Densities and Viscosities for Binary Liquid Mixtures of Biodiesel + 1

Article pubs.acs.org/jced

Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Densities and Viscosities for Binary Liquid Mixtures of Biodiesel + 1‑Pentanol, 2‑Pentanol, or 2‑Methyl-1-Butanol from (288.15 to 338.15) K at 0.1 MPa Leidy T. Vargas-Ibáñez,† Gustavo A. Iglesias-Silva,‡ José J. Cano-Gómez,*,† Carlos Escamilla-Alvarado,† and Miguel A. Berrones-Eguiluz† †

Facultad de Ciencias Químicas Universidad Autónoma de Nuevo León, San Nicolás de los Garza, Nuevo León C.P. 66455, México Departamento de Ingeniería Química Instituto Tecnológico de Celaya Celaya, Guanajuato, C.P. 38010, México

‡

ABSTRACT: This work presents experimentally determined densities and viscosities of biodiesel blended with 1-pentanol, 2-pentanol, and 2-methyl-1-butanol between 288.15 and 338.15 K at 0.1 MPa. The densities are measured using a vibrating tube densimeter, and the kinematic viscosities, using a glass capillary viscometer. The measured density and viscosity of the pure components agree with values reported in the literature within average absolute percentage deviations of 0.04 and 0.83%, respectively. The excess molar volumes and viscosity deviations show positive and negative deviations from ideality, respectively. The Redlich−Kister equation is used to represent the composition behavior of the excess molar volumes and viscosity deviations. The experimental kinematic viscosities have a minimum value over a composition range of 50−90% alcohol by weight. The McAllister equation correlates the kinematic viscosity within an average absolute percentage deviation of 1.77%, while ́ equation correlates the kinematic viscosity within 0.88%. the Nava-Rios

1. INTRODUCTION Globally, the major greenhouse gases (GHG) emitted by human activities are CO2, CO, CH4, N2O, and F-containing gases. The economic activities that most contribute to GHG production are from the agricultural, industrial, transportation, heating, and electricity production sectors.1 Transport accounts for 14% of global GHG emissions, with most carbon dioxide emission coming from the combustion of fossil fuels.2 Biodiesel is an alternative fuel for compression ignition internal combustion engines because it is biodegradable and nontoxic and reduces greenhouse gas emissions by up to 51%.3 However, it has high viscosity and density compared to diesel.4,5 These differences restrict its use as a fuel, affecting engine performance, combustion, exhaust emissions, and the fuel injection system. High viscosities cause poor fuel atomization when the fuel is injected into the combustion chamber, increasing the energy required to pump the fuel through the fuel system components (fuel pump, filter, and transfer and safety valves) and producing deposits in the engine.6,7 Density is a key property that directly affects the volume of fuel supplied to the diesel injection system.5 High-density fuel, such as biodiesel, will influence the output power of the engine because the injected fuel has a different mass.8 An alternative to improving the physicochemical properties of biodiesel is to use alcohols as additives. Simple alcohols such as methanol and ethanol are the most commonly used additives.9 However, these alcohols present some disadvantages such as low lubricity, low solubility at high concentrations, low octane number, and low calorific value.10−12 Higher alcohols such as 1-pentanol, 2-pentanol, and 2-methyl-1-butanol have been used as © XXXX American Chemical Society

additives to overcome the disadvantages of low carbon alcohols and decrease the density and viscosity of biodiesel.13 In addition, a knowledge of new experimental values of density and viscosity for mixtures of biodiesel +1-pentanol, 2-pentanol, and 2-methyl1-butanol is important to the design of the fuel injection system components as well as the study of the spray characteristics of fuel in a combustion chamber. Also, the need for a database of accurate properties such as densities and viscosities is essential to developing predictive models. Unfortunately, densities and viscosities of biodiesel + alcohol blends are scarce in the literature. Barabás14 determined the densities of blends of biodiesel + ethanol from 273.15 to 333.15 K using a vibrating tube densimeter (DMA 4500, Anton Paar). He calculated the excess molar volume from experimental densities showing positive deviations over the entire composition and temperature ranges. Yasin et al.15 studied the physical characteristics of pure biodiesel and fuel mixtures (80% diesel and 20% biodiesel by volume) with methanol and ethanol. They found that the addition of alcohol at concentrations of 5 and 10% by volume decreases the viscosity and density of the fuel under the conditions needed in the engine. Lapuerta et al.16 measured the effect of alcohol concentration on the kinematic viscosity of diesel (or biodiesel) + ethanol or n-butanol blends at 313.15 K. They reported that blends with an ethanol content of less than 36% (by volume) comply with the Special Issue: Emerging Investigators Received: November 14, 2017 Accepted: March 19, 2018

A

DOI: 10.1021/acs.jced.7b00996 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Sample Information

a

initial purity

molar mass

chemical name

source

CAS no.

mass fraction

g·mol−1

purification method

analysis method

1-pentanol methanol 2-pentanol 2-methyl-1-butanol

Sigma-Aldrich J.T. Baker Merck Merck

71-41-0 67-56-1 6032-29-7 137-32-6

0.998 0.999 0.997 0.999

88.15 32.04 88.15 88.15

none none none none

GCa GCa GCa GCa

Gas chromatography provided by the supplier.

EN 590 standard whereas all the blends with n-butanol meet the standard. Recently, Geacai et al.17 measured the density and viscosity of biodiesel + n-butanol mixtures from (293.15 to 323.15) K over the entire composition range. They reported that the densities of the biodiesel + n-butanol mixtures that have an alcohol mass fraction of 0.4 to 0.8 meet the limits set by the diesel fuel standard (EN 590), while all of the blends comply with the standard for kinematic viscosity. In this study, we have measured the experimental densities and viscosities of blends of biodiesel +1-pentanol, 2-pentanol, and 2-methyl-1-butanol from (288.15 to 338.15) K at 0.1 MPa over the entire concentration range. The densities and viscosities of the mixtures are compared with the limits established by the diesel fuel standard (EN 590). We have correlated the kinematic viscosities using the correlations developed by McAllister18 and ́ et al.19 Excess molar volumes and viscosity deviations Nava-Rios are represented using the Redlich−Kister20 equation.

in sealed containers and mixed thoroughly to guarantee a homogeneous system prior to measurement. Preventive measures are taken to avoid exposure to air and evaporation. Additionally, 1-pentanol, 2-pentanol, and 2-methyl-1-butanol are stored with molecular sieves (5 Å) to prevent water absorption. Biodiesel Production. In this work, we have used beef tallow supplied by a slaughterhouse to produce biodiesel. The transesterification of beef tallow is conducted in a 500 mL three-necked flask equipped with a condenser to avoid the loss of methanol by evaporation. A heating mantle (model EMA0500, Cole-Parmer) is used to control the reaction temperature. The moisture in the grease is removed at approximately 383.15 K. The grease is then cooled to the reaction temperature, 333.15 K, and the catalyst (0.5% in mass fraction of NaOH/tallow) is diluted into the methanol to achieve a molar ratio of 6:1 methanol/fat. The reactants are stirred for 60 min at 800 rpm. After the completion of the reaction, the mixture is transferred to a container and held for 8 h to promote the separation of biodiesel and glycerin. The obtained biodiesel is washed with distilled water to remove any residual catalyst, glycerol, and excess methanol. This procedure is repeated until the pH of the rinsewater is equal to that of the distilled water. The biodiesel is then separated from the aqueous phase and heated to 383.15 K for 20 min to remove any residual water and methanol. Finally, the biodiesel is filtered through filter paper (limit 2 μm) and stored in an airtight container. Biodiesel Characterization. The composition of biodiesel is determined by a gas chromatograph (model HP 5890A) equipped with a flame ionization detector (FID). A column of fused silica (model 530 Omegawax) of 30 m length, 0.53 mm inner diameter, and 0.5 μm thickness is used in the separation. The temperature of the injector and detector is set at 523.15 K. The oven temperature is kept at 313.15 K for 2 min and then increased to 513.15 K at a rate of 7 K/min. The oven stays at this temperature for 18 min.21 Apparatuses and Procedures. The densities of the pure substances and mixtures are measured using a vibrating tube densimeter (Anton Paar, DMA 5000). The reproducibilities reported by the manufacturer for density and temperature are 1 × 10−6 g·cm−3 and 0.001 K, respectively. The density of the fluid is related to the period of oscillation of the U-tube filled with the sample when the cell is under a harmonic electromagnetic force. The densimeter is calibrated periodically using ultrapure

