K at 0.1 MPa - American Chemical Society

Article pubs.acs.org/jced

Densities and Viscosities of Corn Oil + n‑Alkanes Blends from (288.15 to 343.15) K at 0.1 MPa Fátima Reyes-García and Gustavo A. Iglesias-Silva* Departamento de Ingeniería Química, Instituto Tecnológico de Celaya, Celaya, Guanajuato CP 38010, México ABSTRACT: In this paper we present densities and viscosities of corn oil with n-alkanes with carbon atoms from C7 to C10 from (288.15 to 343.15) K at atmospheric pressure. A vibrating tube densimeter is used to measure the densities. Viscosities are measured using a pellet microviscometer. Dynamic and kinematic viscosities are correlated using common equations previously presented in the literature. We have used an equation based upon the Gibbs activation energy to correlate the kinematic viscosities of the blends, obtaining the best performance. The average absolute percentage error from this equation is calculated as 0.86%.

1. INTRODUCTION Reduction of sources of fossil fuel has created the necessity of finding alternative energy fuels. Vegetable oils have potential benefits because they are made from renewable resources. Also, their energy content is close to that of a diesel fuel. They have several advantages compared to diesel fuel, such as renewability, higher heat content, and lower sulfur and aromatic content. However, the vegetable oils have some disadvantages, such as their higher viscosity and lower volatility than those of diesel fuel.1 The direct use of vegetable oil in diesel engines can cause serious engine problems, such as poor fuel atomization, poor cold engine start up, oil ring stickening, and formation of gum and other deposits due to their high viscosity. The vegetable oils could be a good option to replace fuels such as diesel if some of their physical properties can be modified using additives to improve their fuel properties. The kinematic viscosities of vegetable oils are between 23 and 53 mm2/s at 311.15 K2−4 while the kinematic viscosity of diesel varies between 1.3 and 4.1 mm2/s at the same temperature.1,2,5,6 The kinematic viscosity of corn oil is about 34.9 mm2/s at 311.15 K.7 Few experimental densities and viscosities of mixtures of vegetable oils + n-alkanes have been reported in the literature. González et al.8 measured the density of sunflower seed oil with n-hexane, n-heptane, and n-octane at temperatures between 298.15 and 313.15 K. Later, González et al.9 measured the densities of olive, corn and grape, pip oils + n-hexane at (298.15 to 313.15) K. They mentioned in their work that the most useful solvent in the edible oil extraction industry is n-hexane. Unfortunately, the viscosity was not measured in their work. In this work, we have measured the densities and viscosities of corn oil + (n-heptane, n-octane, n-nonane, and n-decane) from (288.15 to 343.15) K at atmospheric pressure. Also, we have correlated the viscosities of these blends using common temperature functions used in the fuel industry. The objective is © 2017 American Chemical Society

to obtain a blend with viscosities close to those of fuels such as diesel.

2. EXPERIMENTAL SECTION Samples. The n-alkanes are from J. T. Baker for n-heptane (99%+ in mass fraction) and from Sigma-Aldrich for n-octane (99.1% in mass fraction), n-nonane (99%+ in mass fraction), and n-decane (99%+ in mass fraction). The specifications for nalkanes are shown in Table 1. Commercial corn oil is from Table 1. Sample Information Chemical name n-Heptane n-Octane Anhydrous n-Nonane Anhydrous n-Decane Anhydrous a

Source J. T. Baker SigmaAldrich SigmaAldrich SigmaAldrich

CAS No.

Mass fraction

Analysis methoda

142-82-5 111-65-9

0.99 0.991

GC

111-84-2

0.996

GC

127-18-5

0.997

GC

Gas chromatography provided by the supplier.

Mazola, and Table 2 shows the composition of corn oil.10 Our gas chromatograph capabilities validated the oil composition. Diesel is provided by Pemex, which is the brand of the Mexican Oil Company. The diesel fuel has (proprietary exact composition) 0.045% sulfur and 28% aromatic content in mass percent. The cetane index provided by the supplier is 51. We prepared the blends using an analytical balance (Ohaus Special Issue: Memorial Issue in Honor of Ken Marsh Received: January 31, 2017 Accepted: April 28, 2017 Published: May 10, 2017 2726

DOI: 10.1021/acs.jced.7b00121 J. Chem. Eng. Data 2017, 62, 2726−2739

Journal of Chemical & Engineering Data

Article

shown in Table 3. Comparison with literature values is done using the average absolute percentage deviation defined as

Table 2. Corn Oil Composition

a

Fatty Acid Composition

Mass Fraction Puritya

Myristic Palmitic Stearic Hexadecanoic Oleic Linoleic Saturated Above C18

0.002 0.099 0.029 0.005 0.301 0.562 0.002

Table 3. Comparison between the Experimental Pure Component Liquid Density, ρ, and Viscosity, η, and Literature Values at Pressure p = 0.1 MPaa ρ/g·cm3

Reverse phase partition chromatography.

