% p.a. CODEX (USP_NF)] and methanol ACS-ISOwere acquired from PANREAC (Barcelona, Spain). KOH and metha-nol were used in the transesterification as catalyst and alcohol,respectively. Heptadecanoic acid and tridecanoic acid methyl es-ters from Fluka (Steinheim Germany) were used as internal stan-dards in FAME determination.

Table 1Yield on FAME, fatty ester composition, chain length (LC) and unsaturation degree (UD) of asunflower oil methyl ester; OPME, olive-pomace oil methyl ester; PME, palm oil methyl e

Sample Property

Yield(wt.%)

Total glycerola

(wt.%)C8:0(wt.%)

C10:0(wt.%)

C12:0(wt.%)

C14:0(wt.%)

C1(w

Method

EN14103

EN 14105 EN 14103

OPME 96.96 0.235 0.00 0.00 0.00 0.00 10SFME 98.83 0.163 6.MME 96.77 0.250 12LME 97.58 0.215 5.PME 99.03 0.187 0.20 1.03 44CME 92.70 0.351 7.03 5.90 46.30 17.76 10

1 Triglycerides + diglycerides + monoglycerides + free glycerol.2 LC = R(nCn cn), where nCn is the number of carbon atoms of each fatty acid and cn is3 UD = (1%MU + 2%DU + 3%TU)/100, where %MU is the percentage in weight of monounsat

and %TU is the percentage in weight of triunsaturated methyl esters.

To determine the content of triglycerides (TG), diglycerides(DG) and monoglycerides (MG) in OPME, SFME, LME and MME,the following internal standards were used as established in thestandard EN 14105: glycerine, monolein, diolein, triolein, mono-glyceride stock solution and MSTFA, purchased from Sigma–Al-drich (St. Louis, MO, USA), Tricaprin and 1,2,4 butanetriolacquired from Fluka (Steinheim, Germany). To determine glyce-rides content in methyl esters with fatty acid short chains, i.e.CME and PME, size-exclusion chromatography (SEC) was usedand the following analytical lipid standards were purchased fromLarodan Fine Chemicals (Malmö, Sweden): monoglycerides mix-ture MG Mix 21 (monostearin, monoololein, monolinolein, mono-linolenin), diglycerides mixture DG Mix 51 (distearin, diolein,dilinolein, dilinolenin), tripalmitin, triolein, trilinolein, methyl pal-mitate, methyl stearate, methyl oleate and methyl linoleate. Glyc-erol (99.5%, Sigma–Aldrich, St. Louis, MO, USA) and HPLC grademethanol from Scharlau (Barcelona, Spain) were used as referencestandards (Arzamendi et al., 2006).

Benzoic acid, a primary standard for bomb calorimetry, was ob-tained from IKA-WERKE (Staufen, Germany).

2.3. Analyses and instruments

For very test along the study, each sample was run in triplicate.Yield on FAME (wt.%) and fatty acid composition of each samplewere analyzed following the EU standard EN 14103. However,coconut and palm oil methyl ester yields were analyzed usingthe modified EN 14103 (the initial oven temperature was raisedfrom 150 to 220 �C at 5 �C/min, with this last temperature beingheld for 15 min) and using as internal standard methyl tridecano-ate (C13:0), to make possible the separation of short-chain fattyacid esters (C12–C14) in the chromatogram (Schober et al.,2006). A Perkin Elmer (Waltham, MA, USA) Clarius 500 chromato-graph (GC) equipped with a flame ionization detector (FID) wasused for gas chromatographic determinations. A 30 m � 0.25 mmElite 5-ms Perkin Elmer capillary column (film thickness of0.25 lm) was selected.

For the determination of glycerides (glycerol, MG, DG and TG) inOPME, SFME, MME and LME following the EU Standard EN 14105, aSupelco HT-5 capillary column 12 m � 0.32 mm, df 0.15 lm wasused. A Waters 510 HPLC pump, a Rheodyne 7725i manual injec-tor, a Waters model 410 differential refractive index (RI) detectorand a Viscotec TriSEC� model 270 dual detector were used forSEC determination of glycerides in PME and CME (Arzamendiet al., 2006).

nalyzed samples (CME, coconut oil methyl ester; MME, maize oil methyl ester; SFME,ster; LME, linseed oil methyl ester).