2. EXPERIMENTAL SECTION 2.1. Samples. The samples are provided by Sigma-Aldrich for 1-pentanol (99.8% in mass fraction), J.T. Baker for methanol (99.9% in mass fraction), Merck for 2-pentanol (99.7% in mass fraction), and 2-methyl-1-butanol (99.9% in mass fraction). Table 1 presents the sample specifications. The mixtures are prepared gravimetrically using an analytical balance (Ohaus, OHAUS00240) with a precision of 0.1 mg. The overall standard uncertainty in the mass fraction is 0.002. The samples are placed Table 2. Fatty Acid Methyl Ester (FAME) Composition in Mass Fraction (w) and Molar Fraction (x) Together with the Molar Mass (M) of Beef Tallow Biodiesel fatty acid methyl ester

M/g·mol−1

mass fraction (w)

molar fraction (x)

C14:0 (myristate) C16:0 (palmitate) C16:1 (palmitoleate) C17:0 (heptadecanoate) C18:0 (stereate) C18:1 (oleate) C18:2 (linoleate) C18:3 (linolenate)

242.40 270.46 268.44 284.48 298.51 296.50 294.48 292.46

0.028 0.239 0.029 0.014 0.197 0.409 0.076 0.008

0.033 0.254 0.031 0.014 0.190 0.396 0.074 0.008

Table 3. Some Fuel Properties of Beef Tallow Biodiesel parameters

EN test method

limits EN 14214

beef talow biodiesel

iodine value sediment content (% in volume fraction) acid value (mg KOH·g−1) flash point (K) methanol content (% in mass fraction) density, 288.15 K (g·cm−3) kinematic viscosity, 313.15 K (mm2·s−1)

EN 14111 EN ISO 12937 EN 14104 EN ISO 3679 EN 14110 EN ISO 12185 EN ISO 3104

max. 120 max. 0.05 max. 0.5 >393.15 max. 0.2 0.86−0.90 3.5−5.0

52 0.02 0.22 449.15 not detected 0.876 4.637

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Table 4. Comparison between the Experimental Pure Component Liquid Density, ρ(g·cm−3), and Viscosity, η(mPa·s), at Temperature T and Literature Values at Pressure p = 0.1 MPaa ρ/g·cm−3 T/K

this work

η/mPa·s literature

AAPD %

this work

literature

AAPD %

4.700

4.65533

0.97

25

0.39

4.03229

0.33

4.04633

0.02

3.51034

0.58

33

0.27

3.05435

0.66

3.02629

0.26

2.59922

2.77

29

1.24

2.31429

1.78

2.29925

2.42

2.04229

0.47

1-Pentanol 288.15

0.81859

0.8182824

0.033

0.8141226

0.094

0.8146827

0.026

0.8109428

0.036

0.81832 293.15 298.15

0.81489 0.81123

29

0.007

0.8071126

0.054

0.8075829

0.004

0.8036030

0.029

0.81129 303.15 308.15

0.80755 0.80383

318.15 323.15 328.15 333.15 338.15

0.80008 0.79629 0.79246 0.78856 0.78466 0.78070

4.682 4.045 3.490

3.499 3.034 2.674

29

0.037

0.7997826

0.037

0.7999031

0.022

0.7962030

0.011

0.7964329

0.018

2.04533

0.33

26

0.025

33

0.08

0.7922031

0.033

1.82236

0.59

0.7884032

0.020

1.60833

0.06

0.7883031

0.033

1.58622

1.43

31

0.033

33

0.09

0.7845933

0.009

1.44036

0.52

0.7804031

0.038

1.27231

0.95

0.7806233

0.010

1.28333

0.09

5.063

5.07937

0.33

4.172

4.16146

0.26

3.412

3.38137

0.89

3.42147

0.28

2.825

2.77441

1.81

2.340

2.33045

0.43

2.34841

0.34

1.97941

0.70

0.80353 313.15

0.038

25

0.79266

0.78440

2.640 2.356 2.052 1.811 1.609 1.433 1.284

1.810

1.434

2-Pentanol 288.15

0.81355

0.8128037

0.092

38

0.068

0.8090439

0.068

40

0.037

0.8054040

0.019

41

0.062

0.8009039

0.067

0.8012042

0.030

0.7966037

0.082

38

0.056

0.7936043

0.078

0.7925044

0.061

1.99045

0.15

37

0.067

38

0.82

0.7897038

0.136

1.67537

1.70

0.7840042

0.024

1.46643

0.61

0.7843043

0.014

0.7791745

0.064

6.46838

0.26

0.81410 293.15

0.80959

0.80929 298.15

0.80555

0.80505 303.15 308.15

0.80144 0.79725

0.79770 313.15 318.15 323.15

0.79298 0.78863 0.78419

328.15

0.77967

333.15

0.77507

338.15

0.77037

0.78810

1.993 1.704 1.475

1.718

1.303 1.135 1.012

2-Methyl-1-butanol 288.15 293.15 298.15

0.82302

0.8221448

0.107

6.451

0.81956

48

0.128

5.285

0.8198049

0.029

0.8149038

0.113

0.8159049

0.010

0.81582

0.81851

C

4.492



Article

Table 4. continued ρ/g·cm−3 T/K

a

this work

303.15

0.81203

308.15 313.15

0.80820 0.80433

318.15

0.80039

323.15

0.79639

328.15 333.15 338.15

0.79234 0.78820 0.78384

η/mPa·s literature

AAPD % 2-Methyl-1-butanol 0.127 0.046 0.062 0.128 0.034 0.091 0.117 0.036 0.110 0.051 0.026

0.8110043 0.8124049 0.8077038 0.8033048 0.8046049 0.8036050 0.7994548 0.8001050 0.7955148 0.7968049 0.7966050 0.7888049

this work

literature

AAPD %

3.813

3.80150

0.32

3.258 2.777

3.29550 2.84350

1.14 2.38

2.375

2.34150

1.43

2.057

1.791 1.573 1.377

0.076

Standard uncertainties: ur(η) = 0.01, u(T) = 0.03 K for viscosity, and ur(ρ) = 3 × 10−4, u(T) = 0.01 K for density and u(p) = 10 kPa.

Table 5. Experimental Densities, ρ (g·cm−3), Excess Molar Volumes, VE (cm3·mol−1), Viscosities, η (mPa·s), and Viscosity Deviations, Δη (mPa·s), at Temperature T, Mass Fraction w, and Mole Fraction x, for the System Biodiesel (1) + 1-Pentanol (2) at Pressure p = 0.1 MPaa w2

x2

ρ

0.000 0.100 0.199 0.300 0.399 0.499 0.600 0.699 0.801 0.899 1.000

0.000 0.266 0.447 0.583 0.684 0.764 0.830 0.883 0.929 0.967 1.000

0.87635 0.87001 0.86371 0.85759 0.85159 0.84571 0.84016 0.83455 0.82911 0.82385 0.81859

0.000 0.100 0.199 0.300 0.399 0.499 0.600 0.699 0.801 0.899 1.000

0.000 0.266 0.447 0.583 0.684 0.764 0.830 0.883 0.929 0.967 1.000

0.86170 0.85524 0.84887 0.84269 0.83665 0.83079 0.82514 0.81955 0.81415 0.80885 0.80383

0.000 0.100 0.199 0.300 0.399 0.499 0.600 0.699 0.801 0.899 1.000

0.000 0.266 0.447 0.583 0.684 0.764 0.830 0.883 0.929 0.967 1.000

0.84715 0.84044 0.83394 0.82768 0.82152 0.81555 0.80988 0.80429 0.79885 0.79349 0.78856

