Densities and Viscosities for Binary Liquid Mixtures of Biodiesel + 1

Article pubs.acs.org/jced

Densities and Viscosities for Binary Liquid Mixtures of Biodiesel + 1‑Butanol, + Isobutyl Alcohol, or + 2‑Butanol from 293.15 to 333.15 K at 0.1 MPa José J. Cano-Gómez,† Gustavo A. Iglesias-Silva,*,‡ Pasiano Rivas,† Christian O. Díaz-Ovalle,§ and Felipe de Jesús Cerino-Córdova† †

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 § Departamento de Ingenierías, Instituto Tecnológico de Roque, Celaya, Guanajuato, C.P. 38110, México ‡

ABSTRACT: This paper presents experimental densities and viscosities of binary mixtures of biodiesel with 1-butanol, isobutyl alcohol, and 2butanol from 293.15 to 333.15 K at 0.1 MPa. Densities are from a vibrating tube densimeter while viscosities are from a capillary glass viscometer. Experimental data of density and viscosity of pure alcohols agree with data reported in the literature with an average absolute percentage deviation of 0.06% and 1.3%, respectively. Experimental kinematic viscosities of the mixtures show a minimum value in the concentration range. The Grunberg−Nissan equation successfully correlates kinematic viscosities with an average absolute percentage deviation of 0.98%.

1. INTRODUCTION The emission of greenhouse gases (GG) is a serious environmental problem. One of the main factors is the high consumption of fossil fuels. This problem has increased the interest of producing alternative fuels to stabilize concentrations of greenhouse gases and reduce the excessive exploitation of the reserves of fossil fuels1 and then reducing the dangerous anthropogenic interference of the climate sytem. Recently, biofuels such as biodiesel, ethanol, and biogas have been used because they have a higher regeneration in the life cycle. The advantages of biodiesel are due to its composition of alkyl esters of fatty acids which are produced from vegetable oils or animal fat by transesterification reaction.2−5 Biodiesel is an alternative fuel in compression internal combustion engines because it is biodegradable and nontoxic; however, it presents higher density and viscosity than the diesel.5,6 These differences restrict its use, it affects the performance of the fuel injection and combustion systems. High viscosities cause the formation of drops of great size affecting fuel atomization and reduces consumption efficiency in the long run.7−9 High density increases the amount of fuel supplied and impacts in the design of the components for the supply system: fuel pump and filter, valves of transfer and security.7,9 Notwithstanding the foregoing, biodiesel has a high cetane index. A high cetane index warrants immediate combustion and total fuel consumption which increases the performance of the engine, reducing noise and emissions of solid particles. Thermodynamic properties of biodiesel have been improved using alcohols as additives. The simple alcohols methanol and © 2017 American Chemical Society

ethanol have low lubricity, low index of cetane, high temperature of self-ignition, high vaporization energy, and low solubility to high concentrations.10−12 Alcohols, such as 1butanol, isobutyl alcohol, and 2-butanol, are recommended as additives to overcome the disadvantages of simple alcohols. In addition, these alcohols reduce biodiesel density and viscosity.1 Unfortunately, densities and viscosities of blends of biodiesel + alcohols are scarce in the literature. Park et al.13 measured the effect of the variation of temperature from 273.15 to 373.15 K on the viscosity of pure biodiesel and biodiesel + ethanol at ethanol concentrations from 0 to 50% v/v. The authors found a linear density decrease as the temperature of the fuel and the content of ethanol in the mixture increased. On the other hand, Barabas et al.14 reported the density of 10 binary systems of ethanol + biodiesel from 273.15 to 373.15 K at atmospheric pressure and in all composition ranges of ethanol. They calculated the excess molar volume from the experimental density showing positive deviations from ideality for all mixtures. Recently, Hongya et al.15 measured the density and the surface tension of biodiesel + n-butanol, biodiesel + diesel and diesel + n-butanol at 283.15 and 293.15 K. The authors found negative deviations for the excess surface tensions and excess densities in all the ranges of compositions on all the temperatures. Authors have measured densities and viscosities using different additives. Sacar-Vural et al.16 measured density, Received: May 15, 2017 Accepted: September 13, 2017 Published: September 28, 2017 3391

DOI: 10.1021/acs.jced.7b00440 J. Chem. Eng. Data 2017, 62, 3391−3400

Journal of Chemical & Engineering Data

Article

uncertainty in measurement of 0.03 K. The kinematic viscosity is related to the falling time of a volume of fluid through a glass capillary as

viscosity, and refractive index of binary mixtures of biodiesel + toluene and + benzene at 298.15 and 303.15 K. In this work, we have measured experimental densities and viscosities of binary mixtures of biodiesel + 1-butanol, + isobutyl alcohol, and +2-butanol from 293.15 to 333.15 K at 0.1 MPa over the entire concentration range. Simple empirical models are correlated to the experimental measurements.

