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Viscosities and Densities of Ternary Blends of Diesel + Soybean Biodiesel + Soybean Oil Carlos A. Nogueira, Jr.,† Frederico R. Carmo,† Diego F. Santiago,† Victor M. Nogueira,† Fabiano A. N. Fernandes,‡ Rílvia S. S. Aguiar,† and Hosiberto B. Sant’Ana*,† †

Grupo de Pesquisa em Termofluidodinâmica Aplicada, Chemical Engineering Department, Center of Technology, Universidade Federal do Ceará, Campus do Pici, Bloco 709, CEP: 60455-760, Fortaleza, CE/Brazil ‡ Núcleo de Análise e Desenvolvimento de Processos, Chemical Engineering Department, Center of Technology, Universidade Federal do Ceará, Campus do Pici, Bloco 709, CEP: 60455-760, Fortaleza, CE/Brazil S Supporting Information *

ABSTRACT: This work presents density (ρ) and viscosity (μ) data and correlations of binary and ternary blends containing soybean oil, soybean biodiesel, and petroleum diesel. The data were obtained for different composition ranges, for binary blends data were obtained in a mass fraction (w) in an interval of 0.100 to 0.900. Additionally, ternary data were taken by a random range, at T = (293.15, 313.15, 333.15, 353.15, and 373.15) K, at atmospheric pressure. The experimental data were compared to predictive models based on group contribution method. Density and viscosity data were correlated by a temperature and composition equation (T and w, as independent variables). A statistical analysis has been designed by using chi-square distribution, which revealed an agreement between experimental and estimated data better than 99.5 %.

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INTRODUCTION Biodiesel production has increased as an alternative substitute of fossil fuel, especially due to environmental and renewability concerns, presenting important advantages, for example, nontoxicity, biodegradability, and low production of particular matter.1 Biodiesel molecules are comprised of mono esters with long chains derived, usually, from vegetable oils. The most used method to produce biodiesel is through transesterification reaction of the oil with an alcohol (methanol or ethanol) using hydroxides as a homogeneous catalyst. These reactions produce alkyl-esters and glycerol, which is an undesirable byproduct.2 Several countries are using diesel added with a specific amount of biodiesel. The blends are indicated by the volume fraction (φ) of biodiesel as B5, B7, and B20 that contain respectively (5, 7, and 20) % (v/v) of biodiesel in the blends. It is important to notice that soybean-based biodiesel is one of the most produced and commercialized as a fuel, especially in Brazil.3 Density and viscosity are important thermodynamic properties used to define useable blends containing diesel and biodiesel. These properties can also be used to identify intermolecular interactions between different compounds, as a function of composition and temperature.2 For our knowledge, only few data of ternary systems containing biodiesel + vegetable oil + diesel have been found in the literature.4 For this reason, this work reports thermodynamic properties of biodiesel + diesel + oil systems, by studying three © XXXX American Chemical Society

binary mixtures (soybean biodiesel + diesel, soybean biodiesel + soybean oil, and soybean oil + diesel) and the soybean oil + soybean biodiesel + diesel ternary mixture. In this work density (ρ) and viscosity (μ) data for binary and ternary blends were determined in mass fraction (w) in an interval of 0.100 to 0.900, at T = (293.15, 313.15, 333.15, 353.15, and 373.15) K, at atmospheric pressure. It is important to remember that biodiesel is a complex mixture of alkyl-esters, but in this work it has been considered as a pseudopure compound, to study the influence of soybean oil in the different blends studied, previously described. Equally important, in this work, binary interaction parameters have not been take into account, due to the similarity in molecular arrangements and low molecular interaction. In addition, diesel is also a complex mixture of hydrocarbons. For these reason, n-heptadecane (n-C17) has been used as a pseudocomponent to represent the diesel mixture. This choice has been made based on viscosity comparison for different hydrocarbons from n-C14 to n-C20. The group contribution model called GCVOL-OL-605 was used for predicting density of n-heptadecane, FAMEs (fatty acid methyl esters) of soybean biodiesel, and TGs (triglycerides) of soybean oil. Although, for viscosity prediction the Received: July 26, 2012 Accepted: October 6, 2012

A

dx.doi.org/10.1021/je300838n | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Ceriani6 (for FAMEs and TGs) and Andrade equations7 (for diesel) have been used.