VE

η

T = 288.15 K 0.000 7.843 0.062 6.817 0.134 6.158 0.138 5.623 0.159 5.243 0.157 4.945 0.103 4.710 0.097 4.533 0.053 4.480 0.032 4.524 0.000 4.700 T = 308.15 K 0.000 4.457 0.096 3.959 0.181 3.579 0.191 3.296 0.213 3.101 0.201 2.931 0.157 2.773 0.143 2.698 0.088 2.658 0.068 2.639 0.000 2.674 T = 328.15 K 0.000 2.914 0.153 2.580 0.247 2.333 0.249 2.133 0.277 1.994 0.266 1.869 0.207 1.760 0.178 1.690 0.114 1.626 0.093 1.603 0.000 1.609

Δη

ρ

0.000 −0.190 −0.279 −0.388 −0.451 −0.495 −0.524 −0.534 −0.443 −0.281 0.000

0.87264 0.86628 0.85995 0.85385 0.84784 0.84197 0.83638 0.83077 0.82539 0.82012 0.81489

0.000 −0.024 −0.080 −0.122 −0.137 −0.163 −0.204 −0.184 −0.142 −0.094 0.000

0.85806 0.85154 0.84516 0.83897 0.83292 0.82707 0.82145 0.81581 0.81044 0.80509 0.80008

0.000 0.013 0.003 −0.021 −0.028 −0.047 −0.071 −0.071 −0.075 −0.049 0.000

0.84351 0.83671 0.83016 0.82378 0.81767 0.81171 0.80604 0.80038 0.79491 0.78961 0.78466

VE

η

Δη

T = 293.15 K 0.000 6.658 0.068 5.851 0.148 5.299 0.146 4.863 0.169 4.548 0.165 4.299 0.116 4.094 0.110 3.947 0.056 3.891 0.036 3.943 0.000 4.045 T = 313.15 K 0.000 3.979 0.112 3.525 0.195 3.187 0.202 2.934 0.223 2.755 0.206 2.592 0.154 2.459 0.147 2.368 0.085 2.329 0.071 2.326 0.000 2.356 T = 333.15 K 0.000 2.682 0.174 2.361 0.272 0.272 0.294 1.936 0.300 1.807 0.280 1.683 0.215 1.594 0.193 1.514 0.129 1.464 0.094 1.438 0.000 1.433

ρ

0.000 −0.112 −0.190 −0.272 −0.323 −0.361 −0.395 −0.403 −0.339 −0.189 0.000

0.86899 0.86259 0.85629 0.85014 0.84413 0.83824 0.83262 0.82705 0.82168 0.81644 0.81123

0.000 −0.023 −0.066 −0.099 −0.114 −0.146 −0.173 −0.177 −0.142 −0.084 0.000

0.85442 0.84785 0.84145 0.83524 0.82918 0.82325 0.81759 0.81204 0.80663 0.80131 0.79629

0.000 0.011 2.133 −0.018 −0.021 −0.044 −0.051 −0.065 −0.057 −0.037 0.000

0.83991 0.83301 0.82631 0.81990 0.81372 0.80775 0.80212 0.79642 0.79099 0.78565 0.78070

VE

η

T = 298.15 K 0.000 5.858 0.081 5.114 0.151 4.623 0.160 4.243 0.181 3.978 0.179 3.743 0.135 3.580 0.121 3.462 0.064 3.410 0.039 3.440 0.000 3.490 T = 318.15 K 0.000 3.570 0.123 3.155 0.206 2.858 0.213 2.627 0.232 2.469 0.227 2.313 0.178 2.194 0.151 2.095 0.092 2.029 0.072 2.018 0.000 2.052 T = 338.15 K 0.000 2.450 0.195 2.154 0.322 1.940 0.337 1.767 0.346 1.647 0.317 1.537 0.233 1.444 0.211 1.360 0.134 1.320 0.100 1.286 0.000 1.284

Δη

ρ

0.000 −0.115 −0.176 −0.235 −0.261 −0.305 −0.312 −0.304 −0.248 −0.129 0.000

0.86534 0.85888 0.85256 0.84641 0.84040 0.83450 0.82887 0.82326 0.81787 0.81261 0.80755

0.000 −0.011 −0.033 −0.058 −0.063 −0.097 −0.116 −0.134 −0.131 −0.085 0.000

0.85108 0.84439 0.83789 0.83161 0.82547 0.81951 0.81378 0.80821 0.80277 0.79748 0.79246

VE

η

T = 303.15 K 0.000 5.100 0.099 4.476 0.172 4.055 0.177 3.729 0.196 3.482 0.195 3.276 0.150 3.143 0.141 3.050 0.085 2.982 0.061 2.963 0.000 3.034 T = 323.15 K 0.000 3.205 0.145 2.847 0.238 2.582 0.246 2.361 0.268 2.207 0.256 2.073 0.208 1.968 0.175 1.882 0.111 1.825 0.079 1.791 0.000 1.811

Δη 0.000 −0.075 −0.121 −0.167 −0.205 −0.245 −0.242 −0.225 −0.198 −0.140 0.000 0.000 0.013 0.001 −0.032 −0.045 −0.066 −0.080 −0.092 −0.085 −0.066 0.000

0.000 0.014 0.322 −0.004 −0.006 −0.022 −0.038 −0.060 −0.047 −0.037 0.000

Maximum standard uncertainties: u(w2) = 0.002, u(x2) = 0.002, ur(ρ) = 3 × 10−4, u(VE) = 0.115 cm3·mol−1, ur(η) = 0.01, u(Δη) = 0.093 mPa·s, and u(T) = 0.01 K for density, u(T) = 0.03 K for viscosity, and u(p) = 10 kPa. a

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Table 6. Experimental Densities, ρ (g·cm−3), Excess Molar Volumes, VE (cm3·mol−1), Viscosities, η (mPa·s), and Viscosity Deviations, Δη (mPa·s), at Temperature T, Mass Fraction w, and Mole Fraction x for the System Biodiesel (1) + 2-Pentanol (2) at Pressure p = 0.1 MPaa w2

x2

ρ

0.000 0.101 0.201 0.299 0.399 0.500 0.600 0.699 0.800 0.899 1.000

0.000 0.268 0.450 0.582 0.684 0.765 0.830 0.883 0.929 0.967 1.000

0.87635 0.86905 0.86188 0.85489 0.84819 0.84179 0.83593 0.83000 0.82430 0.81882 0.81355

0.000 0.101 0.201 0.299 0.399 0.500 0.600 0.699 0.800 0.899 1.000

0.000 0.268 0.450 0.582 0.684 0.765 0.830 0.883 0.929 0.967 1.000

0.86170 0.85397 0.84646 0.83931 0.83248 0.82587 0.81980 0.81372 0.80796 0.80239 0.79725

0.000 0.101 0.201 0.299 0.399 0.500 0.600 0.699 0.800 0.899 1.000

0.000 0.268 0.450 0.582 0.684 0.765 0.830 0.883 0.929 0.967 1.000

0.84715 0.83885 0.83112 0.82352 0.81626 0.80931 0.80297 0.79662 0.79066 0.78484 0.77967

VE

η

T = 288.15 K 0.000 7.843 0.161 6.760 0.287 5.860 0.396 5.281 0.414 4.834 0.379 4.568 0.284 4.380 0.240 4.337 0.162 4.418 0.093 4.726 0.000 5.063 T = 308.15 K 0.000 4.457 0.241 3.886 0.402 3.385 0.499 3.028 0.499 2.789 0.464 2.557 0.369 2.421 0.318 2.319 0.219 2.268 0.137 2.301 0.000 2.340 T = 328.15 K 0.000 2.914 0.318 2.511 0.441 2.181 0.570 1.940 0.590 1.772 0.554 1.603 0.445 1.488 0.386 1.403 0.267 1.314 0.177 1.284 0.000 1.303

Δη

ρ

0.000 −0.338 −0.731 −0.945 −1.108 −1.148 −1.155 −1.050 −0.843 −0.430 0.000

0.87264 0.86522 0.85799 0.85094 0.84423 0.83792 0.83201 0.82606 0.82035 0.81486 0.80959

0.000 −0.004 −0.118 −0.198 −0.220 −0.280 −0.279 −0.268 −0.223 −0.110 0.000

0.85806 0.85019 0.84267 0.83543 0.82853 0.82191 0.81571 0.80951 0.80378 0.79816 0.79298

0.000 0.029 −0.007 −0.037 −0.040 −0.078 −0.089 −0.088 −0.104 −0.073 0.000

0.84351 0.83510 0.82722 0.81951 0.81214 0.80511 0.79876 0.79224 0.78612 0.78032 0.77507