model V12140) with a standard uncertainty of 0.3 mg. The blends are reported in volume percent despite the fact that they are prepared by a gravimetric method. The volume fraction is calculated using vi =

mi /ρi N ∑ j = 1 mj /ρj

T/K

n-heptane

298.15

0.67971

n-octane n-nonane n-decane

298.15 298.15 298.15

0.69851 0.71391 0.72605

Corn oil

298.15

0.91592

Diesel fuel

308.15 318.15 328.15 298.15

0.90919 0.90248 0.89580 0.82434

313.15 323.15 333.15 343.15

0.81380 0.80675 0.79968 0.79258

(1)

where mi is the mass and ρi is the mass density of species i. Pure components densities are measured in this work and expressed by a quadratic polynomial at each temperature. The uncertainty in the volume fraction is calculated using a propagation error formula. Standard uncertainties in the mole and volume fraction are 0.0002 and 0.0013, respectively. Atmospheric pressure is measured using a barometer, DRUCK, DPI 145, and its standard uncertainty is 10 kPa. Apparatus and Procedures. Densities are measured with a vibrating tube densimeter (DMA 5000, Anton Paar). The density is determined by an excitation of a U-shaped tube creating a characteristic frequency of vibration. This vibration depends upon the density sample. The calibration of the densimeter is made by the manufacturer11 using two reference fluids: ultrapure water and dry air.12 The reproducibilities claimed by the manufacturer are 1 × 10−6 g·cm−3 for the density and 0.001 K for the temperature. The densimeter has a Pt-100 thermometer to measure the temperature. The standard uncertainties in the density measurements and temperature, given by the manufacturer, are 5 × 10−6 g·cm−3 and 0.01 K, respectively. The estimated relative standard uncertainty in the density is equal to 0.001. The viscosities of the corn oil, alkanes, and their mixtures are measured using a rolling ball microviscometer (AMVn, Anton Paar). The sample is introduced into a capillary tube of 0.5 cm3 together with a steel ball. The viscosity is determined measuring the rolling time of the ball with η = k1 + k 2t(ρb − ρs )

Liquid

This work

η/mPa·s Lit.

0.679413 0.6799914 0.698513 0.71383415 0.7265014 0.72617415 0.727216 0.916059 0.919010 0.917818,b 0.911118,b 0.904418,b 0.897718,b 0.8539719 0.82320 0.812520 0.80620 0.799520 0.79220

This work 0.393 0.523 0.669 0.852

53.677

36.165 25.612 18.895 2.907 2.099 1.739 1.468 1.259

Lit. 0.40013 0.39614 0.52213 0.66915 0.84814 0.86015 0.850916 51.4417

34.7717 24.7917 18.2517

2.38220 1.97120 1.66120 1.42820

a

Standard uncertainties: ur(ρ) = 0.001, ur(η) = 0.05, u(T) = 0.01 K for density, u(T) = 0.05 K for viscosity, u(p) = 10 kPa. bInterpolated densities.

AAD =

100 N

N

∑ i=1

φiexp − φical φiexp

(3)

where N is the number of experimental data points and φi is the mass density. Our n-alkanes densities agree with the literature values within an average absolute percentage deviation of 0.038% at 298.15 K. The absolute percentage deviation of the Mexican diesel density with values of commercial diesel varies from 0.26 to 3.5%. The densities of corn oil have been measured by González et al.9 However, the corn oil has a different composition that the corn oil used in this work. Their mass percent of linoleic acid is 59.1% compared to 56.2% in the corn oil used in this work. They measure the density at four temperatures: (298.15, 303.15, 308.15, and 313.15) K. Our densities agree within an average absolute percentage deviation of 0.22%. There is only one density measurement10 for the same oil used in this work. The density of the corn oil agrees with this literature value within an absolute percentage deviation of 0.34%. Also, we have measured the densities of corn oil + n-alkanes (C7 to C10) from (288.15 to 343.15) K at atmospheric pressure. The concentration range is from 0.1 to 0.6 volume fraction. This concentration is selected such as we obtained a biofuel with a viscosity close to a diesel fuel. Figure 1 shows a comparison of the kinematic viscosity of the blends at different temperatures and at a volume fraction of 0.4. Unfortunately, the densities of these mixtures have not been measured in the literature. Tables 4−7 show the experimental densities of the

(2)

where k1 and k2 are calibration constants, t is the rolling time, ρb is the density of the ball, and ρs is the density of the sample. Measurements are performed with two different capillaries due to the wide range of samples viscosity. The capillary diameters are 1.6 and 1.8 mm with a length of 18.5 cm. The steel ball has a diameter of 1.5 mm and a density of 7.85 g·cm−3. The stated repeatability of the microviscometer by the manufacturer is 0.1%. The estimated relative standard uncertainty of the viscosity measurements is 0.05.

3. RESULTS AND DISCUSSION The densities of the n-alkanes, the vegetable oil, and diesel are measured from (288.15 to 343.15) K. Densities and viscosities are compared with the literature values,10,13−19 and they are 2727



Article

where A and b are adjustable parameters that can be obtained from experimental measurements. Other temperature dependent equations are modifications of the Andrade equation. Abramovic and Klofutar17 use several temperature dependences of the dynamic viscosity correlations. Yilmaz23 correlated the dynamic viscosity of vegetable oils and biofuels using an inverse temperature function similar to the Antoine equation used for the logarithm of the vapor pressure. Also, Yilmaz23 uses two modified Andrade equations reported by Abramovic and Klofutar.17 We have used these equations to check their performance in correlating the viscosities measured in this work. These equations are η=a+

b T+c

(9)

η = ea+b/T Figure 1. Temperature dependent kinematic viscosity for diesel and corn oil blends with n-alkanes (C7−C10) at 0.4 volume fraction and atmospheric pressure: ○, n-heptane; ◇, n-octane; ▽, n-nonane; △, ndecane; and ■, diesel.