ν = K (T )t

where t is the efflux time in seconds and K(T) is the viscometer constant in mm2·s−2. The time is measured with a digital stopwatch with a precision of 0.01 s. According to the manufacturer, the kinetic energy correction is negligible at the efflux times considered in this work. Each value is an average of five runs with a maximum deviation on the viscosity of 0.1%. The estimated standard uncertainty in the measurement of viscosity is 0.003 mPa·s. Density and viscosity uncertainties are calculated using a propagation error formula.18

2. EXPERIMENTAL SECTION Samples. Samples are from SOLBEN for biodiesel, SigmaAldrich for 2-butanol (99.5% in mass fraction), Merck for 1butanol (99.5% in mass fraction) and isobutyl alcohol (99.0% in mass fraction). Table 1 presents the purity, source, and Table 1. Sample Information chemical name 1-butanol isobutyl alcohol 2-butanol

CAS RN

initial purity mass fraction

Merck Tedia

71-36-3 78-83-1

0.995 0.990

none none

GCa HPLCb

SigmaAldrich

78-92-2

0.995

none

GCa

source

purification method

analysis method

(1)

3. RESULTS In this work, we have measured the densities of biodiesel + (1butanol, isobutyl alcohol, and 2-butanol) from 293.15 to 333.15 K at atmospheric pressure in the entire composition range. We have generated the fatty acid profile using a gas chromatograph technique and specification of the biodiesel is presented in Table 2. Comparison of the experimental density and viscosity

a

Gas chromatography provided by the supplier. bHigh-performance liquid chromatography provided by the supplier.

Table 2. Fatty Acid Methyl Ester (FAME) Composition in Mass Fraction (w) of Waste Cook Oil Biodiesel with Its Standard Uncertainty

method of analysis of the samples. The mixtures are prepared in volume fraction using a volumetric buret at 298.15 K. The overall standard uncertainty in the volume fraction is 0.001. The system has been mixed and stirred perfectly in an airtight container with a magnetic agitator which guarantees a homogeneous mixing before performing the experimental measurement. The mixtures are prepared in a humidity free environment and they are measured immediately after being prepared. Preventive measures are taken to avoid humidity and evaporation of the samples. Biodiesel Characterization. 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 in length, 0.53 mm inner diameter, and of 0.5 μm thickness is used in the separation. The temperature of the injector and detector are set at 523.15 K. The oven temperature is kept at 313.15 K for 2 min and then increased up to 513.15 K at a rate of 7 K/min. The oven is kept at this temperature for 18 min. Apparatuses and Procedures. A vibrating tube densimeter (Anton Paar, DMA 5000) is used for the measurement of the density. The stated reproducibility from the manufacturer is 1 × 10−6 g·cm−3 for density and 0.001 K for temperature. The U-tube is subject to a harmonic electromagnetic force, and the oscillation period of the tube filled with sample is related to the fluid density.17 The densimeter is calibrated periodically during the measurements using two reference fluids: dry air and ultrapure water. Density and temperature standard uncertainties are estimated to be 8 × 10−5 g·cm−3 and 0.01 K, respectively. Kinematic viscosities are obtained using two Cannon-Fenske viscometers: size nos. 50 and 75 with viscosity ranges of (0.8− 4) and (1.6−8) × 10−6 m2·s−1, respectively. The measurements are performed according to the ASTM D445 standard. The viscometer is placed into an insulated container with water, and the temperature is controlled using a recirculating bath (Fisher Scientific, Isotemp 3016D). Thermal control is checked with a digital thermometer (Control Company, 4132) with a standard

fatty acid methyl ester C16:0 C16:1 C18:0 C18:1 C18:2 C18:3

(palmitate) (palmitoleate) (stearate) (oleate) (linoleate) (linolenate)

mass fraction (w)

u(w)

0.187 0.009 0.044 0.420 0.306 0.034

0.005 0.0003 0.001 0.014 0.011 0.001

of pure alcohols with values reported in literature are shown in Table 3. We have compared our experimental results with the literature values using the average absolute percentage error defined as AAPD =

|Xiexp − Xicalc or lit| ⎫ 1⎧ ⎨ ⎬ ∑ ⎪ N⎪ Xiexp ⎩ i=1 ⎭ ⎪

N

⎪

(2)

where Xiexp and Xicalc are the experimental and calculated (or literature) viscosities or densities; and N is the number of data. Our density measurements agree with the literature density values19−25 within an AAPD of 0.06%, 0.03%, and 0.08% for the 1-butanol, isobutyl alcohol, and 2-butanol, respectively. Tables 4−6 present the experimental densities of binary mixtures of biodiesel + 1-butanol, + isobutyl alcohol, and + 2-butanol as a function of the alcohol volume fraction, φi =