η

VE

Δη

T = 293.15 K 0.000 6.658 0.190 5.790 0.322 5.004 0.435 4.472 0.446 4.145 0.386 3.912 0.294 3.749 0.249 3.693 0.169 3.716 0.097 3.912 0.000 4.172 T = 313.15 K 0.000 3.979 0.264 3.463 0.407 3.016 0.509 2.684 0.510 2.449 0.463 2.261 0.380 2.124 0.338 2.025 0.224 1.948 0.140 1.965 0.000 1.993 T = 333.15 K 0.000 2.682 0.319 2.307 0.455 1.997 0.586 1.760 0.608 1.599 0.567 1.444 0.457 1.346 0.395 1.254 0.287 1.167 0.179 1.131 0.000 1.135

ρ

0.000 −0.202 −0.534 −0.740 −0.813 −0.844 −0.845 −0.769 −0.633 −0.343 0.000

0.86899 0.86147 0.85404 0.84705 0.84029 0.83378 0.82789 0.82198 0.81634 0.81084 0.80555

0.000 0.016 −0.068 −0.140 −0.172 −0.198 −0.206 −0.200 −0.187 −0.094 0.000

0.85442 0.84645 0.83884 0.83149 0.82441 0.81761 0.81142 0.80525 0.79943 0.79381 0.78863

0.000 0.040 0.012 −0.022 −0.025 −0.054 −0.052 −0.062 −0.078 −0.056 0.000

0.83991 0.83134 0.82331 0.81550 0.80804 0.80087 0.79433 0.78781 0.78152 0.77563 0.77037

η

VE

T = 298.15 K 0.000 5.858 0.209 5.042 0.381 4.387 0.465 3.933 0.475 3.589 0.443 3.360 0.336 3.213 0.275 3.128 0.176 3.134 0.100 3.237 0.000 3.412 T = 318.15 K 0.000 3.570 0.271 3.092 0.417 2.688 0.528 2.394 0.551 2.179 0.523 2.000 0.420 1.882 0.358 1.788 0.245 1.697 0.150 1.692 0.000 1.704 T = 338.15 K 0.000 2.450 0.332 2.120 0.475 1.827 0.601 1.610 0.616 1.465 0.580 1.309 0.468 1.217 0.403 1.128 0.304 1.049 0.194 1.006 0.000 1.012

Δη

ρ

0.000 −0.160 −0.369 −0.502 −0.596 −0.626 −0.614 −0.569 −0.452 −0.257 0.000

0.86534 0.85772 0.85025 0.84319 0.83641 0.82991 0.82379 0.81791 0.81224 0.80671 0.80144

0.000 0.022 −0.041 −0.091 −0.115 −0.142 −0.139 −0.134 −0.140 −0.074 0.000

0.85108 0.84288 0.83520 0.82771 0.82052 0.81362 0.80731 0.80111 0.79513 0.78939 0.78419

VE

η

T = 303.15 K 0.000 5.100 0.225 4.411 0.393 3.847 0.481 3.449 0.485 3.157 0.441 2.926 0.366 2.776 0.291 2.679 0.188 2.646 0.109 2.709 0.000 2.825 T = 323.15 K 0.000 3.205 0.306 2.778 0.434 2.409 0.550 2.152 0.570 1.968 0.538 1.785 0.435 1.668 0.360 1.558 0.256 1.489 0.163 1.467 0.000 1.475

Δη 0.000 −0.079 −0.228 −0.328 −0.387 −0.433 −0.435 −0.412 −0.341 −0.192 0.000 0.000 0.037 −0.017 −0.047 −0.054 −0.096 −0.101 −0.119 −0.109 −0.066 0.000

0.000 0.055 0.025 −0.004 −0.002 −0.041 −0.039 −0.052 −0.065 −0.054 0.000

a Maximum standard uncertainties: u(w2) = 0.002, u(x2) = 0.002, ur(ρ) = 3 × 10−4, u(VE) = 0.115 cm3·mol−1, ur(η) = 0.01, u(Δη) = 0.093 mPa·s, and u(T) = 0.01 K for density, u(T) = 0.03 K for viscosity, and u(p) = 10 kPa.

water and dry air as reference fluids.22 We estimated the relative standard uncertainty in the density to be 3 × 10−4. The kinematic viscosities are measured using two CannonFenske viscometers (sizes 50 and 75) with viscosity ranges of (0.8−4) × 10−6 m2·s−1 and (1.6−8) × 10−6 m2·s−1, respectively. The viscometer is placed inside a vessel with water that is coupled to a recirculating bath to control the temperature. A Pt-100 thermometer is used to measure the temperature with a standard uncertainty of 0.03 K. The kinematic viscosity is obtained by measuring the time of a descending fluid through a capillary tube. Then, the kinematic viscosity is expressed as

v = K (T )t

Standard uncertainties for the density, viscosity, and derived physical properties are calculated using a propagation error formula.23

3. RESULTS In this study, we have measured the densities and viscosities of mixtures of biodiesel + 1-pentanol, + 2-pentanol, and + 2-methyl1-butanol from (288.15 to 338.15) K at atmospheric pressure over the entire composition range. We have determined the profile of the fatty acid methyl esters (FAME) using gas chromatography as shown in Table 2. Also, some properties of the pure biodiesel are depicted in Table 3 together with the requirements of the EN 14214 standard and the employed test methods. Our pure alcohols’ density and viscosity measurements are compared with values reported in the literature,22,24−50 as shown in Table 4. Our density and viscosity measurements agree with the reported values in the literature within average absolute percentage deviations (AAPD) of 0.04% and 0.83%, respectively. The AAPD is defined as

(1)

where t is the falling time of the fluid in seconds and K(T) is the calibration constant of the viscometer in mm2·s−2. The time is measured using a digital timer with an accuracy of 0.01 s. According to the manufacturer’s specifications, the kinetic correction is negligible for the descending time obtained in this work. Each kinematic viscosity measurement is an average of five runs. The estimated relative standard uncertainty in the viscosity is 0.01.

AAPD =

E

N X exp − Xilit or calc ⎫ 100 ⎧ ⎬ ⎨∑ i N ⎩ i=1 Xiexp ⎭ ⎪

⎪

⎪

⎪

(2)



Article

Table 7. Experimental Densities, ρ (g·cm−3), Excess Molar Volumes, VE (cm3·mol−1), Viscosities, η (mPa·s), and Viscosity Deviations, Δη (mPa·s), at Temperature T, Mass Fraction w, and Mole Fraction x for the System Biodiesel (1) + 2-Methyl1-Butanol (2) at Pressure p = 0.1 MPaa w2

x2

ρ

0.000 0.100 0.199 0.300 0.399 0.499 0.600 0.699 0.801 0.899 1.000

0.000 0.266 0.447 0.583 0.684 0.764 0.830 0.883 0.929 0.967 1.000

0.87635 0.87041 0.86438 0.85863 0.85305 0.84758 0.84246 0.83741 0.83251 0.82769 0.82302

0.000 0.100 0.199 0.300 0.399 0.499 0.600 0.699 0.801 0.899 1.000

0.000 0.266 0.447 0.583 0.684 0.764 0.830 0.883 0.929 0.967 1.000

0.86170 0.85536 0.84929 0.84338 0.83775 0.83234 0.82719 0.82205 0.81709 0.81241 0.80820

0.000 0.100 0.199 0.300 0.399 0.499 0.600 0.699 0.801 0.899 1.000

0.000 0.266 0.447 0.583 0.684 0.764 0.830 0.883 0.929 0.967 1.000

0.84715 0.84045 0.83411 0.82808 0.82223 0.81671 0.81145 0.80613 0.80109 0.79631 0.79234

VE

η

T = 288.15 K 0.000 7.843 0.092 7.072 0.216 6.447 0.234 5.988 0.252 5.711 0.248 5.540 0.188 5.507 0.153 5.545 0.088 5.653 0.058 5.982 0.000 6.451 T = 308.15 K 0.000 4.457 0.215 4.029 0.331 3.735 0.370 3.480 0.382 3.279 0.351 3.119 0.283 3.004 0.254 2.953 0.187 2.942 0.128 3.060 0.000 3.258 T = 328.15 K 0.000 2.914 0.292 2.638 0.437 2.426 0.460 2.224 0.483 2.057 0.439 1.945 0.359 1.848 0.333 1.773 0.252 1.715 0.185 1.731 0.000 1.791