6:0t.%)

C18:0(wt.%)

C18:1(wt.%)

C18:2(wt.%)

C18:3(wt.%)

C20:1(wt.%)

LC(%)2

UD(%)3

.05 2.68 76.89 9.59 0.38 0.41 17.81 0.9831 3.94 28.24 60.27 0.60 0.65 17.89 1.51.26 2.12 34.07 50.03 0.60 0.92 17.77 1.37

42 3.82 19.76 15.82 55.19 0.00 17.89 2.17.48 4.25 39.62 10.09 0.33 0.00 17.06 0.61.05 2.88 8.22 1.86 0.00 13.14 0.12

the percentage in weight of each methyl ester containing this fatty acid.urated methyl esters, %DU is the percentage in weight of diunsaturated methyl esters

Fig. 1. Range of length of chain (LC) and unsaturation degree (UD) of analyzedblends. 1LC = R(nCncn), where nCn is the number of carbon atoms of each fatty acidand cn is the percentage in weight of each methyl ester containing this fatty acid;2UD = (1%MU + 2%DU + 3%TU)/100, where %MU is the percentage in weight of mono-unsaturated methyl esters, %DU is the percentage in weight of diunsaturated methylesters and %TU is the percentage in weight of triunsaturated methyl esters; 3Methylester blends: in brackets, volume ratio of the mixture.

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High calorific value (HCV) analysis were carried out followingthe ASTM D240 standard, using an IKA (Staufen, Germany) BombCalorimeter, model C200. Low calorific value (LCV) was calculatedusing the following expression (1):

LCV ¼ HCV� ðhfgmH2OÞ=mCxHyO2 ð1Þ

where hfg is the standard heat of vaporization of water, in kJ/kg(Mehta and Anand, 2009), mCxHyO2 is the mass of methyl ester, inkg and mH2O is the mass of water produced during combustion, inkg, calculated considering the methyl ester chemical reaction(expression 2):

CxHyO2 þmðO2 þ 3:76N2Þ ! xCO2 þ ðy=2ÞH2Oþmð3:76N2Þ ð2Þ

where x and y are the number of atoms of carbon and hydrogen in afatty acid (or methyl ester molecule), respectively and m corre-

Table 2Experimental design matrix for multiple response optimization (CME, coconut oil metholive-pomace oil methyl ester; PME, palm oil methyl ester; LME, linseed oil methyl ester;

Sample Property

Independent factors Variables of response

LC UD LCV (kJ/kg) CN

Method

ASTM D2382-88 (**) (Ramos

OPME 17.81 0.98 37754 (16) 61.72SFME 17.89 1.51 37532 (34) 52.54MME 17.77 1.37 37679 (30) 55.34LME 17.89 2.17 37267 (56) 43.63PME 17.06 0.61 37475 (32) 72.09CME 13.14 0.12 35743 (51) 63.39OPME/CME (1:1)* 15.52 0.55 36845 (57) 62.84OPME/CME (4:1) 16.84 0.80 37174 (16) 62.05SFME/CME (1:1) 15.52 0.82 36660 (40) 57.96SFME/CME (4:1) 16.96 1.21 37177 (48) 55.16MME/CME (1:1) 15.38 0.70 36598 (27) 60.07LME/CME (1:1) 15.51 1.14 36452 (41) 53.47PME/CME (1:1) 15.10 0.36 36544 (28) 67.74OPME/PME (1:1) 17.43 0.79 37526 (59) 66.90SFME/PME (1:1) 17.47 1.06 37420 (12) 62.28MME/PME (1:1) 17.42 0.99 37445 (20) 63.70LME/PME (1:1) 17.47 1.39 37291 (16) 57.84OPME/LME (1:1) 17.85 1.57 37384 (9) 52.67

* Methyl esters blends: in brackets, volume ratio of the mixture.** Errors, in brackets, expressed as relative standard deviation, in percentage (n = 3 repl

sponds to the stoichiometric oxygen requirement. The chemical for-mula of each biodiesel was calculated considering methyl esterscomposition (Table 1).