Table 2. Density (ρ) and Viscosity (μ) Data for Diesel, Soybean Biodiesel, and Soybean Oil at Temperature Ranging from (293 to 373) K in Steps of 20 Ka

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EXPERIMENTAL SECTION Materials. Commercial edible grade soybean oil was obtained from Bunge Alimentos S.A. (Ipojuca, PE, Brazil) with a specified density of 917.0 kg·m−3, and the following chemical composition is presented in Table 1. Based on this

biodiesel diesel

soybean biodiesel

Table 1. Fatty Acid Methyl Ester (FAME) Profile of Soybean Oila fatty acid

mass fraction (w)

palmitic (C16:0) oleic (C18:1) linoleic (C18:2) gadoleic (C20:1) erucic (C22:1)

0.2016 0.0762 0.6723 0.0360 0.0139

soybean oil

a

T/K

ρ/g·cm−3

μ/mPa·s

293.15 313.15 333.15 353.15 373.15 293.15 313.15 333.15 353.15 373.15 293.15 313.15 333.15 353.15 373.15

0.8270 0.8132 0.7990 0.7845 0.7708 0.8855 0.8714 0.8569 0.8421 0.8278 0.9207 0.9073 0.8938 0.8800 0.8671

3.8433 2.3898 1.6445 1.2074 0.9207 6.4872 3.9842 2.7095 1.9712 1.9471 61.358 28.389 15.615 9.6707 6.5043

w is the mass fraction of soybean oil. Standard uncertainties u are u(w) = 0.0018 (0.95 level of confidence).

Standard uncertainties u are u(T) = 0.01 K, u(ρ) = 0.0005 g·cm−3, u(μ) = 0.35 % (0.95 level of confidence).

composition a molecular weight was estimated to be 890 g·mol−1. The soybean oil presented an iodine value of 130 g I2·100 g−1, an acid value of 0.2 mgKOH·g−1, and a saponification value of 195 mg KOH·g−1. Methanol (w = 0.990) and sodium hydroxide (w = 0.970) were supplied by Vetec (Duque de Caxias, Brazil). Glycerol was obtained from Synth (Diadema, Brazil). Diesel S50 was supplied by LUBNOR (Petrobras/LUBNOR, Lubrificantes e Derivados de Petróleo do Nordeste, Fortaleza, Brazil). Transesterification Reaction. The soybean oil was fed with methanol and sodium hydroxide into a glass reactor (1000 mL) with two openings at the top where a reflux condenser, a thermometer, and a mechanical stirrer model R100C were connected. The reactor jacket was connected to a thermostatic bath responsible to maintain the reaction temperature. The reaction condition was set with a methanol to oil molar ratio of 6:1 and 0.01 (w/w) of catalyst to oil was used. More details regarding the transesterification reaction can be obtained in Nogueira, Jr., et al. (2010).8,9 The FAME (fatty acid methyl ester) composition is presented in Table 1. Biodiesel Characterization. The methyl ester content (biodiesel) and molecular characterization were assayed by gas chromatograph (Thermos model Ultra) provided with a flame ionization detector. An OV-1 capillary column with a 30 m length, 0.25 mm inner diameter, and 0.25 μm film thickness was used. The injector and detector temperatures were both set at 523.15 K. The oven temperature started at 323.15 K and was increased to 503.15 K at a rate of 278.15 K·min−1 and held for 10 min. Blends. All binary blends were prepared in the mass fraction range between w = (0.090 and 0.900), at 298.15 K and atmospheric pressure. Ternary blends were prepared in the mass fraction range of diesel between w = (0.800 and 0.940) and in the mass fraction range of soybean biodiesel and oil between w = (0.030 and 0.110). Viscosity and Density Measurements of the Blends. The properties to be analyzed, density (ρ) and viscosity (μ) data, were read in an Anton Paar SVM 3000 digital oscillation U-tube apparatus. Initially, a calibration procedure has been