Δη 0.000 −0.401 −0.773 −1.044 −1.180 −1.239 −1.180 −1.068 −0.897 −0.515 0.000 0.000 −0.109 −0.186 −0.278 −0.358 −0.421 −0.458 −0.445 −0.401 −0.238 0.000 0.000 0.023 0.014 −0.036 −0.089 −0.110 −0.134 −0.149 −0.156 −0.097 0.000

ρ

VE

η

T = 293.15 K 0.87264 0.000 6.658 0.86664 0.120 6.060 0.86061 0.248 5.525 0.85480 0.283 5.108 0.84909 0.328 4.856 0.84362 0.322 4.703 0.83846 0.266 4.649 0.83351 0.214 4.641 0.82856 0.155 4.726 0.82394 0.096 4.999 0.81956 0.000 5.285 T = 313.15 K 0.85806 0.000 3.979 0.85165 0.231 3.621 0.84555 0.347 3.334 0.83958 0.393 3.091 0.83395 0.397 2.912 0.82849 0.371 2.764 0.82332 0.301 2.658 0.81818 0.266 2.579 0.81321 0.196 2.572 0.80851 0.136 2.627 0.80433 0.000 2.777 T = 333.15 K 0.84351 0.000 2.682 0.83673 0.302 2.426 0.83033 0.448 2.220 0.82420 0.483 2.025 0.81839 0.483 1.865 0.81280 0.443 1.758 0.80736 0.386 1.662 0.80199 0.359 1.588 0.79711 0.243 1.525 0.79219 0.191 1.521 0.78820 0.000 1.573

Δη 0.000 −0.233 −0.519 −0.750 −0.863 −0.905 −0.869 −0.804 −0.656 −0.332 0.000 0.000 −0.038 −0.107 −0.188 −0.245 −0.296 −0.323 −0.338 −0.290 −0.190 0.000 0.000 0.039 0.034 −0.011 −0.059 −0.076 −0.099 −0.114 −0.127 −0.089 0.000

ρ

VE

η

T = 298.15 K 0.86899 0.000 5.858 0.86283 0.168 5.265 0.85684 0.276 4.783 0.85093 0.329 4.452 0.84527 0.358 4.226 0.83985 0.338 4.078 0.83480 0.260 3.972 0.82971 0.229 3.952 0.82477 0.166 4.009 0.82018 0.100 4.237 0.81582 0.000 4.492 T = 318.15 K 0.85442 0.000 3.570 0.84793 0.248 3.225 0.84181 0.359 2.988 0.83579 0.409 2.760 0.83009 0.420 2.574 0.82458 0.396 2.444 0.81947 0.306 2.344 0.81425 0.280 2.263 0.80923 0.212 2.218 0.80451 0.150 2.275 0.80039 0.000 2.375 T = 338.15 K 0.83991 0.000 2.450 0.83301 0.315 2.213 0.82650 0.470 2.021 0.82032 0.494 1.839 0.81443 0.494 1.683 0.80872 0.462 1.567 0.80337 0.372 1.468 0.79755 0.378 1.402 0.79281 0.257 1.357 0.78778 0.211 1.346 0.78384 0.000 1.377

Δη 0.000 −0.230 −0.464 −0.610 −0.698 −0.736 −0.752 −0.699 −0.580 −0.301 0.000 0.000 −0.027 −0.047 −0.114 −0.179 −0.212 −0.234 −0.251 −0.242 −0.140 0.000

ρ

VE

η

T = 303.15 K 0.86534 0.000 5.100 0.85907 0.199 4.595 0.85304 0.310 4.211 0.84721 0.337 3.931 0.84151 0.371 3.708 0.83611 0.343 3.539 0.83103 0.267 3.448 0.82591 0.238 3.402 0.82092 0.180 3.429 0.81634 0.110 3.590 0.81203 0.000 3.813 T = 323.15 K 0.85108 0.000 3.205 0.84441 0.284 2.900 0.83815 0.410 2.674 0.83215 0.432 2.475 0.82633 0.453 2.295 0.82065 0.446 2.173 0.81558 0.333 2.083 0.81033 0.299 2.005 0.80531 0.220 1.964 0.80043 0.172 1.981 0.79639 0.000 2.057

Δη 0.000 −0.163 −0.313 −0.419 −0.512 −0.577 −0.584 −0.561 −0.475 −0.266 0.000 0.000 0.000 −0.017 −0.061 −0.125 −0.154 −0.169 −0.186 −0.174 −0.114 0.000

0.000 0.048 0.051 0.014 −0.033 −0.063 −0.091 −0.100 −0.096 −0.067 0.000

a Maximum standard uncertainties: u(w2) = 0.002, u(x2) = 0.002, ur(ρ) = 3 × 10−4, u(VE) = 0.115 cm3·mol−1, ur(η) = 0.01, u(Δη) = 0.093 mPa·s, and u(T) = 0.01 K for density, u(T) = 0.03 K for viscosity, and u(p) = 10 kPa.

or calc where Xexp and Xlit are experimental and literature (or i i calculated) densities or viscosities, respectively, and N is the number of experimental data points. Tables 5−7 show the experimental densities and viscosities of biodiesel blends with 1-pentanol, 2-pentanol, and 2-methyl-1-butanol as a function of the mass fraction of alcohol,

wi =

mi 2 ∑i = 1 mi

biodiesel + 2-methyl-1-butanol mixtures, the minima are found between (0.7 and 0.9) and (0.5 and 0.9), respectively. Lapuerta et al.16 measured the kinematic viscosity of biodiesel + methanol, ethanol, propanol, butanol, and 1-pentanol mixtures at 313.15 K over the entire composition range. The authors found that blends with a high content of 1-pentanol had lower viscosities than pure 1-pentanol. They attributed this behavior to a synergistic effect due to the interaction between biodiesel molecules and 1-pentanol. Recently, Cano-Gómez et al.21 measured the kinematic viscosity and density of biodiesel blends with 1-butanol, isobutyl alcohol, and 2-butanol from (293.15 to 333.15) K over the entire composition range. They found that the kinematic viscosity of the pure components was greater than the viscosities of the biodiesel + 1-butanol, isobutyl alcohol, and 2-butanol mixtures at alcohol concentrations by volume of between 80% and 90%. Their results agree with our findings for the mixtures considered in this work. We compared our density and kinematic viscosity values with the limits set by European standard EN 590 for diesel fuel. The limits

(3)

where mi is the total mass of species i. Experimental densities and viscosities are measured at atmospheric pressure and from (288.15 to 338.15) K. To the best of our knowledge, the densities and viscosities of these mixtures have not been reported in the literature. We have found that the kinematic viscosity of these mixtures presents a minimum as a function of the temperature and mass fraction, as shown in Figure 1. For the biodiesel + 1-pentanol mixture, the minimum is at an alcohol mass fraction of between 0.8 and 0.9, while for the biodiesel + 2-pentanol and F



Article

where mi is the mass of pure component i, Mi is the molar mass of component i, and i denotes the biodiesel and alcohol components.

Figure 2. Excess molar volumes, VE, of binary mixtures at T = 303.15 K (a) and T = 323.15 K (b) as a function of mole fraction x2: ▲, biodiesel (1) + 1-pentanol (2); ○, biodiesel (1) + 2-pentanol (2); □, biodiesel (1) + 2-methyl-1-butanol (2); and −, corresponding to eq 8.