The flash point (FP) method was calculated by means of a Stan-hope-Seta (Chertsey, UK) Setaflash Series 3 flash point tester, fol-lowing the European Standard ISO 3679. Kinematic viscosity (l)was measured with a Canon–Fenske capillary viscometer im-mersed in a constant temperature (40 �C) bath, following the Euro-pean norm EN ISO 3104.

The testing device used to determine CFPP was a NTL 450Normalab Analis. This test provides an estimate of the lowest tem-perature at which a fuel will give trouble free flow in certain fuelsystems. Analyses were carried out by ENAC (Official SpanishEntity of Accreditation) accredited laboratory CEMITEC (Noain,Navarra, Spain), following the EU standard EN 116. Cetane number(CN) for biodiesel was predicted using expression (3):

CN ¼ RXMEðwt:%ÞCNME ð3Þ

where XME is the weight in percentage of each methyl ester andCNME is the cetane number of individual methyl esters (Ramoset al., 2009).

2.4. Statistical analysis software

Statgraphics� centurion XVI (StatPoint Technologies, Warren-ton-Virginia, USA) was used for building and analyzing the re-sponse surfaces, allowing to design the multiple responseoptimization and graphical responses.

3. Results and discussion

3.1. Statistical analysis

A surface design of 18 experiments (from 18 blends using sixdifferent kinds of biodiesel, Table 1 and Fig. 1) for multipleresponse optimization was carried out. Five of the most importantphysical properties of biodiesel, namely LCV, CN, l, FP and CFPPwere considered dependent variables. The independent factors

yl ester; MME, maize oil methyl ester; SFME, sunflower oil methyl ester; OPME,LC, length of chain; UD, unsaturation degree).

FP (�C) l at 40 �C (mm2/s) CFPP (�C)

et al., 2009) prEN ISO 3679 (**) EN ISO 3104 (**) EN 116:1998

171.7 (1.7) 5.20 (0.02) �8.00168.0 (1.6) 4.70 (0.01) �5.00168.3 (1.7) 4.84 (0.04) �3.00156.7 (3.9) 4.07 (0.04) �8.00169.0 (1.4) 5.64 (0.03) 11.00108.0 (1.4) 3.65 (0.05) �6.00123.7 (0.9) 4.42 (0.01) �5.00141.0 (0.8) 4.90 (0.01) �9.00121.3 (0.9) 4.18 (0.04) �9.00140.3 (0.5) 4.50 (0.03) �9.00122.0 (1.0) 4.25 (0.05) �8.00122.3 (1.2) 3.85 (0.01) �9.00123.3 (1.2) 4.63 (0.05) 2.00171.0 (1.4) 5.41 (0.04) 7.00167.3 (1.2) 5.15 (0.06) 4.00168.0 (0.8) 5.2 (0.03) 5.00166.7 (0.5) 4.83 (0.03) 5.00164.0 (6.2) 4.61 (0.02) �9.00

icate).

Fig. 2. Estimated response surface on (a) low calorific value (LCV); (b) cetane number (CN); (c) kinematic viscosity (l); (d) flash point (FP); (e) cold filter plugging point(CFPP). Independent Factors: chain length (LC) and unsaturation degree (UD).

S. Pinzi et al. / Bioresource Technology 102 (2011) 7280–7288 7283

were LC (calculated as the average of carbon number in fatty acidchains) and UD (calculated as the average of the number of doublebounds in fatty acid chains). The experimental matrix is shown inTable 2.

3.2. Low calorific value

This parameter indicates the energy released when a fuelundergoes complete combustion, excluding the heat of vaporiza-tion of the water vapor. Due to a content of oxygen about 11%,FAME consistently have lower heating value than fossil diesel fuel.To achieve the same torque and power of petrodiesel using fuelswith lower heating values, an increase of injection volumes isneeded (Mittelbach and Remschmidt, 2004). This, naturally, leadsto higher specific fuel consumptions.

Whereas the term higher calorific value has wider acceptance inthe literature (Demirbas, 2000; Freedman and Bagby, 1989), thethermodynamics combustion calculations usually prefers lowerheating values of the fuels, since the water in the combustionproducts is not condensed and remains as vapor. In a recent work(Mehta and Anand, 2009), the lower heating value of biodiesel andvegetable oils were estimated from the bond energy values relatedto the molecular composition and the structure of the fatty acid/methyl ester content of these fuels.