made by using a Cannon mineral oil (CAS no. 68037.01.4) at a temperature range from (293.15 to 373.15) K. The sample volume of 5 mL was injected into the equipment to measure such properties of pure diesel, biodiesel and oil, and their binary and ternary blends. The determination of viscosity was done in a cell containing a tube fully filled with sample rotating at constant speed. The density was determined by a densimeter using U-tube principle. Both measurements were done simultaneously. The density measurement has an uncertainty of 0.0005 g·cm−3, and the viscosity measurement has an error of 0.35 %. The binary and ternary blends were prepared using an electronic balance (Shimatzu AY220) with an accuracy of 0.0001 g. The uncertainty in mole fractions reported in this work is estimated to be less than ± 1.8·10−3. The measurements were measured according to the standard test method for dynamic viscosity and density of liquids by Stabinger viscometer, followed by ASTM D7042-04.

a

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MATHEMATICAL MODELS AND CORRELATIONS Density. For n-heptadecane, FAMEs and TGs the GCVOL model developed by Elbro et al.10 was used with the revised parameters by Ihmels and Gmehling:6 M M ρL = = n ∑i = 1 niΔvi V (1) where M is the molecular weight and V is the molar volume. Elbro et al. calculated the molar volume by summing of the all group volume contributions, Δvi with ni being the number of groups i appearing in the compound, and Δvi is expressed as a polynomial function of the absolute temperature: Δvi = Ai + Bi T + CiT 2

(2) −1

where the units are K for temperature and cm ·mol for Δvi (see Table S1 of the Supporting Information). For the blends the density was calculated by Kay’s mixing rules:11,12 ρblend = x1ρ1 + x 2ρ2 (3) 3

B



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Table 3. Dynamic Viscosity Data, μ (mPa·s), and Density Data, ρ (g·cm−3), for the Binary Blends (w1 Soybean Oil + (1 − w1) Soybean Biodiesel) at Temperatures Ranging from (293 to 373) K in Steps of 20 Ka w1

T/K = 293.15

T/K = 313.15

T/K = 333.15

T/K = 353.15

T/K = 373.15

3.2583 3.7942 4.5011 5.2865 6.2793 7.5244 9.0321 10.724 13.054

2.3342 2.6533 3.1100 3.6400 4.2105 5.0215 5.8903 6.9022 8.2349

1.7565 1.9530 2.2846 2.6587 3.1611 3.5861 4.1228 4.8000 5.5224

0.8614 0.8650 0.8686 0.8722 0.8759 0.8795 0.8832 0.8866 0.8905

0.8464 0.8503 0.8543 0.8576 0.8618 0.8653 0.8689 0.8725 0.8764

0.8326 0.8361 0.8399 0.8438 0.8477 0.8518 0.8557 0.8595 0.8630

μ/mPa·s 0.104 0.205 0.305 0.399 0.504 0.602 0.707 0.801 0.903

8.1679 9.8744 12.304 15.018 18.696 23.446 29.777 37.080 47.882

4.8918 5.7913 7.0245 8.3715 10.150 12.397 15.239 18.454 23.052 ρ/g·cm−3

0.104 0.205 0.305 0.399 0.504 0.602 0.707 0.801 0.903

0.8899 0.8935 0.8967 0.9001 0.9039 0.9071 0.9106 0.9137 0.9172

0.8757 0.8793 0.8827 0.8862 0.8899 0.8934 0.8969 0.9003 0.9039

a w1 is the mass fraction of soybean oil. Standard uncertainties u are u(T) = 0.01 K, u(ρ) = 0.0005 g·cm−3, and u(μ) = 0.35 % (0.95 level of confidence).