Figure 1. Experimental kinematic viscosity ν(exp) of biodiesel blends at different temperatures T as a function of mass fraction w2: (a) biodiesel (1) + 1-pentanol (2); (b) biodiesel (1) + 2-pentanol (2); (c) biodiesel (1) + 2-methyl-1-butanol (2): ●, 288.15 K; ○, 293.15 K; ▼, 298.15 K; Δ, 303.15 K; ■, 308.15 K; □, 313.15 K; ◆, 318.15 K; ◇, 323.15 K; ▲, 328.15 K; ▽, 333.15 K; ⬢, 338.15 K.

established for the density are 0.82 g·cm−3 and 0.845 g·cm−3 at 288.15 K. For the mixtures investigated in this study, the densities complied with the limits of the EN 590 standard at mass fractions of between 0.5 and 0.8. The kinematic viscosity limits established by EN 590 are 2 mm2·s−1 and 4.5 mm2·s−1 at 313.15 K. Our experimental viscosity values for the biodiesel + 1-pentanol, + 2-pentanol, and + 2-methyl-1-butanol mixtures are within these limits. We calculated the excess molar volumes from the experimental densities using ⎛1 ⎛1 VE 1⎞ 1⎞ ⎜ ⎟⎟ ⎟ ⎜ x M x M = − + − ⎜ ⎟ ⎜ 1 1 2 2 ρ1 ⎠ ρ2 ⎠ (cm 3·mol−1) ⎝ρ ⎝ρ

(4)

where ρ is the density of the mixture, ρi is the density of pure component i, Mi is the molar mass of component i, xi is the molar fraction, and i indicates species 1 or 2. The molar fraction, xi, is calculated as follows xi =

Figure 3. Viscosity deviations, Δη, of binary mixtures at T = 303.15 K (a) and T = 323.15 K (b) as a function of mole fraction x2: ▲, biodiesel (1) + 1-pentanol (2); ○, biodiesel (1) + 2-pentanol (2); □, biodiesel (1) + 2-methyl-1-butanol (2); and −, corresponding to eq 8.

mi /Mi 2

∑i = 1 mi /Mi

(5) G



Article

temperatures from (298.15 to 308.15) K. For the mixtures of biodiesel + 1-pentanol and + 2-methyl-1-butanol, this condition occurs at x2 = 0.9 but at temperatures from (313.15 to 338.15) K. The same occurs for the mixture of biodiesel + 2-pentanol at compositions around x2 = 0.8 and x2 = 0.9 but at temperatures of (288.15 to 318.15) K and (323.15 to 338.15) K, respectively. The viscosity deviations change sign from positive to negative at alcohol compositions of less than x2 = 0.6 for all of the mixtures. This condition occurs at temperatures greater than 323.15, 313.15, and 328.15 K for mixtures of biodiesel + 1-pentanol, + 2-pentanol, and + 2-methyl-1-butanol, respectively. From (288.15 to 308.15) K, viscosity deviations are negative throughout the entire concentration range. Dubey et al.53 mention that negative deviations in Δη indicate that the dispersion interactions are dominant in the mixture. The presence of these interactions indicates that the molecules have different molecular shapes and sizes. Also, the negative values of Δη reveal the inclusion of small molecules (1-pentanol, 2-pentanol, and 2-methyl-1-butanol) in the structure of larger molecules such as methyl esters.53 We have represented the excess molar volume and viscosity deviation using the Redlich−Kister equation20

We have calculated the average molecular mass of biodiesel from the distribution of fatty acids as i th

Mbio =

∑ xiMi

(6)

i=1

where Mbio is the average molecular mass of biodiesel and Mi and xi are the molar mass of the ith component of biodiesel and the concentration of the ith fatty acid methyl esters, respectively. The maximum standard uncertainty estimated in the excess molar volume is 0.115 cm3·mol−1. Tables 5−7 show positive deviations for excess molar volumes for blends of biodiesel + 1-pentanol, + 2-pentanol, and + 2-methyl-1-butanol from (288.15 to 338.15) K over the entire composition ranges. Figure 2 shows the excess molar volume for these mixtures at 303.15 K and 323.15 K. At 303.15 K, the maximum values of VE are (0.196, 0.485, 0.371) cm3·mol−1 for the blends of biodiesel + 1-pentanol, + 2-pentanol, and + 2-methyl-1-butanol, respectively, and they occur at approximately x2 = 0.684. The VE for these mixtures follows the order 2-pentanol > 2-methyl-1-butanol > 1-pentanol. The maximum value of the excess molar volume occurs at this composition for all of the mixtures investigated in this work from (288.15 to 338.15) K. The numerical value of VE increases as the temperature increases for all of the mixtures, as shown in Figure 2. This is due to a decrease in the volume contraction caused by the kinetic energy increase of the molecules, inducing a reduction of the intermolecular associations between the molecules of alcohol and methyl esters.51,52 Barabás14 and Djojoputro et al.52 suggest that the positive deviations of VE are attributed to different factors such as repulsion forces due to the electronic charges of alcohol and methyl esters, the ungrouping of alcohol molecules in the presence of methyl esters, and greater domination of steric hindrance in the methyl ester molecules. Also, Iglesias-Silva et al.33 reported that VE has positive values because the physical contribution of the dispersion interactions between different molecules is less than that between molecules of the same type, resulting in an expansion of the mixture. The viscosity deviations are calculated from experimental viscosities using Δη =η− (mPa ·s)

n

J E = x1x 2 ∑ ai(x1 − x 2)i

Table 8. Parameters for the Redlich−Kister20 Equation Used to Calculate Excess Molar Volumes, VE (cm3·mol−1) σ system

T/K

a0

a1

a2

cm3·mol−1

biodiesel + 1-pentanol

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 288.15

0.5562 0.5943 0.6279 0.6848 0.7326 0.7890 0.8326 0.9593 0.9859 1.1155 1.3114 1.3809 1.5319 1.7016 1.7392 1.7711 1.7992 1.8741 1.9586 2.0060 2.0584 2.1117 0.9000

−0.4612 −0.4789 −0.4968 −0.4846 −0.5641 −0.5092 −0.5334 −0.5937 −0.5805 −0.5968 −0.6798 −1.2886 −1.2508 −1.3438 −1.3231 −1.3332 −1.2589 −1.4648 −1.3716 −1.4158 −1.4952 −1.4808 −0.8059

−0.0602 −0.0060 0.1323 0.3597 0.2424 0.2271 0.3275 0.4167 0.4697 0.3866 0.1887 −0.0559 −0.1600 −0.1477 0.0622 0.3708 0.5968 0.7647 0.9391 1.0816 1.0769 1.1938 −0.1246

0.0122 0.0133 0.0107 0.0126 0.0134 0.0156 0.0131 0.0126 0.0180 0.0161 0.0195 0.0179 0.0201 0.0121 0.0067 0.0180 0.0197 0.0170 0.0207 0.0258 0.0260 0.0293 0.0129

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15

1.0454 1.2024 1.2798 1.3649 1.4372 1.4979 1.6514 1.7283 1.7722 1.8269

−1.0691 −0.9436 −0.8042 −0.8054 −0.8240 −0.8422 −0.8167 −0.8797 −0.8933 −0.8664

0.4560 0.4829 0.6716 0.7114 0.7895 0.9200 1.0879 1.2225 1.3211 1.4158

0.0136 0.0151 0.0196 0.0224 0.0227 0.0282 0.0339 0.0385 0.0379 0.0490

2

∑ xiηi i=1

(8)

i=0


(7)

where η is the dynamic viscosity of the mixture, ηi is the viscosity of the pure component, xi is the molar fraction, and i indicates species 1 or 2. Viscosity deviations for the biodiesel + 1-pentanol, + 2-pentanol, and + 2-methyl-1-butanol blends are shown in Tables 5−7. The maximum standard uncertainty estimated in the viscosity deviation is 0.093 mPa·s. Figure 3 shows this behavior for all of the mixtures at 303.15 K and 323.15 K. At 303.15 K, the minimum value of the viscosity deviation occurs at around x2 = 0.8 with values of (−0.245, −0.435, and −0.584) mPa·s for the blends of biodiesel + 1-pentanol, + 2-pentanol, and + 2-methyl1-butanol, respectively. At 323.15 K, the minimum value of Δη occurs at around x2 = 0.9 with values of (−0.092, −0.119, −0.186) mPa·s for 1-pentanol, 2-pentanol, and 2-methyl1-butanol mixtures, respectively. The numerical value of Δη for these mixtures follows the order 1-pentanol > 2-pentanol > 2-methyl-1-butanol, and the viscosity deviations increase with increasing temperature. However, the minimum value of the viscosity deviation occurs at different compositions as shown in Tables 5−7. The minimum value of the viscosity deviation for the mixture of biodiesel + 1-pentanol is present at around x2 = 0.8 at

biodiesel + 2-methyl1-butanol

H



Article

Table 9. Parameters for the Redlich−Kister20 Equation to Calculate Viscosity Deviations, Δη (mPa·s) σ system biodiesel + 1-pentanol


biodiesel + 2-methyl-1-butanol

T/K

a0

a1

a2

a3

mPa·s

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15

−1.2968 −0.8909 −0.7892 −0.5578 −0.3806 −0.3109 −0.1731 −0.0494 −0.0243 0.0004 0.0245 −3.2809 −2.4922 −1.6995 −1.0751 −0.5917 −0.3918 −0.2500 −0.1167 −0.0790 −0.0120 0.0508 −3.5656 −2.4638 −2.1045 −1.4236 −0.8871 −0.5587 −0.2956 −0.1391 −0.0266 0.0589 0.1538