According to previous works (Knothe, 2005), LCV shows a lineartrend, increasing with LC (due to the increment of the ratio ofcarbons and hydrogen relative to oxygen content) and decreasingwith UD (as a result of fewer hydrogen atoms). As shown inFigs. 2a and 3a, the factor that has the most significant effect overLCV is the chain length. An F-ratio of 566.49 corroborated this find-ing. Therefore, as depicted in Fig. 2a and according to previousstudies (Mittelbach and Remschmidt, 2004), to optimize LCV of

biodiesel, oil sources with a high proportion of long-chain satu-rated compounds should be selected for transesterification.

To predict LCV considering UD and LC, the best model that fitsexperimental results is a first-order equation with an R2 of98.22% (Table 3). The prediction resulting from the proposed linearmodel was compared with experimental results and with othermodels from the literature (Mehta and Anand, 2009), as shownin Fig. 4a. It may be noticed that the proposed model follows thesame trend as the one by Mehta and Anand, although their modelshows slightly higher LCV experimental values. This result wasconfirmed in the validation study, where the developed predictionmodel was used to determine LCV of biodiesel from several feed-stocks and results were compared with experimental data foundin literature (Fig. 5a).

3.3. Cetane number

This parameter gives a measurement of the combustion qualityduring ignition. It provides information about the ignition delay(ID) of a diesel fuel upon injection into the combustion chamber.Fuels with low CN tend to cause diesel knocking and show in-creased gaseous and particulate exhaust emissions due to incom-plete combustion (Mittelbach and Remschmidt, 2004). Moreover,excessive engine deposits are reported. According to engine ex-haust emissions, higher CN is correlated with reduced nitrogen oxi-des (NOx) (Ladommatos et al., 1996), although this may not alwayshold for all types of engine technologies (Knothe et al., 2003).

To predict CN from UD and LC values of fatty acid compositionof the raw material used for biodiesel production, a second orderequation model was developed (Table 3). It was confirmed(Lapuerta et al., 2009) that UD is the factor with most significanteffect over the response variable CN (showing the highest slope

Fig. 3. Main effect plot for: (a) low calorific value (LCV); (b) cetane number (CN); (c) kinematic viscosity (l); (d) flash point (FP); (e) cold filter plugging point (CFPP).Independent factors: chain length (LC) and unsaturation degree (UD).

Table 3Models developed to predict quality parameters individually (LC, length of chain; UD, unsaturation degree).

Quality parameter Equation model (with LC and UD) R2 (%) res (standard error/average)

LCV (kJ/kg) LCV = 29385.4 + 486.866 LC�387.766 UD 98.22 0.002CN CN = 46.6632–1.7357 LC + 12.3976 UD + 0.243275 LC2�2.64964 LC UD + 5.65655 UD2 95.15 0.03l at 40 �C (mm2/s) l = �1.8327 + 0.209794 LC + 0.738911 UD + 0.0166791 LC2�0.16336 LC UD + 0.335547 UD2 96.69 0.03FP (�C) FP = 1008.48–136.166 LC + 142.578 UD + 5.14811 LC2�10.6906 LC UD + 9.26352 UD2 95.94 0.04CFPP (�C) CFPP = 82.3069–17.831 LC + 50.9813 UD + 0.8584 LC2�5.5148 LC UD + 11.949 UD2 55.56 0.39

CFPP = 90.5901 + 41.4424 l�19.4541 LC + 37.2859 UD 94.4 0.19

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in Fig. 3b). Therefore, in agreement with previous studies (Harring-ton, 1986; Knothe et al., 2003), the rising of UD means a reductionof CN which leads to an increment of the ignition delay (ID)- andsubsequent poorer combustion. Longer chain on fatty acids leadsto a slight improvement on CN (Fig. 3b). In Fig. 2b, it may be seenthat saturated long straight chains in fatty esters provide high CN.Furthermore, the selected design of experiments (surface responsemethodology) allows the study of the joint effect of the factors(unsaturation degree and length of chain) and it was observed thatto achieve the same CN with shorter long chain, a slight decrease inUD is needed.