Table 4. Dynamic Viscosity Data, μ (mPa·s), and Density Data, ρ (g·cm−3), for the Binary Blends (w1 Soybean Biodiesel + (1 − w1) Diesel) at Temperatures Ranging from (293 to 373) K in Steps of 20 Ka w1

T/K = 293.15

T/K = 313.15

T/K = 333.15

T/K = 353.15

T/K = 373.15

1.7220 1.8107 1.9182 2.0475 2.1593 2.2754 2.3559 2.4890 2.6491

1.2569 1.3298 1.4050 1.4972 1.5802 1.6580 1.7165 1.8122 1.9261

0.94697 1.0150 1.0757 1.1444 1.2101 1.2642 1.3090 1.3788 1.4779

0.8052 0.8105 0.8170 0.8233 0.8288 0.8351 0.8400 0.8460 0.8526

0.7911 0.7959 0.8028 0.8087 0.8145 0.8207 0.8256 0.8315 0.8381

0.7765 0.7821 0.7882 0.7946 0.8000 0.8061 0.8111 0.8168 0.8233

μ/mPa·s 0.107 0.208 0.316 0.423 0.518 0.623 0.714 0.806 0.909

4.0418 4.2447 4.5234 4.8684 5.1307 5.4466 5.6344 5.9723 6.3867

2.5076 2.6349 2.8017 2.9981 3.1598 3.3448 3.4617 3.6621 3.9091

0.107 0.208 0.316 0.423 0.518 0.623 0.714 0.806 0.909

0.8329 0.8383 0.8449 0.8512 0.8569 0.8634 0.8683 0.8745 0.8811

0.8191 0.8246 0.8311 0.8373 0.8430 0.8493 0.8542 0.8602 0.8669

ρ/g·cm−3

w1 is the mass fraction of soybean oil. Standard uncertainties u are u(T) = 0.01 K, u(ρ) = 0.0005 g·cm−3, and u(μ) = 0.35 % (0.95 level of confidence). a

Viscosity. The viscosity model used for the n-heptadecane10 (diesel) was based on the Andrade equation:8 ln μ = A +

B T

ln[μ/(mPa· s)] =

⎡

∑ Nk⎢A1k + k

⎣

⎤ B1k − C1k ln(T /K) − D1k (T /K)⎥ ⎦ (T /K)

⎡ B2k + Mi ∑ Nk ⎢A 2k + − C2k ln(T /K) ⎣ ( /K) T k

(4)

⎤ − D2k (T /K)⎥ + Q ⎦

where parameters A and B have been taken from the literature. The Ceriani model7 was used for viscosity prediction for the FAMEs.

(5)

where Nk is the number of groups k in molecule i; M is the component molecular weight that multiplies the perturbation C



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Table 5. Dynamic Viscosity Data, μ (mPa·s), and Density Data, ρ (g·cm−3), for the Binary Blends (w1 Soybean Oil + (1 − w1) Diesel) at Temperatures Ranging from (293 to 373) K in Steps of 20 Ka w1

T/K = 293.15

T/K = 313.15

T/K = 333.15

T/K = 353.15

T/K = 373.15

2.0659 2.5614 3.2287 4.0021 5.0193 6.2306 7.7819 10.080 12.468

1.4993 1.8340 2.2726 2.7663 3.4179 4.1694 5.1137 6.4996 7.9018

1.1477 1.3759 1.6878 2.0223 2.4806 2.9874 3.6167 4.5232 5.4200

0.8085 0.8175 0.8272 0.8362 0.8457 0.8551 0.8642 0.8753 0.8845

0.7942 0.8034 0.8133 0.8225 0.8321 0.8413 0.8507 0.8619 0.8711

0.7803 0.7895 0.7993 0.8086 0.8181 0.8276 0.8370 0.8482 0.8575

μ/mPa·s 0.105 0.210 0.314 0.414 0.514 0.610 0.704 0.815 0.905

5.0308 6.5773 8.6865 11.317 14.919 19.528 25.693 35.428 46.117

3.0499 3.8857 4.9787 6.3234 8.0845 10.265 13.120 14.449 22.065 ρ/g·cm−3

0.105 0.210 0.314 0.414 0.514 0.610 0.704 0.815 0.905

0.8359 0.8448 0.8544 0.8633 0.8729 0.8820 0.8911 0.9022 0.9112

0.8222 0.8312 0.8408 0.8498 0.8593 0.8686 0.8777 0.8887 0.8978

a w1 is the mass fraction of soybean oil. Standard uncertainties u are u(T) = 0.01 K, u(ρ) = 0.0005 g·cm−3, and u(μ) = 0.35 % (0.95 level of confidence).