Vi ∑i Vi

(3)

where Vi is the total volume of specie i. We have measured the viscosity of biodiesel + (1-butanol, isobutyl alcohol, and 2-butanol) from 293.15 to 333.15 K at atmospheric pressure. Our viscosity measurements for the pure alcohols agree with the literature22,24,26−40 data within an AAPD of 1.1% for 1-butanol and 2-butanol and 1.6% for isobutyl alcohol, respectively. A comparison is shown in Table 3. Also, Tables 4−6 present the viscosity measurements for the 3392



Article

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

this work

293.15

0.80901

298.15

0.80587

303.15

0.80206

308.15

0.79818

313.15

0.79426

318.15

0.79030

323.15

0.78629

328.15

0.78202

333.15

0.77781

293.15

0.80198

298.15 303.15

0.79813 0.79424

308.15 313.15

0.79029 0.78630

318.15

0.78224

ρ/g·cm−3

μ/mPa·s lit.

1-Butanol 0.809519 0.8091720 0.805719 0.8055420 0.801919 0.8019020 0.79819 0.7946020 0.794119 0.794121 0.790119 0.7909720 0.786119 0.786521 0.782119 0.7823922 0.778321 0.7782822 Isobutyl Alcohol 0.8015823 0.8017524 0.7980923 0.7940923 0.7939924 0.7901222 0.7861222 0.7860424 0.7820622

this work

lit.

T/K

this work

2.970

2.939626

323.15

0.77812

2.547

2.541626 2.57127 2.275126 2.27127 1.997826 1.98127 1.78626 1.744227 1.58926 1.571227 1.42726 1.42128 1.27826 1.26929 1.14726 1.13729

328.15 333.15

0.77392 0.76965

293.15

0.80717

298.15

0.80305

303.15

0.79885

308.15

0.79455

313.15

0.79016

318.15

0.78566

323.15

0.78105

328.15

0.77634

333.15

0.77151

2.237 1.980 1.757 1.568 1.404 1.255 1.132

4.077 3.394 2.949 2.540 2.208 1.855

4.08524 4.02330 3.40430 2.88230 2.87724 2.50831 2.11632 2.15433 1.86134 1.87035

μ/mPa·s lit.

Isobutyl Alcohol 0.7779322 0.7778524 0.7737322 0.7694422 0.7693624 2-Butanol 0.8065720 0.806725 0.8022820 0.802425 0.7979920 0.798425 0.7937220 0.7940522 0.7894320 0.7896522 0.7851720 0.7851522 0.780219 0.7805522 0.775519 0.7758322 0.770719 0.7709922

this work

lit.

1.621

1.62933 1.60232

1.425 1.250

3.742

3.73736

3.093

3.080437 3.06834 2.56738 2.60622 2.16222 2.12839 1.84022 1.794237 1.55737 1.53339 1.33237 1.31532 1.15037

2.579 2.147 1.826 1.555 1.337 1.142

1.00137 1.02540

0.992

a

Standard uncertainties u are ur(μ) = 0.009, u(T) = 0.03 K for viscosity, and u(ρ) = 8 × 10−5 g·cm−3, u(T) = 0.01 K for density and u(p) = 10 kPa.

ρ = αφ + βT + δ

mixtures considered in this work. To the best of our knowledge, viscosity measurements of these blends have not been reported in the literature. We have found that the kinematic viscosity of these mixtures shows a minimum as a function of temperature and volume fraction. Figure 1 depicts this behavior. For the mixture biodiesel +1-butanol the minimum is found a 293.15 K and disappears when the temperature increases. For the mixtures of biodiesel + isobutyl alcohol and +2-butanol the minimum is found at volume concentration between 80 and 90% of alcohol, respectively. Also, it has been found that the kinematic viscosity shows a minimum for mixtures of this biodiesel with higher carbon chain alcohols.41 However, it could be that this behavior is not shown with another biodiesel due to the diversity of the composition. Lapuerta et al.42 measured the viscosity of mixtures of diesel with methanol, ethanol, 1-propanol, 1-butanol, and 1-pentanol at different concentrations from (0 to 95 v/v %) and 313.15 K. These authors found that the viscosity of pure components is greater than the viscosity of mixtures of diesel + 1-butanol, + 1pentanol at intermediate concentrations. Their results agree with our findings for the mixtures treated in this work. They mention that this characteristic could be used to improve the performance of the injection system. ́ Ramirez-Verduzco et al.7 developed an empirical correlation for the prediction of the density of binary mixtures as a function of temperature and concentration,