η = ea+b/T+c/T

⎞ ⎟ ⎟ ⎠

(4)

the average percentage bias 100 Bias = N

N

∑

φiexp − φical

i=1

φiexp

(5)

the standard deviation, ⎛ ∑N (φ exp ⎜ i=1 i

σ=⎜ ⎝

− ϕical)2 ⎞ ⎟ ⎟ N−m ⎠

1/2

(6)

and the root-mean-square deviation, ⎛ ∑N (φ exp − φ cal)2 ⎞1/2 i ⎟ RMSD = ⎜⎜ i = 1 i ⎟ N ⎝ ⎠

(7)

(11)

⎛ b c ⎞ v1 v2 νm = (ν1,313.15 ν2,313.15 ) exp⎜a + + 2⎟ ⎝ T T ⎠

(12)

⎛ b c ⎞ 1/3 1/3 νm = (v1ν1,313.15 + v2ν2,313.15 )3 exp⎜a + + 2⎟ ⎝ T T ⎠

(13)

⎛ b ⎞ v1 v2 ⎟ ) exp⎜a + νm = (ν1,313.15 ν2,313.15 ⎝ T + c⎠

(14)

⎛ b ⎞ 1/3 1/3 ⎟ )3 exp⎜a + νm = (v1ν1,313.15 + v2ν2,313.15 ⎝ T + c⎠

(15)

where νm, ν1, 313.15, and ν2, 313.15 are the kinematic viscosity in mm2·s−1 of the mixture and components 1 and 2 at 313.15 K, respectively; v1 and v2 are the volume fractions of components 1 and 2; T is the temperature in kelvin; and a, b, and c are the adjustable parameters obtained from the viscosity data. The performances of eqs 12 and 14 and eqs 13 and 15 should be similar since they have the same function for the composition and the temperature, and they are similar since

where m is the number of adjustable parameters and φi is the dynamic or kinematic viscosity. Temperature Dependent Correlations. The variation with the temperature of the dynamic viscosity has been represented by the Andrade equation,21

μ = Aeb / T

2

where η is the dynamic viscosity in mPa·s, T is the temperature in kelvin, and a, b, and c are adjustable parameters. The average AAD values for the correlation for the kinematic viscosity of corn oil blends with n-heptane, n-octane, n-nonane, and ndecane using eqs 9−11 are (0.314, 0.308, 0.313, 0.366) %, (0.956, 0.986, 1.030, 1.203) %, and (0.096, 0.064, 0.073, 0.113) %, respectively. Figures 2−4 show the percentage deviations of eqs 9−11 when correlating the dynamic viscosity of corn oil blends. The best correlative performance in our experimental results is using eq 11. The maximum AAD and bias using this equation are (0.25, 0.13, 0.22, 0.35) % and (−3.06 × 10−3, −1.68 × 10−3, −6.02 × 10−3, and −6.40 × 10−3) % for the mixtures with n-heptane, n-octane, n-nonane, and n-decane, respectively. Table 9 shows the parameters and a summary of the deviations using eq 11. All the above correlations present higher standard deviations for corn oil than for the blends. This result agrees with the findings of Yilmaz23 for peanut, soy, sunflower, and waste vegetable oils. The AAD and bias for the corn oil are (0.056 and −5.18 × 10−3) % when using eq 11. Temperature−Concentration Dependent Correlations. Moradi et al.20 combines the Andrade equation with the Grunberg−Nissan24 equation to have several temperature− concentration correlations,

corn oil + n-alkanes (C7 to C10), respectively, and Table 8 presents the experimental data of diesel. Also, we have measured the viscosities of the corn oil + nalkanes (C7 to C10) blends. A comparison of the experimental viscosities with the literature values13−16 at 298.15 K of the nalkanes is given in Table 3. We have correlated the experimental dynamic and kinematic viscosities of the corn oil + n-alkanes blends using temperature dependent,4,19,21−23 composition dependent24,25 and temperature−composition dependent20 functionalities from the literature. We compare the performance of the correlations using average absolute percentage deviation, eq 3, the maximum percentage deviation, ⎛ φ exp − φ cal MD = max⎜⎜100 i exp i φi ⎝

(10)

(8) 2728


2729

a

mPa·s

η

T = 288.15 K 0.68813 0.432 0.71303 0.672 0.73761 1.029 0.76182 1.606 0.78649 2.667 0.80945 4.467 0.83297 8.008 0.92269 84.329 T = 313.15 K 0.66689 0.348 0.69232 0.513 0.71742 0.745 0.74220 1.079 0.76728 1.678 0.79069 2.681 0.81462 4.406 0.90583 30.273 T = 338.15 K 0.64484 0.293 0.67100 0.411 0.69713 0.572 0.72223 0.793 0.74805 1.166 0.77187 1.819 0.79625 2.805 0.88915 14.475

g·cm

−3

0.455 0.612 0.820 1.098 1.559 2.357 3.523 16.280

0.521 0.741 1.038 1.453 2.187 3.391 5.409 33.420

0.627 0.943 1.396 2.108 3.392 5.519 9.614 91.395

mm ·s

2 −1

ν −3

mPa·s

η

T = 293.15 K 0.68393 0.412 0.70892 0.633 0.73360 0.958 0.75798 1.461 0.78266 2.406 0.80600 3.982 0.82930 7.021 0.91930 66.735 T = 318.15 K 0.66255 0.335 0.68811 0.489 0.71330 0.704 0.73822 1.005 0.76364 1.549 0.78692 2.460 0.81097 3.983 0.90248 25.612 T = 343.15 K 0.64029 0.284 0.66662 0.395 0.69291 0.545 0.71814 0.750 0.74412 1.095 0.76830 1.699 0.79303 2.594 0.88583 12.790