Table 6. Dynamic Viscosity Data, μ (mPa·s), and Density Data, ρ (g·cm−3), for the Ternary Blends (w2 Diesel + w3 Soybean Biodiesel + (1 − w2 − w3) Soybean Oil) at Temperatures Ranging from (293 to 373) K in Steps of 20 Ka w2

w3

T/K = 293.15

0.025 0.040 0.057 0.083 0.100

0.029 0.041 0.059 0.070 0.090

4.1425 4.3478 4.5633 4.7766 5.0724

0.025 0.040 0.057 0.083 0.100

0.029 0.041 0.059 0.070 0.090

0.8308 0.8326 0.8351 0.8378 0.8403

T/K = 313.15 μ/mPa·s 2.5511 2.6724 2.7940 2.9173 3.0823 ρ/g·cm−3 0.8170 0.8189 0.8213 0.8241 0.8266

T/K = 333.15

T/K = 353.15

T/K = 373.15

1.7351 1.8244 1.9035 1.9828 2.0852

1.2625 1.3314 1.3872 1.4446 1.5133

0.9619 1.0101 1.0543 1.0994 1.1470

0.8031 0.8051 0.8072 0.8101 0.8125

0.7887 0.7907 0.7930 0.7961 0.7984

0.7749 0.7767 0.7787 0.7816 0.7842

w2 is the mass fraction of diesel, and w3 is the mass fraction of soybean biodiesel. Standard uncertainties u are u(T) = 0.01 K, u(ρ) = 0.0005 g·cm−3, and u(μ) = 0.35 % (0.95 level of confidence).

a

term; A1k, B1k, C1k, D1k, A2k, B2k, C2k, and D2k are parameters obtained from the regression of the experimental data (see Table S2 of the Supporting Information); k represents the groups of component i, and Q is a correction term expressed as Q = ξ1q + ξ2

atoms of the alcoholic part (NCS) in fatty esters. They are given as:

(6)

β − γ ln(T /K) − δ(T /K) (T /K)

(8)

ξ2 = s0 + NCSs1

(9)

where f 0, f1, s0, and s1 are optimized constants. All parameters of Ceriani model are reported in the Supporting Information (Table S2). Viscosity of Mixtures and Blends. The Grunberg−Nissan equation was used for viscosity calculations of the soybean biodiesel, oil biodiesel, and all blends (eq 10).

where q is a function of the absolute temperature, given by: q=α+

ξ1 = f0 + NCTf1

(7)

where α, β, γ, and δ are optimized parameters obtained by regression of the data. The effect of functional groups on the dynamic viscosity was corrected by the term Q according to the total number of carbon atoms, NCT, in the molecules. ξ1 is a function applicable to all compounds, and ξ2 describes the differences between the vapor pressure of NC isomer esters at the same temperature and is related to the number of carbon

n

ln μ =

∑ xi ln μi + i=1

1 2

n

n

∑ ∑ xixjGij i=1 j=1

(10)

where μi is the viscosity of each component of system and Gij is the binary parameter of interaction between two components. D



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w3

T/K = 293.15

0.028 0.039 0.052 0.067 0.079

0.029 0.049 0.068 0.089 0.114

4.1322 4.4619 4.6545 4.9443 5.2837

0.028 0.039 0.052 0.067 0.079

0.029 0.049 0.068 0.089 0.114

0.8308 0.8336 0.8357 0.8381 0.8413

T/K = 313.15 μ/mPa·s 2.5490 2.7326 2.8476 3.0085 2.1881 ρ/g·cm−3 0.8171 0.8198 0.8217 0.8243 0.8274

T/K = 333.15

T/K = 353.15

T/K = 373.15

1.7469 1.8622 1.9362 2.0388 2.1515

1.2818 1.3593 1.4113 1.4822 1.5602

0.98086 1.0368 1.0757 1.1268 1.1839

0.8032 0.8059 0.8080 0.8104 0.8136

0.7889 0.7918 0.7937 0.7964 0.7994

0.7748 0.7774 0.7794 0.7822 0.7850


a


w2

T/K = 293.15

0.025 0.041 0.059 0.078 0.095

0.030 0.046 0.063 0.084 0.101

4.1420 4.3582 4.6204 4.9359 5.1864

0.025 0.041 0.059 0.078 0.095

0.030 0.046 0.063 0.084 0.101

0.8307 0.8330 0.8357 0.8385 0.8411

T/K = 313.15 μ/mPa·s 2.5546 2.6768 2.8239 3.0062 3.1320 ρ/g·cm−3 0.8170 0.8195 0.8220 0.8248 0.8272