0.5234 0.4710 0.4373 0.3861 0.3115 0.1696 −0.1106 0.1067 0.0335 0.0896 −0.0598 2.8465 2.1765 1.6758 1.0972 0.8554 0.6857 0.4757 0.1727 0.0753 0.1355 0.0968 2.8879 2.6077 1.5037 1.0807 0.6331 0.5135 0.3987 0.3494 0.2977 0.2452 0.3134

−1.8771 −1.3233 −1.1298 −0.9358 −0.4199 −0.4480 −0.2796 −0.2775 −0.2098 −0.2777 −0.1369 −2.2727 −0.7372 −1.2653 −0.8327 −0.3339 −0.1984 −0.0706 0.0964 0.0334 0.1067 0.2002 −2.5452 −1.9095 −1.5845 −1.8105 −1.8254 −1.0834 −1.2373 −0.9601 −0.7514 −0.5666 −0.7279

5.2072 4.0398 2.4897 2.0629 2.0558 2.1464 2.4091 1.3833 1.2889 0.8313 1.1215 7.4903 6.5118 3.9810 3.5986 2.5469 2.1448 1.6959 2.1336 1.9852 1.4536 1.5407 7.5319 4.9103 5.8135 4.8800 4.5037 3.7923 2.6260 1.9788 1.8697 1.6789 1.1203

0.0340 0.0217 0.0118 0.0179 0.0106 0.0070 0.0134 0.0121 0.0088 0.0081 0.0081 0.0291 0.0304 0.0172 0.0140 0.0131 0.0149 0.0145 0.0093 0.0149 0.0150 0.0143 0.0515 0.0343 0.0259 0.0213 0.0256 0.0225 0.0248 0.0184 0.0203 0.0207 0.0094

where JE refers to VE or Δη, n is the number of estimated parameters, ai represents the adjustment parameters calculated for each property, and x1 and x2 are the molar fractions of biodiesel and alcohol, respectively. Tables 8 and 9 show the value of parameter ai together with the standard deviation, defined as ⎡ ∑N (J E,exp − J E, calc )2 ⎤1/2 i ⎥ σ = ⎢ i=1 i ⎥⎦ ⎢⎣ N−n

where νm is the kinematic viscosity of the mixture; x1 and x2 are the molar fractions of biodiesel (1) and alcohol (2), respectively; and δν12, δg*12, and δg*21 are temperature-dependent parameters obtained from the experimental kinematic viscosity data. These parameters are related to a characteristic activation energy difference for the types of molecular interactions.19 Parameter δν12 is associated with two possible interactions of types (1 + 1 + 2) and (1 + 2 + 2), while parameters δg12 * and δg21 * are related to the interactions of types (1 + 1 + 2) and (1 + 2 + 2), respectively. Terms M112 and M122 are the average molecular masses of the components involved in the (1 + 1 + 2)- and (1 + 2 + 2)-type interactions, respectively. Property Mijk is defined as

(9)

where σ is the standard deviation, N is the number of experimental data points, and n is the number of parameters. Superscripts exp and calc indicate the experimental and calculated values, respectively. For the correlation of the kinematic viscosity values of the binary mixtures when considering the biodiesel to be a pseudó et al.19 equation. This component, we have used the Nava-Rios equation has its basis in quadratic mixing rules for nonrandom ́ et al.19 equation is mixtures. The Nava-Rios

Mijk =

(11)

3

Table 10 shows the values of the parameters in eq 10 together with the AAPD, σ, bias, and maximum absolute percentage deviation (MAPD)

ln νm = − ln(M mix ) + x1 ln ν1 + x1 ln(M1) + x 2 ln ν2 + x 2 ln(M 2) (mm 2·s−1) ⎡ ⎛ M3 ⎞ * ) + x 23 ln(δg * ) + x1 ln⎜ 112 ⎟ + x1x 2⎢ln(δν12) + x13 ln(δg12 2 21 ⎢⎣ ⎝ M1 M 2 ⎠ ⎛ M 3 ⎞⎤ + x 2 ln⎜ 1222 ⎟⎥ ⎝ M1M 2 ⎠⎥⎦

(Mi + Mj + Mk)

bias =

100 N

N

∑ i=1

(viexp − vicalc) viexp

(12)

⎤ ⎡ ν exp − ν calc MAPD = max⎢ i exp i × 100⎥ ⎥⎦ ⎢⎣ νi

(10) I

(13)



Article

Table 10. Correlated Nava−Rios et al.19 Equation Parameters T/K

δν12

δg12*

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15

1.2958 1.3133 1.2835 1.3208 1.3521 1.3772 1.4097 1.4219 1.4826 1.5317 1.5259

0.6446 0.6809 0.7029 0.7017 0.7503 0.7232 0.7245 0.7971 0.7454 0.7107 0.7500

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15

1.0784 1.0019 1.1949 1.3255 1.3920 1.4505 1.4951 1.6309 1.7146 1.6842 1.7872

0.7647 1.1210 0.8002 0.7694 0.8881 0.9105 0.9211 0.8271 0.7586 0.9213 0.9271

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15

0.8587 0.9188 1.0250 1.1628 1.3218 1.3272 1.4485 1.5125 1.6036 1.6575 1.8489

1.0269 1.0961 0.8040 0.6585 0.5379 0.6641 0.5714 0.5892 0.5906 0.6274 0.5431

δg21*

AAPD

bias

σ

MAPD

%

%

mm2·s−1

%

−0.572 −0.417 −0.244 −0.419 0.068 −0.199 −0.528 −0.407 −0.185 −0.434 −0.372

0.092 0.067 0.041 0.039 0.034 0.034 0.043 0.029 0.024 0.018 0.022

2.519 2.270 1.553 1.876 1.469 1.296 2.699 2.058 1.684 1.465 1.810

−0.427 −0.309 −0.579 −0.563 −0.337 −0.483 −0.558 −0.614 −0.690 −0.693 −0.750

0.088 0.081 0.055 0.053 0.040 0.037 0.033 0.036 0.037 0.032 0.032

2.445 2.856 2.206 2.587 2.166 2.991 3.153 2.941 3.517 3.675 3.780

−0.570 −0.420 −0.415 −0.624 −0.611 −0.701 −0.829 −0.716 −0.749 −0.658 −0.477

0.101 0.067 0.072 0.068 0.068 0.062 0.053 0.040 0.039 0.037 0.023

2.810 2.394 2.504 2.781 3.234 1.931 3.680 2.732 3.349 3.261 1.990

Biodiesel + 1-Pentanol 0.3725 0.993 0.4234 0.847 0.4997 0.587 0.5355 0.565 0.5297 0.558 0.5397 0.711 0.6568 0.990 0.7623 0.694 0.7318 0.666 0.7939 0.593 0.8776 0.787 Biodiesel + 2-Pentanol 0.0968 0.948 0.1618 1.096 0.1864 0.847 0.2373 0.966 0.3672 0.785 0.4459 0.844 0.5902 0.780 0.6248 1.101 0.6146 1.185 0.8651 1.077 0.8776 1.217 Biodiesel + 2-Methyl-1-butanol 0.2077 0.781 0.2498 0.608 0.2049 0.908 0.2059 0.944 0.2001 1.109 0.2858 1.155 0.3229 1.019 0.3721 0.878 0.3877 0.982 0.4329 1.027 0.3844 0.755