g·cm

ρ

0.444 0.593 0.787 1.044 1.471 2.211 3.271 14.438

0.506 0.710 0.987 1.362 2.028 3.126 4.911 28.380

0.603 0.893 1.306 1.927 3.074 4.940 8.466 72.593

mm ·s

2 −1

ν −3

mPa·s

η

T = 298.15 K 0.67971 0.393 0.70481 0.599 0.72958 0.897 0.75405 1.346 0.77883 2.181 0.80195 3.575 0.82563 6.178 0.91592 53.677 T = 323.15 K 0.65819 0.324 0.68387 0.467 0.70919 0.666 0.73423 0.947 0.75976 1.437 0.78314 2.282 0.80730 3.623 0.89913 21.892

g·cm

ρ

0.493 0.683 0.939 1.290 1.891 2.913 4.488 24.348

0.579 0.849 1.229 1.785 2.801 4.458 7.483 58.605

mm ·s

2 −1

ν −3

mPa·s

η

T = 303.15 K 0.67547 0.377 0.70067 0.568 0.72554 0.840 0.75012 1.243 0.77499 1.990 0.79820 3.228 0.82195 5.490 0.91255 43.778 T = 328.15 K 0.65379 0.312 0.67965 0.447 0.70505 0.631 0.73023 0.886 0.75587 1.336 0.77935 2.109 0.80363 3.310 0.89580 18.895

g·cm

ρ

Standard uncertainties: ur(ρ) = 0.001, ur(η) = 0.05, u(v1) = 0.0013, u(T) = 0.01 K for density, u(T) = 0.05 K for viscosity, u(p) = 10 kPa.

0.0000 0.1006 0.2009 0.2995 0.4013 0.5000 0.6008 1.0000

0.0000 0.1006 0.2009 0.2995 0.4013 0.5000 0.6008 1.0000

0.0000 0.1006 0.2009 0.2995 0.4013 0.5000 0.6008 1.0000

v1

ρ

0.478 0.658 0.896 1.214 1.768 2.706 4.119 21.092

0.558 0.810 1.158 1.657 2.568 4.044 6.679 47.973

mm ·s

2 −1

ν −3

mPa·s

η

T = 308.15 K 0.67120 0.362 0.69651 0.539 0.72149 0.789 0.74617 1.148 0.77114 1.823 0.79445 2.935 0.81828 4.901 0.90919 36.165 T = 333.15 K 0.64933 0.302 0.67534 0.428 0.70122 0.601 0.72619 0.839 0.75197 1.247 0.77568 1.956 0.79994 3.041 0.89246 16.438

g·cm

ρ

0.465 0.634 0.857 1.156 1.658 2.522 3.801 18.419

0.539 0.774 1.094 1.538 2.363 3.694 5.989 39.777

mm2·s−1

ν

Table 4. Experimental Densities, ρ, Dynamic Viscosities, η, and Kinematic Viscosities, v, as a Function of Temperature, T, and Volume Composition, v, for Corn Oil (1) + nHeptane (2) at Pressure p = 0.1 MPaa

Journal of Chemical & Engineering Data Article


2730

a

mPa·s

η

T = 288.15 K 0.70654 0.585 0.72908 0.861 0.75147 1.304 0.77384 1.994 0.79565 3.189 0.81749 5.366 0.83900 8.525 0.92269 84.329 T = 313.15 K 0.68634 0.450 0.70928 0.635 0.73204 0.916 0.75478 1.323 0.77696 1.985 0.79912 3.113 0.82097 4.596 0.90583 30.273 T = 338.15 K 0.66555 0.365 0.68911 0.495 0.71225 0.691 0.73549 0.955 0.75808 1.375 0.78066 2.056 0.80293 2.892 0.88915 14.475

g·cm

−3

0.549 0.719 0.970 1.298 1.814 2.634 3.602 16.280

0.656 0.895 1.252 1.753 2.555 3.895 5.598 33.420

0.827 1.180 1.735 2.577 4.008 6.564 10.161 91.395

mm ·s

2 −1

ν −3

mPa·s

η

T = 293.15 K 0.70253 0.552 0.72514 0.804 0.74760 1.206 0.77004 1.819 0.79193 2.868 0.81382 4.747 0.83539 7.412 0.91930 66.735 T = 318.15 K 0.68224 0.431 0.70526 0.602 0.72812 0.861 0.75094 1.232 0.77320 1.831 0.79544 2.843 0.81736 4.146 0.90248 25.612 T = 343.15 K 0.66128 0.352 0.68517 0.474 0.70824 0.657 0.73159 0.901 0.75428 1.290 0.77695 1.917 0.79930 2.670 0.88583 12.790

g·cm

ρ

0.532 0.691 0.928 1.231 1.710 2.467 3.341 14.438

0.631 0.853 1.183 1.640 2.368 3.574 5.073 28.380

0.785 1.109 1.613 2.363 3.622 5.833 8.873 72.593

mm ·s

2 −1

ν −3

mPa·s

η

T = 298.15 K 0.69851 0.523 0.72120 0.756 0.74373 1.120 0.76624 1.670 0.78819 2.593 0.81015 4.235 0.83178 6.505 0.91592 53.677 T = 323.15 K 0.67811 0.412 0.70122 0.572 0.72417 0.809 0.74712 1.152 0.76943 1.696 0.79175 2.606 0.81375 3.760 0.89913 21.892