(4) −3

where ρ is the density of the mixture in g·cm ; φ is volume fraction of alcohol in the mixture with biodiesel, T is the temperature in kelvin; α, β, and δ are parameters obtained from the experimental measurements. Table 7 depicts the value of the parameters together with the AAPD, standard deviation, and maximum absolute percentage deviation defined as ⎡ ∑ N (X exp − X calc)2 ⎤1/2 i i ⎥ σ = ⎢ i=1 ⎢⎣ ⎥⎦ N−n

(5)

⎤ ⎡ |X exp − X calc| i max dev% = max dev ⎢ i 100⎥ exp ⎥⎦ ⎢⎣ Xi

(6)

respectively. In the above equations, Xiexp and Xicalc are the experimental and calculated densities or kinematic viscosities; N is the number of data, and n is the number of parameters in the equation. Equation 4 correlates our density values within an AAPD of 0.06%, 0.05%, and 0.1%, for 1-butanol, isobutyl alcohol, and 2-butanol mixtures, respectively. Figure 2 shows the predictive capability of eq 4. The European standard norm, EN 590, establishes that the limit density values for a diesel fuel are 0.82 g·cm−3 and 0.845 g·cm−3 at 288.15 K. In this work we have not measured the densities at 288.15 K; however, because of the linear behavior in temperature and composition; we have 3393


a

φ2

3394

0.86332 0.85530 0.84790 0.84050 0.83330 0.82630 0.81920 0.81204 0.80520 0.79773 0.79030

0.88230 0.87390 0.86682 0.85960 0.85300 0.84591 0.83890 0.83210 0.82494 0.81820 0.80901

g·cm

−3

φ2

T/K = 298.15 7.532 0.000 6.501 0.100 5.750 0.200 5.151 0.300 4.718 0.400 4.316 0.500 3.958 0.600 3.763 0.700 3.656 0.800 3.655 0.900 3.671 1.000 T/K = 323.15 4.301 0.000 3.631 0.100 3.259 0.201 2.925 0.301 2.680 0.401 2.461 0.501 2.273 0.601 2.140 0.701 2.051 0.801 2.013 0.900 1.984 1.000

mm ·s

2 −1

ν −3

0.85968 0.85150 0.84408 0.83630 0.82930 0.82262 0.81524 0.80806 0.80100 0.79372 0.78629

0.87791 0.87000 0.86250 0.85527 0.84841 0.84160 0.83475 0.82763 0.82080 0.81390 0.80587

g·cm

ρ φ2

T/K = 303.15 6.742 0.000 5.723 0.100 5.063 0.200 4.545 0.300 4.172 0.400 3.831 0.500 3.498 0.600 3.326 0.700 3.222 0.800 3.201 0.900 3.161 1.000 T/K = 328.15 3.895 0.000 3.291 0.100 2.942 0.201 2.645 0.301 2.424 0.401 2.241 0.501 2.042 0.601 1.941 0.701 1.853 0.801 1.807 0.900 1.786 1.000

mm ·s

2 −1

ν −3

0.85604 0.84790 0.84024 0.83260 0.82530 0.81830 0.81124 0.80400 0.79710 0.78980 0.78202

0.87430 0.86610 0.85880 0.85146 0.84458 0.83827 0.83090 0.82378 0.81726 0.80990 0.80206

g·cm

ρ φ2

T/K = 308.15 5.946 0.000 5.054 0.100 4.502 0.200 4.032 0.300 3.695 0.400 3.411 0.500 3.118 0.600 2.955 0.700 2.882 0.800 2.832 0.900 2.789 1.000 T/K = 333.15 3.562 0.000 3.008 0.101 2.689 0.201 2.404 0.301 2.208 0.401 2.027 0.501 1.864 0.601 1.763 0.701 1.683 0.801 1.631 0.901 1.605 1.000

mm ·s

2 −1

ν −3

0.85240 0.84400 0.83639 0.82825 0.82113 0.81440 0.80720 0.79990 0.79300 0.78556 0.77781

0.87061 0.86220 0.85490 0.84764 0.84073 0.83438 0.82703 0.81990 0.81337 0.80561 0.79818

g·cm

ρ φ2

3.269 2.786 2.470 2.206 2.022 1.844 1.697 1.607 1.524 1.484 1.455

T/K = 313.15 5.321 0.000 4.486 0.100 4.016 0.200 3.604 0.300 3.303 0.400 3.042 0.500 2.794 0.600 2.650 0.700 2.546 0.800 2.512 0.900 2.481 1.000

mm ·s

2 −1

ν −3

0.86696 0.85900 0.85171 0.84450 0.83760 0.83065 0.82340 0.81620 0.80920 0.80169 0.79426

g·cm

ρ

Standard uncertainties u are u(w2) = 0.002, u(φ2) = 0.001, ur(ν) = 0.009, u(T) = 0.03 K for viscosity, and u(ρ) = 8 × 10−5 g·cm−3, u(T) = 0.01 K for density and u(p) = 10 kPa.