calc In eqs 12−13, νexp i and νi are the experimental and calculated values of the kinematic viscosity, and N is the number of experimental data points. Equation 10 correlates the experimental kinematic viscosities within average absolute percentage deviations of (0.73, 0.99, and 0.92) % for the biodiesel mixtures with 1-pentanol, 2-pentanol, and 2-methyl-1-butanol, respectively. However, the MAPD for the mixtures follows the order 2-pentanol > 2-methyl-1-butanol > 1-pentanol, as shown in Table 10. Figure 4 shows the relative deviations between the ́ et al.19 experimental and calculated viscosities by the Nava-Rios equation. The relative deviations are randomly distributed around zero for the mixtures. For the biodiesel + 2-pentanol mixture at 323.15 K, the relative deviations show a nonrandom pattern, indicating that the model is not able to capture some implicit information. Additionally, we have used the McAllister18 equation to correlate the kinematic viscosity of the biodiesel + alcohol blends. This equation assumes that three-body interactions exist for binary mixtures and that all occur in a plane. In addition, it assumes that the proportion of each individual interaction is proportional to the activation energy and postulates that the logarithm of the kinematic viscosity18 is

ln νm = x13 ln ν1 + 3x12x 2 ln ν12 + 3x1x 22 ln ν21 + x 23 ln ν2 (mm 2·s−1) ⎡ 2 + M2 ⎤ ⎡ 1 + 2M2 ⎤ ⎡ x 2M 2 ⎤ M1 ⎥ M1 ⎥ ⎢ 2 2 ⎢ − ln⎢x1 + + 3x1x 2 ln⎢ ⎥ + 3x1 x 2 ln⎢ ⎥ 3 ⎥ 3 M1 ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎛M ⎞ + x 23 ln⎜ 2 ⎟ ⎝ M1 ⎠

(14)

where νm is the kinematic viscosity of the mixture; x1 and x2 are the molar fractions of biodiesel (1) and alcohol (2), respectively; M1 and M2 are the molecular weights of species 1 and 2; and ν12 and ν21 are the temperature-dependent parameters obtained from the kinematic viscosity data. Parameters ν12 and ν21 are associated with the interactions of types (1 + 1 + 2) and (1 + 2 + 2), respectively. The McAllister18 equation correlates the kinematic viscosity within AAPD values of 1.31%, 1.82%, and 2.17% for the biodiesel + 1-pentanol, + 2-pentanol, and + 2-methyl-1-butanol blends, respectively. Table 11 shows the value of the parameters for eq 14 together with the AAPD, σ, bias, and MAPD for the mixtures considered in this study. The numerical value of the MAPD for these mixtures follows the order 2-pentanol > 2-methyl-1-butanol > 1-pentanol. All of the parameters are statistically valid within J



Article

Figure 5. Percent relative deviations Δν = ν(exp) − ν(calc) of experimental kinematic viscosities ν(exp) of biodiesel mixtures from values ν(calc) obtained with the correlation of McAllister18 as a function of the temperature T: ▲, biodiesel (1) + 1-pentanol (2); ○, biodiesel (1) + 2-pentanol (2); and □, biodiesel (1) + 2-methyl-1-butanol (2).

Figure 4. Percent relative deviations Δν = ν(exp) − ν(calc) of experimental kinematic viscosities ν(exp) of biodiesel mixtures from ́ et al.19 as a values ν(calc) obtained with the correlation of Nava-Rios function of temperature T: ▲, biodiesel (1) + 1-pentanol (2); ○, biodiesel (1) + 2-pentanol (2); □, biodiesel (1) + 2-methyl-1-butanol (2).

́ et al.19 equation better correlates the In this work, the Nava-Rios kinematic viscosities than the McAllister equation.18

a 95% confidence interval. Figure 5 shows the relative deviations for the mixtures considered in this work. At 288.15 K, 293.15 K, and 298.15 K, the relative deviations for the biodiesel + 1-pentanol and + 2-pentanol mixtures increase as temperature decreases. This could indicate that the addition of a temperature term to eq 14 could improve the fit of the model to the experimental data.

4. CONCLUSIONS We have measured the densities and viscosities for blends of biodiesel + 1-pentanol, + 2-pentanol, and + 2-methyl-1-butanol

Table 11. Correlated McAllister18 Equation Parameters AAPD system biodiesel + 1-pentanol


biodiesel + 2-methyl-1- butanol

bias

T/K

ν12

ν21

%

%

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15

8.7453 7.4115 6.4354 5.6788 4.8771 4.3948 3.9067 3.5568 3.1894 2.9686 2.6463 9.8686 8.1645 7.1224 6.0952 5.2155 4.5714 4.0069 3.5321 3.2050 2.9348 2.6961 9.9415 8.4656 7.1532 6.3999 5.6541 4.9606 4.4360 3.9333 3.5805 3.2697 3.0477

6.0467 5.3910 4.7699 4.2198 3.9109 3.4710 3.2020 2.9202 2.6955 2.4442 2.3071 4.4578 4.0475 3.6697 3.4131 3.2010 2.9720 2.7524 2.5630 2.3500 2.1981 2.0375 5.4359 4.8231 4.3306 3.8344 3.5128 3.2754 3.0087 2.7702 2.5556 2.3877 2.1519

2.065 1.755 1.355 1.288 1.155 1.336 1.477 1.044 1.039 0.843 1.009 2.964 2.502 2.330 2.255 1.633 1.528 1.238 1.486 1.639 1.189 1.300 2.155 1.773 2.274 2.487 2.804 2.416 2.272 1.953 1.962 1.871 1.876

−1.597 −1.345 −0.863 −0.778 −0.872 −0.933 −1.100 −0.872 −0.874 −0.651 −0.863 −1.977 −1.863 −1.564 −1.465 −0.872 −1.159 −0.836 −0.872 −1.087 −0.872 −0.815 −1.435 −1.241 −1.595 −1.536 −1.940 −1.752 −1.772 −1.434 −1.666 −1.672 −1.419

K

σ 2 −1

mm ·s

0.171 0.126 0.085 0.071 0.056 0.057 0.058 0.038 0.034 0.025 0.028 0.236 0.171 0.137 0.112 0.071 0.060 0.044 0.045 0.044 0.032 0.032 0.213 0.151 0.160 0.150 0.149 0.114 0.099 0.075 0.069 0.060 0.051

MAPD % 4.506 4.117 2.895 2.538 2.381 2.929 3.856 2.494 2.819 2.006 2.773 6.420 6.051 4.818 4.971 3.728 4.460 3.977 3.905 4.664 3.980 3.973 4.871 4.198 5.355 5.348 6.221 5.232 5.706 4.507 5.261 5.130 3.971



Article

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from 288.15 K to 338.15 K at 0.1 MPa. The densities and viscosities of the pure components agree with values reported in the literature within average absolute percentage deviations of 0.04% and 0.83%, respectively. Our experimental values of kinematic viscosity present a minimum at a certain mass fraction composition for all of the mixtures reported herein. This condition occurs at mass concentrations of alcohol of between 80% and 90% for the biodiesel + 1-pentanol mixture while for the biodiesel + 2-pentanol and + 2-methyl-1-butanol mixtures the minima are between (70 and 90)% and (50 and 90)%, respectively. The Redlich−Kister20 equation correlates the excess molar volumes and viscosity deviations within average standard deviations of 0.020 cm3·mol−1 and 0.019 mPa·s, respectively. The ́ et al.19 correlates the kinematic viscosity equation of Nava-Rios within an average absolute percentage deviation of 0.88%, while the McAllister18 equation correlates within 1.77%. The results presented in this work can contribute to the elucidation of the effect of biodiesel + higher alcohol mixtures on the spray characteristics in the combustion chamber and the internal flow in the fuel injection system.

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AUTHOR INFORMATION

Corresponding Author

*Tel: 011 52 81 8329 4000. Fax: (81) 8376 2929. E-mail: [email protected]. ORCID

Gustavo A. Iglesias-Silva: 0000-0001-7260-2308 José J. Cano-Gómez: 0000-0003-3761-7736 Notes

The authors declare no competing financial interest. Funding

The authors thank Consejo Nacional de Ciencia and Tecnologiá (CONACyT) for providing financial support for this work through project CB-2016-285320.

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