g·cm

ρ

0.608 0.815 1.117 1.542 2.204 3.291 4.621 24.348

0.748 1.048 1.506 2.179 3.290 5.227 7.821 58.605

mm ·s

2 −1

ν −3

mPa·s

η

T = 303.15 K 0.69448 0.496 0.71725 0.710 0.73985 1.044 0.76243 1.539 0.78445 2.362 0.80648 3.799 0.82818 5.757 0.91255 43.778 T = 328.15 K 0.67395 0.395 0.69719 0.543 0.72023 0.766 0.74326 1.078 0.76566 1.579 0.78807 2.399 0.81015 3.429 0.89580 18.895

g·cm

ρ


0.0000 0.0999 0.1999 0.3000 0.4000 0.5000 0.5998 1.0000

0.0000 0.0999 0.1999 0.3000 0.4000 0.5000 0.5998 1.0000

0.0000 0.0999 0.1999 0.3000 0.4000 0.5000 0.5998 1.0000

v1

ρ

0.587 0.779 1.064 1.451 2.062 3.044 4.232 21.092

0.714 0.991 1.412 2.019 3.011 4.711 6.951 47.973

mm ·s

2 −1

ν −3

mPa·s

η

T = 308.15 K 0.69042 0.473 0.71327 0.671 0.73595 0.978 0.75861 1.425 0.78071 2.161 0.80280 3.430 0.82458 5.126 0.90919 36.165 T = 333.15 K 0.66977 0.379 0.69317 0.518 0.71627 0.730 0.73938 1.013 0.76188 1.472 0.78437 2.217 0.80653 3.142 0.89246 16.438

g·cm

ρ

0.566 0.747 1.020 1.371 1.932 2.827 3.895 18.419

0.684 0.941 1.329 1.878 2.768 4.273 6.216 39.777

mm2·s−1

ν

Table 5. Experimental Densities, ρ, Dynamic Viscosities, η, and Kinematic Viscosities, v, as a Function of Temperature, T, and Volume Composition, v, for Corn Oil (1) + nOctane (2) at Pressure p = 0.1 MPaa



2731

a

mPa·s

η

T = 288.15 K 0.72164 0.763 0.74248 1.090 0.76321 1.607 0.78374 2.431 0.80420 3.781 0.82444 6.119 0.84451 9.928 0.92269 84.329 T = 313.15 K 0.70220 0.564 0.72333 0.776 0.74434 1.087 0.76516 1.559 0.78588 2.290 0.80638 3.457 0.82669 5.272 0.90583 30.273 T = 338.15 K 0.68231 0.443 0.70383 0.590 0.72521 0.796 0.74638 1.099 0.76746 1.555 0.78828 2.241 0.80891 3.244 0.88915 14.475

g·cm

−3

0.649 0.839 1.098 1.472 2.027 2.843 4.011 16.280

0.803 1.073 1.461 2.038 2.914 4.287 6.377 33.420

1.057 1.468 2.106 3.102 4.702 7.421 11.756 91.395

mm ·s

2 −1

ν −3

mPa·s

η

T = 293.15 K 0.71778 0.713 0.73867 1.011 0.75945 1.475 0.78003 2.201 0.80054 3.377 0.82083 5.383 0.84094 8.578 0.91930 66.735 T = 318.15 K 0.69826 0.535 0.71947 0.731 0.74054 1.016 0.76142 1.444 0.78221 2.103 0.80277 3.140 0.82314 4.733 0.90248 25.612 T = 343.15 K 0.67826 0.425 0.69988 0.563 0.72134 0.753 0.74260 1.034 0.76375 1.453 0.78465 2.080 0.80535 2.986 0.88583 12.790

g·cm

ρ

0.626 0.804 1.044 1.392 1.902 2.651 3.708 14.438

0.766 1.016 1.372 1.897 2.689 3.911 5.750 28.380

0.993 1.369 1.942 2.822 4.218 6.557 10.200 72.593

mm ·s

2 −1

ν −3

mPa·s

η

T = 298.15 K 0.71391 0.669 0.73485 0.942 0.75568 1.358 0.77632 2.005 0.79688 3.039 0.81721 4.769 0.83737 7.479 0.91592 53.677 T = 323.15 K 0.69430 0.509 0.71558 0.691 0.73673 0.953 0.75767 1.343 0.77854 1.940 0.79915 2.867 0.81958 4.272 0.89913 21.892

g·cm

ρ

0.733 0.966 1.294 1.772 2.492 3.588 5.212 24.348

0.937 1.282 1.797 2.583 3.813 5.836 8.932 58.605

mm ·s

2 −1

ν −3

mPa·s

η

T = 303.15 K 0.71003 0.630 0.73103 0.880 0.75192 1.256 0.77261 1.834 0.79322 2.750 0.81361 4.258 0.83381 6.674 0.91255 43.778 T = 328.15 K 0.69033 0.485 0.71168 0.654 0.73291 0.896 0.75392 1.252 0.77484 1.796 0.79553 2.631 0.81603 3.879 0.89580 18.895

g·cm

ρ


0.0000 0.1002 0.2005 0.3000 0.4000 0.5000 0.6004 1.0000

0.0000 0.1002 0.2005 0.3000 0.4000 0.5000 0.6004 1.0000

0.0000 0.1002 0.2005 0.3000 0.4000 0.5000 0.6004 1.0000

v1

ρ

0.702 0.919 1.222 1.660 2.318 3.307 4.754 21.092

0.887 1.204 1.671 2.374 3.467 5.234 8.004 47.973

mm ·s

2 −1

ν −3

mPa·s

η

T = 308.15 K 0.70612 0.594 0.72719 0.825 0.74813 1.167 0.76889 1.686 0.78955 2.504 0.81000 3.825 0.83025 5.910 0.90919 36.165 T = 333.15 K 0.68634 0.462 0.70777 0.621 0.72907 0.843 0.75016 1.172 0.77116 1.668 0.79191 2.424 0.81247 3.539 0.89246 16.438

g·cm

ρ

0.674 0.877 1.157 1.562 2.163 3.060 4.356 18.419

0.842 1.135 1.559 2.192 3.172 4.722 7.119 39.777

mm2·s−1

ν

Table 6. Experimental Densities, ρ, Dynamic Viscosities, η, and Kinematic Viscosities, v as a Function of Temperature, T, and Volume Composition, v, for Corn Oil (1) + nNonane (2) at Pressure p = 0.1 MPaa