The proposed model was applied to biodiesel from other rawmaterials and CN predictions were compared with experimentaldata found in literature (Fig. 5b). A good correlation and low

percentage of errors demonstrate the robustness of this statisticalmodel.

3.4. Kinematic viscosity

Fuel viscosity has impact on injection and combustion. Higherviscosity leads to a higher drag in the injection pump, thus causinghigher pressures and injection volumes, especially at low engineoperating temperature (Graboski and McCormick, 1998). As a di-rect consequence, the timing for fuel injection tends to be slightlyadvanced for biodiesel (Mittelbach and Remschmidt, 2004).

In agreement with previous works (Knothe, 2005; Knothe andSteidley, 2005), lowest values of kinematic viscosity were achievedfor higher unsaturated and shorter fatty acid chains. In this sense,

Fig. 4. Comparison between the proposed models, others developed in literature and experimental values: (a) low calorific value (LCV); (b) kinematic viscosity (l); (c) flashpoint (FP); (d) cold filter plugging point (CFPP). (a) LCV ¼ 0:0109ðCO Þ

3 � 0:3516ðCO Þ2 þ 4:2ðCOÞ þ 21:066�Ndb where C is the number of carbon atoms, O is the number of oxygen

atoms and Ndb is the number of double bonds; (b) ln lSatC12:0C18:0 = �2.177–0.202z + 403.66/T + 109.77z/T. ln lC18:1 = �5.03 + 2051.5/T, ln lC18:2 = �4.51 + 1822.5/T, lC18:3

(not included in Krisnangkura et al. model) (Knothe and Steidley, 2005). lnlbiodiesel ¼Pn

i yi lnli where yi is the mass fraction (wt.%) of each methyl ester, T is the temperatureat which kinematic viscosity was measured (313 K) and z is the number of atoms of carbon. (c) FPðKÞ ¼ 1:477T0:79856

eb vapH0:16545n�0:05945, where Teb is the boiling point of thecompound (K), DvapH� is the standard enthalpy of vaporization at 298.15 K of the compound (kJ mol�1) and n is the number of atoms of carbon in the fuel molecule. (d) CFPP1

(�C) = 0.4880� + 36.0548 (0 < X < 88); CFPP2 (�C) = 2.7043X + 232.0036 (88 < X < 100), where X is the percentage (wt.%) of unsaturated fatty acids.

S. Pinzi et al. / Bioresource Technology 102 (2011) 7280–7288 7285

in Fig. 2c it is possible to appreciate an optimal area where viscos-ity is minimized (2.8 mm2/s), from 13 atoms of carbons (LC) and anaverage of 0.8 of double bounds (UD) to 14.6 (LC) and a UD of 2.4.

In agreement with other dynamic viscosity model (Allen et al.,1999), a curvilinear relationship between viscosity, LC and UDwas found (Fig. 3c). In this case, again, the most significant de-crease on viscosity was found when unsaturation increased fromsaturated to monounsaturated fatty acid (UD from 0.17 to 1.4) witha lower decrease when the unsaturation increased up to two dou-ble bounds. Furthermore, as shown in Table 3, the best model thatfits experimental results is a second order equation with an R2 of96.69%. In Fig. 4b, the proposed model was compared with exper-imental data and other thermodynamic model (Krisnangkura et al.,2006). As can be seen, both models follow the same trend, butKrinsangkura et al.’s model slightly underestimate experimentalresults, especially in case of coconut blend samples (samples withshorter chains of methyl esters). In agreement with Krinsangkuraet al., the highest errors between predicted viscosities and experi-mental data were found for the shorter fatty acids (from C6:0 toC12:0) (Krisnangkura et al., 2006). Fig. 5c shows the validation ofthe proposed model with values of kinematic viscosity found inthe literature using biodiesel from different raw materials andcompared with Krisnangkura et al. model results.

Allen et al. found that small amounts of glycerides significantlyincrease biodiesel absolute viscosity (Allen et al., 1999). However,in the current work, the content of glycerides resulted too low tohave a significant effect in kinematic viscosity prediction (Table 1).