T/K = 293.15 0.000 0.000 0.093 0.100 0.187 0.200 0.283 0.300 0.380 0.400 0.479 0.500 0.579 0.600 0.682 0.700 0.785 0.800 0.891 0.900 1.000 1.000 T/K = 318.15 0.000 0.000 0.093 0.100 0.187 0.200 0.283 0.301 0.380 0.401 0.479 0.501 0.579 0.601 0.682 0.701 0.785 0.800 0.891 0.900 1.000 1.000

w2

ρ

4.762 4.023 3.596 3.242 2.977 2.745 2.500 2.381 2.279 2.242 2.212

mm2·s−1

ν

Table 4. Experimental Densities ρ (g·cm−3) and Kinematic Viscosities ν (mm2·s−1) for Biodiesel (1) + 1-Butanol (2) at Various Mass Fractions w2 and Volume Fractions φ2 of 1-Butanol and at the Pressure p = 0.1 MPaa

Journal of Chemical & Engineering Data Article


a

φ2

3395

0.86332 0.85410 0.84552 0.83737 0.82959 0.82193 0.81386 0.80627 0.79797 0.79037 0.78224

0.88230 0.87290 0.86453 0.85663 0.84864 0.84150 0.83390 0.82600 0.81778 0.81015 0.80198

g·cm

−3

φ2

T/K = 298.15 7.532 0.000 6.686 0.100 6.105 0.200 5.613 0.300 5.325 0.400 5.070 0.500 4.901 0.600 4.744 0.700 4.712 0.800 4.722 0.900 5.083 1.000 T/K = 323.15 4.301 0.000 3.708 0.100 3.364 0.201 3.097 0.301 2.885 0.401 2.719 0.501 2.572 0.601 2.471 0.701 2.391 0.801 2.336 0.900 2.372 1.000

mm ·s

2 −1

ν −3

0.85968 0.85030 0.84167 0.83345 0.82562 0.81791 0.80980 0.80220 0.79386 0.78625 0.77812

0.87791 0.86870 0.86076 0.85282 0.84521 0.83765 0.82967 0.82214 0.81391 0.80629 0.79813

g·cm

ρ φ2

T/K = 303.15 6.742 0.000 5.856 0.100 5.377 0.200 4.944 0.300 4.639 0.400 4.436 0.500 4.261 0.600 4.100 0.700 4.056 0.800 4.054 0.900 4.253 1.000 T/K = 328.15 3.895 0.000 3.373 0.101 3.038 0.201 2.803 0.301 2.599 0.401 2.439 0.501 2.313 0.601 2.214 0.701 2.111 0.801 2.068 0.901 2.083 1.000

mm ·s

2 −1

ν −3

0.85604 0.84650 0.83781 0.82951 0.82162 0.81386 0.80571 0.79807 0.78969 0.78207 0.77392

0.87426 0.86500 0.85697 0.84899 0.84134 0.83376 0.82577 0.81823 0.80999 0.80238 0.79424

g·cm

ρ φ2

T/K = 308.15 5.946 0.000 5.195 0.100 4.724 0.200 4.343 0.300 4.086 0.400 3.881 0.500 3.690 0.600 3.546 0.700 3.512 0.800 3.503 0.900 3.713 1.000 T/K = 333.15 3.562 0.000 3.074 0.101 2.775 0.201 2.541 0.301 2.351 0.402 2.213 0.502 2.085 0.602 1.989 0.701 1.886 0.801 1.832 0.901 1.842 1.000

mm ·s

2 −1

ν −3

0.85240 0.84290 0.83393 0.82553 0.81758 0.80976 0.80156 0.79388 0.78546 0.77781 0.76965

0.87061 0.86160 0.85316 0.84514 0.83745 0.82985 0.82183 0.81429 0.80603 0.79843 0.79029

g·cm

ρ

3.269 2.829 2.529 2.334 2.144 1.999 1.882 1.789 1.689 1.627 1.625

5.321 4.590 4.205 3.861 3.627 3.435 3.280 3.135 3.077 3.044 3.213

mm ·s

2 −1

ν T/K = 313.15 0.000 0.100 0.200 0.301 0.401 0.501 0.601 0.700 0.800 0.900 1.000

φ2

−3

0.86696 0.85760 0.84935 0.84126 0.83354 0.82590 0.81786 0.81030 0.80202 0.79443 0.78630

g·cm

ρ


T/K = 293.15 0.000 0.000 0.092 0.100 0.185 0.200 0.281 0.300 0.378 0.400 0.476 0.500 0.577 0.600 0.680 0.700 0.784 0.800 0.891 0.900 1.000 1.000 T/K = 318.15 0.000 0.000 0.092 0.100 0.185 0.201 0.281 0.301 0.378 0.401 0.476 0.501 0.577 0.601 0.680 0.701 0.784 0.801 0.891 0.900 1.000 1.000