2732

a

mPa·s

η

T = 288.15 K 0.73357 0.987 0.75291 1.403 0.77228 2.030 0.79145 3.057 0.81061 4.574 0.82946 7.163 0.84859 10.985 0.92269 84.329 T = 313.15 K 0.71469 0.703 0.73425 0.963 0.75383 1.322 0.77322 1.862 0.79258 2.680 0.81164 3.974 0.83096 5.628 0.90583 30.273 T = 338.15 K 0.69548 0.536 0.71534 0.714 0.73520 0.944 0.75486 1.286 0.77450 1.780 0.79381 2.556 0.81343 3.422 0.88915 14.475

g·cm

−3

0.771 0.999 1.284 1.703 2.298 3.219 4.207 16.280

0.984 1.312 1.754 2.409 3.381 4.896 6.773 33.420

1.346 1.863 2.629 3.863 5.642 8.635 12.945 91.395

mm ·s

2 −1

ν −3

mPa·s

η

T = 293.15 K 0.72981 0.915 0.74919 1.293 0.76860 1.844 0.78780 2.700 0.80700 4.052 0.82589 6.311 0.84505 9.439 0.91930 66.735 T = 318.15 K 0.71088 0.663 0.73050 0.902 0.75012 1.228 0.76956 1.717 0.78897 2.450 0.80807 3.606 0.82744 5.037 0.90248 25.612 T = 343.15 K 0.69159 0.512 0.71152 0.678 0.73144 0.889 0.75417 1.203 0.77086 1.658 0.79024 2.364 0.80991 3.143 0.88583 12.790

g·cm

ρ

0.740 0.953 1.216 1.595 2.150 2.992 3.881 14.438

0.932 1.235 1.638 2.231 3.105 4.462 6.087 28.380

1.254 1.725 2.399 3.427 5.021 7.641 11.170 72.593

mm ·s

2 −1

ν −3

mPa·s

η

T = 298.15 K 0.72605 0.852 0.74547 1.196 0.76491 1.685 0.78416 2.440 0.80340 3.619 0.82232 5.572 0.84152 8.192 0.91592 53.677 T = 323.15 K 0.70706 0.627 0.72673 0.849 0.74641 1.124 0.76590 1.589 0.78536 2.248 0.80452 3.281 0.82392 4.537 0.89913 21.892

g·cm

ρ

0.886 1.168 1.505 2.074 2.862 4.079 5.507 24.348

1.173 1.604 2.203 3.112 4.505 6.775 9.734 58.605

mm ·s

2 −1

ν −3

mPa·s

η

T = 303.15 K 0.72228 0.797 0.74174 1.107 0.76123 1.549 0.78052 2.219 0.79980 3.253 0.81876 4.943 0.83800 7.171 0.91255 43.778 T = 328.15 K 0.70321 0.593 0.72295 0.800 0.74268 1.071 0.76222 1.476 0.78174 2.074 0.80095 3.003 0.82046 4.109 0.89580 18.895

g·cm

ρ


0.0000 0.0997 0.2003 0.3000 0.4000 0.5000 0.5999 1.0000

0.0000 0.0997 0.2003 0.3000 0.4000 0.5000 0.5999 1.0000

0.0000 0.0997 0.2003 0.3000 0.4000 0.5000 0.5999 1.0000

v1

ρ

0.844 1.106 1.442 1.936 2.652 3.750 5.008 21.092

1.104 1.493 2.035 2.843 4.068 6.037 8.557 47.973

mm ·s

2 −1

ν −3

mPa·s

η

T = 308.15 K 0.71849 0.747 0.73800 1.032 0.75753 1.429 0.77687 2.027 0.79619 2.944 0.81520 4.418 0.83448 6.328 0.90919 36.165 T = 333.15 K 0.69936 0.563 0.71915 0.754 0.73895 1.004 0.75855 1.375 0.77812 1.917 0.79738 2.760 0.81694 3.739 0.89246 16.438

g·cm

ρ

0.805 1.049 1.359 1.812 2.464 3.461 4.577 18.419

1.040 1.398 1.887 2.610 3.698 5.420 7.583 39.777

mm2·s−1

ν

Table 7. Experimental Densities, ρ, Dynamic Viscosities, η, and Kinematic Viscosities, v, as a Function of Temperature, T, and Volume Composition, v, for Corn Oil (1) + nDecane (2) at Pressure p = 0.1 MPaa




Article

Table 8. Experimental Densities, ρ, Dynamic Viscosities, η, and Kinematic Viscosities, ν, as a Function of Temperature, T, for Diesel Fuel at Pressure p = 0.1 MPaa T K 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

ρ g·cm

−3

0.83136 0.82785 0.82434 0.82083 0.81731 0.81380 0.81027 0.80675 0.80322 0.79968 0.79614 0.79258

η

ν

mPa·s

mm2·s−1

3.748 3.287 2.907 2.590 2.324 2.099 1.906 1.739 1.595 1.468 1.358 1.259

4.508 3.971 3.526 3.155 2.844 2.579 2.352 2.155 1.985 1.836 1.705 1.589

Figure 4. Percentage deviations from eq 11 for the corn oil blends dynamic viscosity as a function of temperature: ●, n-heptane; ○, noctane, ▼, n-nonane; and △, n-decane.

a

Standard uncertainties: ur(ρ) = 0.001, ur(η) = 0.05, u(T) = 0.01 K for density, u(T) = 0.05 K for viscosity, u(p) = 10 kPa.