T/K = 333.15

T/K = 353.15

T/K = 373.15

1.7508 1.8284 1.9224 2.0437 2.1184

1.2838 1.3349 1.4028 1.4801 1.5367

0.9820 1.0272 1.0698 1.1232 1.1669

0.8031 0.8057 0.8081 0.8109 0.8133

0.7891 0.7913 0.7938 0.7967 0.7992

0.7746 0.7768 0.7794 0.7827 0.7851


a

It should be important to explain that Gij binary parameters for all blends were considered equal to zero, once intermolecular forces have been not taken into account. The oil was considered as a blend of simple TGs as suggested by Su et al.13

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Viscosity and density data were correlated as a function of the independent variables temperature (T) and mass fraction (w). For binary blends, the density data were fitted by eq 11.

ρ = A + BT + Cw1

(11)

The data showed good agreement with the equation previously presented. Viscosity data of binary blends were correlated to eq 12.

RESULTS AND DISCUSSION

The thermodynamic properties, viscosity and density, of pure oil, biodiesel and diesel were obtained at different temperatures (293.15 to 373.15 K with 20 K intervals). Densities and viscosities of binary and ternary blends were also measured at the same conditions. Table 2 presents the values of density and viscosity of pure components varying with the temperature. Tables 3 to 8 present the influence of temperature and mass fraction on density and viscosity of binary and ternary systems. Figures 1, 2, and 3 depict viscosity and density behavior of binary systems with mass fraction and temperature variations. Experimental and estimated data obtained from all regressions were submitted to chi-square statistical test to verify the goodness of fit. According to this method, a close agreement between experimental and estimated values (in our case density and viscosity) leads to small values of chi-square (χ2; see Table 9).14

ln μ = A +

B + Cw1 T

(12)

For binary blends the values of chi-square showed a maximum of 7.12·10−7 and 7.78·10−1 for density and viscosity, respectively. Density data of ternary blends were fitted by a first-order equation related to mass fraction and temperature, respectively, according to eq 13. ρ = A + BT + Cw1 + Dw2

(13)

Viscosity data of ternary blends were fitted by an exponential equation represented by eq 14. ln μ = A + E

B + Cw1 + Dw2 T

(14)



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Figure 1. (a) Temperature and mass fraction effect on density for blends of soybean oil (1) + soybean biodiesel (2); (b) temperature and mass fraction effect on dynamic viscosity for blends of soybean oil (1) + soybean biodiesel (2); temperature ranging from (293.15 to 373.15) K in steps of 20 K.

Figure 2. (a) Temperature and mass fraction effect on density for blends of soybean biodiesel (1) + diesel (2); (b) temperature and mass fraction effect on dynamic viscosity for blends of soybean biodiesel (1) + diesel (2); temperature ranging from (293.15 to 373.15) K in steps of 20 K.

For ternary blends the values of chi-square were 9.45·10−6 and 6.29·10−1 for density and viscosity, respectively. The χ2 values obtained for all binary and ternary systems showed a good agreement between experimental and estimated values obtained from eqs 11 to 14 greater than 99.5 %. Figure 4 shows the behavior of density (ρ) and viscosity (μ) as a function of temperature and mass fraction. The results of the predictions of density and viscosity for all systems are presented in Tables 10 and 11, respectively. The statistical parameter used for comparison of prediction was the average absolute error (AAE): n