w2

ρ

4.762 4.105 3.763 3.457 3.231 3.055 2.892 2.751 2.704 2.656 2.808

mm2·s−1

ν

Table 5. Experimental Densities ρ (g·cm−3) and Kinematic Viscosities ν (mm2·s−1) for Biodiesel (1) + Isobutyl Alcohol (2) at Various Mass Fractions w2 and Volume Fractions φ2 of Isobutyl Alcohol and at the Pressure p = 0.1 MPaa



a

φ2

3396

0.86332 0.85392 0.84592 0.83781 0.82974 0.82218 0.81473 0.80727 0.80017 0.79281 0.78566

0.88230 0.87330 0.86528 0.85757 0.84987 0.84263 0.83547 0.82828 0.82137 0.81417 0.80717

g·cm

−3

φ2

T/K = 298.15 7.532 0.000 6.498 0.100 5.675 0.200 5.107 0.300 4.751 0.400 4.429 0.500 4.250 0.600 4.146 0.700 4.140 0.800 4.199 0.900 4.636 1.000 T/K = 323.15 4.301 0.000 3.626 0.101 3.147 0.201 2.857 0.301 2.598 0.402 2.391 0.502 2.238 0.602 2.075 0.701 2.003 0.801 1.947 0.901 1.980 1.000

mm ·s

2 −1

ν −3

0.85968 0.85012 0.84199 0.83378 0.82560 0.81795 0.81042 0.80287 0.79570 0.78827 0.78105

0.87791 0.86907 0.86144 0.85367 0.84591 0.83862 0.83143 0.82420 0.81728 0.81007 0.80305

g·cm

ρ φ2

T/K = 303.15 6.742 0.000 5.690 0.100 4.943 0.200 4.482 0.300 4.162 0.400 3.867 0.500 3.687 0.600 3.553 0.700 3.537 0.800 3.551 0.900 3.852 1.000 T/K = 328.15 3.895 0.000 3.288 0.101 2.819 0.201 2.578 0.302 2.345 0.402 2.141 0.502 2.000 0.602 1.847 0.702 1.776 0.801 1.697 0.901 1.712 1.000

mm ·s

2 −1

ν −3

0.85604 0.84631 0.83805 0.82972 0.82143 0.81368 0.80605 0.79840 0.79115 0.78364 0.77634

0.87426 0.86529 0.85759 0.84974 0.84192 0.83458 0.82733 0.82006 0.81211 0.80588 0.79885

g·cm

ρ φ2

T/K = 308.15 5.946 0.000 4.984 0.100 4.355 0.200 3.960 0.300 3.671 0.401 3.395 0.501 3.218 0.601 3.059 0.700 3.036 0.800 3.037 0.900 3.228 1.000 T/K = 333.15 3.562 0.000 3.003 0.101 2.568 0.202 2.346 0.302 2.109 0.403 1.929 0.503 1.810 0.603 1.657 0.702 1.574 0.802 1.494 0.901 1.471 1.000

mm ·s

2 −1

ν −3

0.85240 0.84249 0.83408 0.82564 0.81722 0.80936 0.80162 0.79386 0.78651 0.77890 0.77151

0.87061 0.86151 0.85371 0.84579 0.83789 0.83049 0.82314 0.81586 0.80877 0.80161 0.79455

g·cm

ρ

3.269 2.758 2.393 2.154 1.933 1.753 1.619 1.478 1.403 1.328 1.285

5.321 4.478 3.894 3.536 3.246 3.011 2.841 2.673 2.635 2.595 2.703

mm ·s

2 −1

ν T/K = 313.15 0.000 0.100 0.201 0.301 0.401 0.501 0.601 0.701 0.801 0.900 1.000

φ2

−3

0.86696 0.85772 0.84982 0.84181 0.83383 0.82635 0.81899 0.81159 0.80456 0.79726 0.79016

g·cm

ρ


T/K = 293.15 0.000 0.000 0.092 0.100 0.186 0.200 0.282 0.300 0.380 0.400 0.479 0.500 0.580 0.600 0.682 0.700 0.786 0.800 0.892 0.900 1.000 1.000 T/K = 318.15 0.000 0.000 0.092 0.100 0.186 0.201 0.282 0.301 0.380 0.401 0.479 0.501 0.580 0.601 0.682 0.701 0.786 0.801 0.892 0.900 1.000 1.000

w2

ρ

4.762 4.014 3.465 3.164 2.898 2.672 2.517 2.358 2.288 2.220 2.311

mm2·s−1

ν

Table 6. Experimental Densities ρ (g·cm−3) and Kinematic Viscosities ν (mm2·s−1) for Biodiesel (1) + 2-Butanol (2) at Various Mass Fractions w2 and Volume Fractions φ2 of 2-Butanol and at the Pressure p = 0.1 MPaa




Article

Figure 2. Fractional deviations Δρ = ρ(exp) − ρ(calc) of experimental densities ρ(exp) of biodiesel mixtures from values ρ(calc) obtained ́ with the correlation of Ramirez−Verduzco et al.7 as a function of temperature T: ◇, biodiesel + 1-butanol ; ○, biodiesel + isobutyl alcohol; ▲, biodiesel + 2-butanol.