⎛ b ⎛ b ⎞ ⎜ T ⎜ ⎟ = ⎝T + c ⎠ ⎜1 + ⎝

c T

⎞ 2 3 ⎟ ≈ b − bc + bc − bc ... ⎟ T T4 T2 T3 ⎠

(16)

Unfortunately, eqs 12−15 could not correlate adequately the experimental kinematic viscosities of the blends of this work, as shown in Figure 5. The percentage deviations of eqs 12 and 13 in the correlation of the kinematic viscosity of corn oil + nheptane could be as high as 130 and 300%, respectively. Table 10 shows the correlative performance of eqs 12−15 together with the parameters a, b, and c. Concentration Dependent Correlations. The simplest way to represent the concentration dependence of the viscosity is using the Grunberg−Nissan24 equation. However, this equation considers a simple composition average of the pure component viscosities which is equivalent to considering an ideal behavior of an equilibrium thermodynamic property. The blends considered in this work do not follow the composition dependence of the Grunberg−Nissan24 equation since when used it can predict the viscosity within an AAD higher than 25%. ́ et al.25 developed a correlation for the Recently, Nava-Rios kinematic viscosities of binary mixtures. They used quadratic mixing rules for the Gibbs activation energy to obtain


ln νm = −ln(Mmix) + x1 ln ν1 + x1 ln(M1) + x 2 ln ν2 ⎡ * + x 2 ln(M 2) + x1x 2⎢ln(δν12) + x13 ln δg12 ⎢⎣ ⎛ M 3 ⎞⎤ ⎛ M3 ⎞ * + x1 ln⎜ 112 ⎟ + x 2 ln⎜ 122 ⎟⎥ + x 23 ln δg21 2 2 ⎝ M1M 2 ⎠⎥⎦ ⎝ M1 M 2 ⎠ (17)

where νm, ν1, and ν2 are the kinematic viscosities of the mixture and components 1 and 2, respectively; Mmix, M1, and M2 are the molecular weights of the mixture and components 1 and 2, respectively; x1 and x2 are the mole fractions of components 1 and 2; M112 and M122 are calculated using Mijk = (Mi + Mj + Mk)/3, and δν12, δg*12, and δg*21 are temperature dependent parameters obtained from the experimental data. The molecular weight of the mixture is calculated using


2733



Article

Table 9. Parameters for the Correlation of the Dynamic Viscosity of Corn Oil Blends Using Eq 11 v1

a

b

c

0.0000 0.1006 0.2009 0.2995 0.4013 0.5000 0.6008 1.0000

−2.4453 −2.9843 −2.9562 −1.1065 −1.8308 −0.5424 −0.2718 3.9723

118.3 496.7 526.3 −619.0 −128.6 −771.2 −929.5 −3742.1

99205.9 71628.7 96153.2 309385 270505 391473 463192 1116651

0.0000 0.0999 0.1999 0.3000 0.4000 0.5000 0.5998 1.0000

−2.7057 −2.9847 −2.3544 −2.2619 1.316 −0.6014 0.1991 3.9723

282.8 512.1 189.0 165.3 −369.8 −761.6 −1253.9 −3742.1

98552.8 87730 163040 197416 312071 408855 522680 1116651

0.0000 0.1002 0.2005 0.3000 0.4000 0.5000 0.6004 1.0000

−2.4243 −2.6568 −2.436 −1.8564 −1.1824 −0.4052 −0.5571 3.9723

107.6 317.1 217.5 −94.5 −456.2 −907.3 −765.1 −3742.1

147723 136349 178965 255072 339994 445440 457088 1116651

0.0000 0.0997 0.2003 0.3000 0.4000 0.5000 0.5999 1.0000

−2.5096 −2.43 −2.0824 0.0086 −0.7587 −0.4210 0.7398 3.9723

169.8 190.7 −1.5618 −1272.7 −727.2 −870.2 −1627.8 −3742.1

158318 174933 232076 458358 398683 449357 606568 1116651

1.0000

−0.4770

−1193.9

493296

AAD/%

MD/%

σ

Bias/%

Corn oil + n-Heptane 0.089 0.288 0.034 0.076 0.050 0.102 0.247 0.542 0.053 0.120 0.180 0.508 0.060 0.142 0.056 0.171 Corn oil + n-Octane 0.038 0.069 0.061 0.112 0.126 0.425 0.054 0.127 0.079 0.204 0.046 0.115 0.049 0.162 0.056 0.171 Corn oil + n-Nonane 0.059 0.085 0.020 0.036 0.050 0.155 0.071 0.129 0.071 0.193 0.041 0.121 0.216 0.670 0.056 0.171 Corn oil + n-Decane 0.055 0.107 0.050 0.103 0.062 0.123 0.348 0.740 0.107 0.251 0.151 0.292 0.071 0.220 0.056 0.171 Diesel 0.083 0.238