AAE = 100·∑ i=1

θiexp − θicalc θiexp

The density predictions for all systems using the GCVOLOL-60 model presented good results. The best results for density predictions was observed for soybean biodiesel (AAE = 0.93 %), and the worst results was observed for the ternary blend of soybean oil + soybean biodiesel + diesel (AAE = 6.16 %). The Ceriani model did not result in good agreement of viscosity prediction for soybean biodiesel and soybean oil. The results for both systems were 25.02 % and 12.86 % for AAE, respectively. The worst results for prediction were observed with the soybean oil + soybean biodiesel blend (AAE = 31.71 %). It should be mentioned that for both components (soybean oil and biodiesel) Ceriani's method has been employed. This method presents a larger deviation for biodiesel prediction, as it has been observed by do Carmo et al. (2012).16 Nevertheless,

(15)

where θ is the density or the viscosity. F



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Figure 3. (a) Temperature and mass fraction effect on density for blends of soybean oil (1) + diesel (2); (b) temperature and mass fraction effect on dynamic viscosity for blends of soybean oil (1) + diesel (2); temperature ranging from (293.15 to 373.15) K in steps of 20 K.

Figure 4. (a) Temperature and mass fraction effect on density for blends of soybean oil (1) + soybean biodiesel (2) + diesel (3); (b) temperature and mass fraction effect on dynamic viscosity for blends of soybean oil (1) + soybean biodiesel (2) + diesel (3); temperature ranging from (293.15 to 373.15) K in steps of 20 K.

Table 9. Empirical Correlations of Density, ρ (g·cm−3), and Dynamic Viscosity, μ (mPa·s), for Binary (eqs 11 and 12) and Ternary (eqs 13 and 14) Blends χ2

parameters system soybean oil (1) + diesel (2) soybean oil (1) + soybean biodiesel (2) soybean biodiesel (1) + diesel (2) soybean oil (1) + soybean biodiesel (2) + diesel (3)

eq

A

B

C

11 12 11 12 11 12 13 14

1.0254 9.3859 1.0903 −8.5473 1.0359 −5.6382 1.0349 −5.8089

−0.0007 3136.2 0.0007 3049.2 −0.0007 2045.0 −0.0007 2099.5

0.0952 2.7733 0.0367 2.2198 0.0585 0.5398 0.0725 1.6643

G

D

agreement

0.0721 1.1084

7.12·10−7/> 0.995 7.72·10−1/>0.995 3.06·10−7/>0.995 7.78·10−1/>0.995 1.96·10−7/>0.995 9.55·10−3/>0.995 9.45·10−6/>0.995 6.29·10−1/>0.995



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Table 10. AAE for Density Prediction of All Systems Studied AAE (%) system

T/K = 293.15

T/K = 313.15

T/K = 333.15

T/K = 353.15

T/K = 373.15

overall

soybean oil soybean biodiesel diesel (n-heptadecane) soybean oil + soybean biodiesel soybean oil + diesel soybean biodiesel + diesel soybean oil + soybean biodiesel + diesel

2.08 0.53 5.61 0.83 5.12 3.27 5.59

1.78 0.89 5.98 1.04 5.45 3.64 5.97

1.61 1.08 6.23 1.19 5.71 3.88 6.25

1.61 1.10 6.38 1.22 5.88 3.99 6.44

1.62 1.06 6.56 1.22 5.99 4.02 6.54

1.74 0.93 6.15 1.10 5.63 3.76 6.16

Table 11. AAE for Viscosity Prediction of All Systems Studied AAE (%) system

T/K = 293.15

T/K = 313.15

T/K = 333.15

T/K = 353.15

T/K = 373.15

overall

soybean oil soybean biodiesel diesel (n-heptadecane) soybean oil + soybean biodiesel soybean oil + diesel soybean biodiesel + diesel soybean oil + soybean biodiesel + diesel

15.18 24.99 3.51 29.69 39.56 4.13 13.35

6.82 25.98 6.10 25.30 31.13 2.40 6.15

8.12 28.85 10.35 23.90 29.29 3.78 3.81

13.86 34.99 11.71 23.93 28.92 4.42 3.96

20.31 10.29 12.42 46.58 29.65 21.05 4.71

12.86 25.02 8.82 29.88 31.71 7.15 6.40

e Gás (PRH-ANP/MCT), and also Petrobras for financial support.

Andrade’s equation used for n-heptadecane prediction shows a good approximation for diesel viscosity.