⎛ ω⎞ ν = exp⎜ξ + Ω·φ + ⎟ ⎝ T⎠

(7) 2 −1

where ν is the kinematic viscosity in mm ·s ; T is the temperature in Kelvin; φ is volume fraction of alcohol in the mixture with biodiesel; and ξ, Ω, and ω are adjustable parameters. Krisnangkura et al.44 modified eq 7 to include an extra temperature term to correlate the viscosity of mixtures, ⎛ γφ ⎞ ω ⎟ ν = exp⎜ξ + Ω·φ + + ⎝ T T ⎠

(8)

Figures 3 and 4 show the percentage deviation of eqs 7 and 8 when correlating the kinematic viscosity. Also, in this work we

Figure 1. Experimental kinematic viscosity, ν (exp) of biodiesel blends at different temperatures T as a function of volume fraction φ2: (a) biodiesel (1) + 1-butanol (2); (b) biodiesel (1) + isobutyl alcohol (2); (c) biodiesel (1) + 2-butanol (2): ●, T = 293.15 K; ■, T = 298.15 K; ▲, T = 303.15 K; ◆, T = 308.15 K; ▼, T = 313.15 K; ○, T = 318.15 K; □, T = 323.15 K; △, T = 328.15 K; ◇, T = 333.15 K.

extrapolated the density behavior at this temperature using eq 4. For the mixtures considered in this work, the density is within compliance to the limits of the norm EN 590 at volume fraction between 0.6 and 0.8. In this work we have correlated the viscosity data with three models reported in the literature. Joshi et al.43 proposed an empirical model to predict the kinematic viscosity of mixtures as a function of temperature and volume fraction,

Figure 3. Fractional deviations Δν = ν(exp) − ν(calc.) of experimental kinematic viscosities ν(exp.) of biodiesel mixtures from values ν(calc) obtained with the correlation of Joshi et al.43 as a function of temperature T: ◇, biodiesel + 1-butanol; ○, biodiesel + isobutyl alcohol; ▲, biodiesel + 2-butanol.

Table 7. Parameters of eq 4 Together with AADP in %, σ in g·cm−3, and max dev in % parameters system

T/K

no. points

α

β

δ

AAPD %

σ g·cm−3

max dev %

biodiesel + 1-butanol biodiesel + isobutyl alcohol biodiesel + 2-butanol

293.15−333.15 293.15−333.15 293.15−333.15

99 99 99

−7.2652 × 10−2 −7.9035 × 10−2 −7.7075 × 10−2

−7.7855 × 10−4 −7.9539 × 10−4 −8.2924 × 10−4

1.1105 1.1143 1.1251

0.056 0.048 0.098

6.121 × 10−4 6.996 × 10−4 1.062 × 10−3

0.166 0.358 0.413

3397



Article

Table 9. Parameters for eq 10 T/K 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

Figure 4. Fractional deviations Δν = ν(exp) − ν(calc.) of experimental kinematic viscosities ν(exp.) of biodiesel mixtures from values ν(calc) obtained with the correlation of Krisnangkura et al.44 as a function of temperature T: ◇, biodiesel + 1-butanol; ○, biodiesel + isobutyl alcohol; ▲, biodiesel + 2-butanol.

have used the Grunberg-Nissan45equation for the correlation of the viscosity of liquid blends, N

ln μ =

N

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

N

∑ xi ln μi + ∑ ∑ xixjGij i=1

(9)

i=1 j=1

where μ is the dynamic viscosity of the mixture in mPa·s; μi is the viscosity of the pure component in mPa·s; xi and xj are the molar fraction of species 1 and 2; N is the number of data points; and Gij is an interaction parameter with Gij = 0 when i = j. We have replaced the dynamic viscosity by the kinematic viscosity and the mole fraction by the volume fraction in eq 9, and considered the biodiesel as a pseudocomponent, ln ν = φ1 ln ν1 + φ2 ln ν2 + φ1φ2G12