3.5. Flash point

It is a property that defines safety storage and manipulation of asubstance. Biodiesel has higher flash point than petrodiesel, so itsmanipulation is less dangerous. Furthermore, EN 14214 fixes thelower limit of flash point at 122 �C. FP depends on the boiling point(bp) of the substance (Catoire et al., 2006) and, consequently, on itschemical structure. Moreover, low FP may indicate the presence ofmethanol (bp: 64.7 �C) in biodiesel.

To predict biodiesel flash point, a second order model consideringUD and LC was proposed, as shown in Table 3. As may be seen fromFig. 3d, the number of carbons (LC) is the most important factor thataffect the flash point response variable. A comparative study be-tween the proposed model, experimental data and a previous model(Catoire et al., 2006) was carried out. Fig. 4c shows the comparisonbetween both models and experimental data from this study. To val-idate the proposed model, results from both models were comparedwith values of flash point found in literature for different feedstocks(Fig. 5d). It may be noticed that both models fit the experimentaldata and no significant differences are appreciated.

3.6. Cold filter plugging point

CFPP is the temperature at which fuel causes a filter to plug as aresult of its crystallization (Sarin et al., 2010). It must be consid-ered when compression-ignition engines are operated in a moder-ate temperature climate during winter.

Table 4Desirability function of multiple response design (LC, length of chain; UD, unsaturation degree).

Response Measured values Selected range Weight

Minimum Maximum Low High Goal

LCV (kJ/kg) 35743.3 37754.6 35743.3 37754.6 Maximize 1.0CN 43.63 72.09 51.0* 72.09 Maximize 1.0l at 40 �C (mm2/s) 3.65 5.64 3.5* 5.0* Minimize 1.0FP (�C) 108.0 171.7 120.0* 171.7 Maximize 1.0CFPP (�C) �9.0 11.0 �9.0 0.0 Minimize 1.0

* Limits established by the EU standard EN 14214.

Fig. 5. Comparison between the proposed models, others developed and experimental values found in literature: (a) low calorific value (LCV); (b) cetane number (CN); (c)kinematic viscosity (l); (d) flash point (FP); (e) cold filter plugging point (CFPP).

Table 5Combination of factor levels to maximize the desirability function over the indicatedregion (LC, length of chain; UD, unsaturation degree).

Optimum Response variable

LC = 16.96 LCV = 37.2 � 103 kJ/kgUD = 1.16 CN = 57.0Desirability function = 0.4267 l = 4.62 mm2/s

FP = 147.5 �CCFPP = �4.9 �C

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In the present work, to predict CFPP from LC and UD a secondorder model was developed. As may be seen from Fig. 3e, CFPPdecreases with the increase of UD because the unsaturated fattycompounds have lower melting points than the saturated ones.However, similarly to viscosity, the most significant decrease onCFPP was found when the unsaturation increased from saturatedto monounsaturated fatty acid (UD from 0.17 to 1.8), showing aslight increase when unsaturation increased up to two doublebounds. Due to the lower melting points of shorter fatty acidchains with respect to the longer ones (Knothe, 2008), the longer

Fig. 6. Estimated response surface of desirability considering five different biodiesel key quality parameters: (a) 3-D plot and (b) 2D plot.

S. Pinzi et al. / Bioresource Technology 102 (2011) 7280–7288 7287

the LC the higher the CFPP value. The model developed is depictedin Table 3. Due to the low R2 statistic achieved (0.43) and the high-normalized error (0.39), a multiple lineal model was proposedincluding viscosity as independent variable (Table 3). The secondmodel shown in Table 3 provides more robust and accurate resultsand demonstrates the linear relationship between kinematic vis-cosity and cold properties of biodiesel. Even thought a direct corre-lation between UD and CFPP was not found, this outcome is inagreement with previous results (Park et al., 2008; Sarin et al.,2010), which showed a lineal relationship between CFPP and pal-mitic methyl ester content (the most significant saturated fattyacid), but not a lineal relationship between CFPP and polyunsatu-rated methyl esters. This may be due to the quadratic effect ofunsaturation on kinematic viscosity (see Section 3.4). The proposedmodel was validated and compared with experimental data and aprevious model found in literature (Park et al., 2008) (Figs. 4d and5e). It may be noticed that both models depict a similar trend forsamples with a number of carbons between 17 and 18 (LC),whereas when the chain length is shorter, the Park et al.’s modeloverestimate the real CFPP values. This limitation may be ex-plained because the Park et al.’s model was developed only consid-ering UD The suitability of this model for medium chain acids is arelevant result because the saturated medium chain acids improveviscosity and cold properties, while almost providing similar satu-rated long chain properties.