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Notes

CONCLUSIONS Densities and viscosities of pseudopure soybean biodiesel, diesel, and soybean oil, binary mixtures (soybean biodiesel + diesel; soybean biodiesel + soybean oil; and soybean oil + diesel), and the soybean oil + soybean biodiesel + diesel ternary mixture have been determined in this work. These data have been fitted according to an expression proposed by Baroutian et al.15 for binary and ternary systems, revealing χ2 values with an agreement greater than 99.5 %. A linear behavior as function of temperature has been observed for density measured data. For viscosity, the data show an exponential decrease with the increase of the temperature for binary and ternary systems. The GCVOL-OL-60 model used to predict density showed relative differences between experimental and estimated values of maximum AAE of 6.56 %. The Ceriani model used to predict viscosity showed great differences between experimental and estimated values, resulting in relative differences of a maximum AAE of 46.58 %.

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The authors declare no competing financial interest.

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(1) Janaun, J.; Ellis, N. Perspectives on biodiesel as a sustainable fuel. Renewable Sustainable Energy Rev. 2010, 14, 1312−1320. (2) Knothe, G.; Van Gerpen, J. H. The Biodiesel Handbook, 2nd ed.; AOCS Publishing: Urbana, IL, 2009. (3) Brazilian Regulatory Agency (Standard Resolution No. 7, de 19.3.2008). In Portuguese. http://www.anp.gov.br/petro/legis_ biodieselasp (accessed December 20, 2010). (4) Baroutian, S.; Aroua, M. K.; Raman, A. A. A.; Sulaiman, N. M. N. Viscosities and Densities of Binary and Ternary Blends of Palm Oil + Palm Biodiesel + Diesel Fuel at Different Temperatures. J. Chem. Eng. Data 2010, 55, 504−507. (5) Ihmels, E. C.; Gmehling, J. Extension and Revision of the Group Contribution Method GCVOL for the Prediction of Pure Compound Liquid Densities. Ind. Eng. Chem. Res. 2003, 42, 408−412. (6) Ceriani, R.; Gonçalves, C. B.; Rabelo, J.; Caruso, M.; Cunha, A. C. C.; Cavaleri, F. W.; Batista, E. A. C.; Meireles, A. J. A. Group Contribution Model for Predicting Viscosity of Fatty Compounds. J. Chem. Eng. Data 2007, 52, 965−972. (7) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: Boston, MA, 1987. (8) Nogueira, C. A., Jr.; Feitosa, F. X.; Fernandes, F. A. N.; Santiago, R. S.; de Sant'Ana, H. B. Densities and Viscosities of Binary Mixtures of Babassu Biodiesel + Cotton Seed or Soybean Biodiesel at Different Temperatures. J. Chem. Eng. Data 2010, 55, 5305−5310. (9) Parente, R. C.; Nogueira, C. A., Jr.; Carmo, F. R.; Lima, L. P.; Fernandes, A. N.; Santiago-Aguiar, R. S.; Sant’Ana, H. B. Excess Volumes and Deviations of Viscosities of Binary Blends of Sunflower Biodiesel + Diesel and Fish Oil Biodiesel + Diesel at Various Temperatures. J. Chem. Eng. Data 2011, 56, 3061−3067. (10) Elbro, H. S.; Fredenslund, A.; Rasmussen, P. Group Contribution Method for the Prediction of Liquid Densities as a Function of Temperature Solvents, Oligomers, and Polymers. Ind. Eng. Chem. Res. 1991, 30, 2576−2582. (11) Kay, W. Density of hydrocarbon gases and vapors at high temperature and pressure. Ind. Eng. Chem. 1936, 28, 1014−1019.

ASSOCIATED CONTENT

S Supporting Information *

Parameters of the GCVOL-OC-60 and Ceriani models. This material is available free of charge via the Internet at http:// pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail address: [email protected]. Tel.: +55 85 3366-9611. Funding

The authors thank the following Brazilian national agencies: ́ CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnológico), Agência Nacional do Petróleo, Gás Natural e ́ Biocombustiveis (ANP), Financiadora de Estudos e Projetos (FINEP), Ministério da Ciência e Tecnologia (MCT), Programa de Recursos Humanos da ANP para o Setor Petróleo H



Article

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