G12

σ mm2·s−1

AAPD %

Biodiesel + 1-Butanol −0.78888 0.842 0.052 −0.82621 0.740 0.047 −0.76822 0.688 0.038 −0.77476 0.644 0.042 −0.74517 0.751 0.040 −0.73045 0.854 0.043 −0.72773 0.818 0.037 −0.70045 0.810 0.034 −0.70739 0.676 0.024 Biodiesel + Isobutyl Alcohol −0.82113 1.039 0.079 −0.81823 0.953 0.065 −0.82371 1.136 0.060 −0.80715 1.246 0.061 −0.77070 1.367 0.059 −0.67131 1.056 0.047 −0.64230 1.005 0.038 −0.63239 1.040 0.035 −0.59282 0.987 0.031 Biodiesel +2-Butanol −1.17115 1.113 0.077 −1.14408 1.165 0.068 −1.06309 1.237 0.062 −0.97762 1.051 0.049 −0.91404 1.238 0.054 −0.83897 1.155 0.048 −0.79072 1.034 0.039 −0.69717 0.984 0.042 −0.63304 0.737 0.031

max dev % 2.550 2.120 1.783 2.488 2.508 2.935 2.759 2.687 2.262 3.992 2.290 3.185 3.259 3.999 2.875 2.353 2.477 2.209 4.293 3.484 2.689 2.579 3.644 3.976 3.413 4.279 3.276

4. CONCLUSIONS This paper reports experimental densities and viscosities of binary liquid mixtures of biodiesel + 1-butanol, + isobutyl alcohol, and + 2-butanol from 293.15 to 333.15 K at 0.1 MPa. Our density measurements agree with the literature density values within an AAPD of 0.06%. Our values of viscosity present a minimum value on the range of concentration for biodiesel binary mixtures with 2-butanol and isobutyl alcohol. This condition is presented at volume concentrations of alcohol between 80% and 90% at temperatures from 293.15−323.15 K for both systems. The Ramirez-Verduzco et al.7 equation correlates satisfactorily the density of mixtures within an AAPD of (0.06, 0.05, and 0.1) % for biodiesel + (1-butanol, isobutyl alcohol, and 2-butanol), respectively. Also, we have correlated the kinematic viscosity with different equations presented in the literature. The viscosity correlations agree with the experimental data within 6.3%.

(10)

where ν is the kinematic viscosity of the mixture in mm2·s−1, and φi is the volume fraction of specie i. The subscripts 1 and 2 represent the pure components in the system. Tables 8 and 9 show the values of the parameters for eqs 7, 8, and 10 together with the AAPD, standard deviation, and maximum absolute percentage deviation for each of the mixtures considered in this work. All parameters are statistically valid with a 95% confidence interval. Figure 5 shows the correlative capability of eq 10. We have also checked our viscosity values with the limits established by the norm EN 590. These limits are for a diesel fuel of 2 mm2·s−1 and 4.5 mm2·s−1 at 313.15 K. All our experimental densities of biodiesel + 1-butanol, + isobutyl alcohol, and + 2-butanol at 313.15 K are between these limits.

Table 8. Parameters for the Equations Proposed by Joshi et al.43 (eq 7) and Krisnangkura et al.44 (eq 8) parameters system biodiesel + 1-butanol

T/K

no. points

eq

ξ

Ω

ω

293.15−333.15

99

7 8 7 8 7 8

−5.3099 −5.2577 −5.9405 −5.8919 −5.9105 −6.0652

−0.7612 −0.7469 −0.5537 −0.5390 −0.7171 −0.7020

2111.55 2095.68 2307.27 2292.80 2282.87 2332.70

biodiesel + isobutyl alcohol

293.15−333.15

99

biodiesel + 2-butanol

293.15−333.15

99

3398

γ −5.2915 −7.1454 −6.9847

AAPD %

σ mm2·s−1

max dev %

4.995 4.997 4.702 4.706 6.298 6.387

0.250 0.252 0.285 0.289 0.375 0.368

15.520 16.055 22.083 22.885 31.199 30.749



Article

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Figure 5. Fractional deviations Δν = ν(exp) − ν(calc.) of experimental kinematic viscosities ν(exp.) of biodiesel mixtures from values ν(calc) obtained with the correlation of eq 10 as a function of temperature T: ◇, biodiesel + 1-butanol; ○, biodiesel + isobutyl alcohol; ▲, biodiesel + 2-butanol.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: 011 52 461 611 7575. Fax: 011 52 461 611 7744. E-mail: [email protected]. ORCID

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

The Universidad Autónoma de Nuevo León have provided financial support for this work. UANL provided support through PRODEP Project DSA/103.5/16/10510, UANL-PTC920. G.A.I.-S. thanks Consejo Nacional de Ciencia y Tecnologiá (CONACyT) for providing financial support through project CB-2012-177920. Notes

The authors declare no competing financial interest.

■

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Densities and Viscosities for Binary Liquid Mixtures of Biodiesel + 1

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