3.7. Desirability function

To simultaneously improve the analyzed quality parametersand to achieve the optimal fatty acid profile to produce a biodieselthat fits EN 14214, taking into account the antagonistic require-ments of some properties, the desirability function of Derringerand Suich (1980) was used.

The desirability function approach is one of the most widelyused methods for the optimization of multiple response processesin industry. It is based on the idea that the quality of a product orprocess that depends on multiple quality characteristics, one ofthem being outside of some desired limits, is completely unaccept-able. The method finds operating conditions x that provide themost desirable response values (Massart et al., 1997).

The multicriteria problem is reduced to a single criterion prob-lem. The method consists in transforming the measured propertyof each response to a dimensionless desirability scale, di, definedas a partial desirability function; its value varies from zero (unde-sirable response) to one (optimal response). This enables the com-bination of results obtained for properties measured on differentscales and allows optimization considering the relative importanceof each response, while selecting the most appropriate form of thepartial desirability function (Pinzi et al., 2010). One of the objec-tives of the present study is to maximize the overall desirabilityfunction. Therefore, it is necessary to calculate a partial desirabilityfunction for each output response, concluding in an overall desir-

ability (D). A linear partial desirability function was selected foreach response. For this kind of desirability functions, it is assumedthat there is a target value for the response, above which the goalsare totally satisfied. A lower threshold below which the results arenot acceptable was selected following the EN 14214 standardlimits.

Depending on whether a particular response is to be maxi-mized, minimized or assigned a target value, different desirabilityfunctions di may be used. In the present work, the target was toachieve the maximum values of LCV, FP, CN and the minimum val-ues of CFPP and l.

High and low responses assigned to each quality parameter aredepicted in Table 4. Table 5 shows the combination of parameterlevels that maximize the desirability function (the maximum valueachieved was 0.4770) over the indicated region as well as the com-bination of the parameters that provides the optimum value.

In the present work, global desirability represents the mostsuitable fatty acid composition, expressed as a combination be-tween LC and UD, to optimize five of the most important physicalfuel properties. It was calculated by combining single desirabilityfunctions. The three-dimensional plots of global desirability areshown in Fig. 6a, whereas two-dimensional plots are depicted inFig. 6b.

An average double bound value (UD) of 1.16 in the fatty acidchain appears to be the optimal value to achieve the best compro-mise between LCV, CN, FP, CFPP and l. This result partially agreewith previous studies, that found monounsaturated fatty acidchains were the best solution (Knothe, 2005, 2008). An importantand innovative result is related to the achieved optimal length ofchain. The best result was provided by an average value of 17 car-bon atoms. Moreover, if chain length is reduced, it is possible to usea lower degree of unsaturation keeping the desirability function atthe same level, thus avoiding problems due to oxidation stability.

4. Conclusions

Prediction models of five biodiesel quality properties (LCV,l, FP, CN and CFPP) covering a wide range of fatty acids were pro-posed. Equations show a lineal trend for LCV, CN and CFPP,whereas l and FP models follow a quadratic tendency. Modelsdeveloped to predict viscosity and CFPP improve the fittingnessof prediction for biodiesel composed by medium chain acids (fromC8 to C14). A suitable fatty acid composition expressed as LC andUD of FAME to simultaneously optimize fuel properties has beenfound. Results show that reducing FAME LC, UD decreases, whilekeeping biodiesel specifications under EN 14214 limits.

Acknowledgements

This research was supported by the Spanish Ministry ofEducation and Science (ENE2010-15159) and the AndalusianResearch, Innovation and Enterprise Council, Spain (TEP-4994).

7288 S. Pinzi et al. / Bioresource Technology 102 (2011) 7280–7288

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.biortech.2011.05.005.

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