RMSD

−1.63 −6.71 −2.45 −2.30 −8.31 −3.06 1.18 −5.18

× × × × × × × ×

10−4 10−5 10−4 10−3 10−4 10−3 10−3 10−3

4.57 2.57 5.26 3.81 1.13 5.92 4.53 1.85

× × × × × × × ×

10−4 10−4 10−4 10−3 10−3 10−3 10−3 10−2

3.95 2.23 4.56 3.30 9.80 5.13 3.92 1.60

× × × × × × × ×

10−4 10−4 10−4 10−3 10−4 10−3 10−3 10−2

−8.64 −1.85 −2.28 −6.82 −1.22 −9.25 −1.68 −5.18

× × × × × × × ×

10−5 10−4 10−4 10−4 10−3 10−4 10−3 10−3

2.32 5.45 1.71 1.05 2.06 1.96 3.29 1.85

× × × × × × × ×

10−4 10−4 10−3 10−3 10−3 10−3 10−3 10−2

2.01 4.72 1.48 9.14 1.79 1.70 2.85 1.60

× × × × × × × ×

10−4 10−4 10−3 10−4 10−3 10−3 10−3 10−2

−1.98 −1.36 −5.42 −8.57 −1.42 −1.07 −6.02 −5.18

× × × × × × × ×

10−4 10−4 10−4 10−4 10−3 10−3 10−3 10−3

4.09 2.17 7.24 1.45 2.19 1.78 2.43 1.85

× × × × × × × ×

10−4 10−4 10−4 10−3 10−3 10−3 10−2 10−2

3.54 1.88 6.27 1.26 1.90 1.54 2.11 1.60

× × × × × × × ×

10−4 10−4 10−4 10−3 10−3 10−3 10−2 10−2

−2.07 5.50 −8.00 −6.40 −2.39 3.75 −2.85 −5.18

× × × × × × × ×

10−4 10−5 10−4 10−3 10−3 10−3 10−3 10−3

5.32 6.92 1.24 1.05 3.56 1.03 4.83 1.85

× × × × × × × ×

10−4 10−4 10−3 10−2 10−3 10−2 10−3 10−2

4.60 6.00 1.07 9.13 3.08 8.90 4.19 1.60

× × × × × × × ×

10−4 10−4 10−3 10−3 10−3 10−3 10−3 10−2

−2.19 × 10−3

2.13 × 10−3

1.84 × 10−3

N

Mmix =

∑ xiMi i=1

(18)

Equation 17 has not been previously used for the viscosity correlation of corn oil blends. The mole fractions are calculated using an average molecular weight using the composition of the oil reported by Kuksis and Beveridge.10 We have also used eq 17, substituting the mole fraction by the volume fraction, since the latter is a common variable used in the fuel industry. Figure 6 shows the performance of eq 17 using volume and mole fractions as composition variables. The correlation decreases the percentage deviation from 6 to 4% when using the volume fraction. Tables 11 and 12 show the adjustable parameters and the deviations when the volume and mole fraction are used , respectively. The maximum AAD and bias used in the equation for the volume fraction are (1.118, 1.515, 0.408, 1.288) % and (1.63 × 10−3, 5.62 × 10−3, 1.57 × 10−3, 4.80 × 10−3) % for the blends with n-heptane, n-octane, n-nonane, and n-decane, respectively. Using the mole fraction, the maximum AAD and bias are (1.256, 2.080, 0.317, 1.084) % and (3.38 × 10−3, 1.41 × 10−2, 1.72 × 10−3, 5.54 × 10−3) %, for the same blends.

Figure 5. Kinematic viscosity as a function of fraction volume for corn oil blends with ●, n-heptane and △, n-decane at 298.15 K. Lines are eq 12 for n-heptane, − ··−, eq 12 for n-decane; ---, eq 13 for n-heptane; −·−, eq 13 for n-decane.

2734



Article

Table 10. Parameters Used in Eqs 12−15 for the Correlation of the Kinematic Viscosity of Corn Oil + n-Alkanes Blends Blend

a

b

Corn Corn Corn Corn

oil oil oil oil

+ + + +

n-Heptane n-Octane n-Nonane n-Decane

1.5451 1.5884 1.6031 1.6768

−4212.4 −4230.2 −4225.0 −4257.2

Corn Corn Corn Corn

oil oil oil oil

+ + + +


1.8108 1.8357 1.7993 1.8562

−4379.6 −4385.1 −4347.1 −4369.3

Corn Corn Corn Corn

oil oil oil oil

+ + + +


−4.9300 −4.9049 −4.8768 −4.8381

736.8 731.3 726.0 717.4

Corn Corn Corn Corn

oil oil oil oil

+ + + +


−4.8530 −4.8305 −4.8113 −4.7778

698.7 694.2 691.9 684.9

c Eq 1166361 1167558 1164397 1167015 Eq 1183045 1182255 1173927 1175161 Eq −163.4 −163.7 −163.9 −164.4 Eq −165.9 −166.1 −166.0 −166.4

AAD/%

MD/%

Bias/%

σ

RMSD

34.840 30.787 28.410 25.961

139.876 118.723 111.154 97.603

−0.628 −0.615 −0.636 −0.644

1.663 1.730 1.793 1.884

1.637 1.703 1.764 1.855

90.268 75.435 65.728 55.348

309.720 256.648 219.339 177.294

−1.835 −1.766 −1.717 −1.645

4.684 4.644 4.575 4.522

4.611 4.571 4.503 4.451

34.886 30.825 28.448 25.996

140.041 118.875 111.303 97.744

−0.628 −0.615 −0.636 −0.644

1.663 1.730 1.793 1.884

1.637 1.703 1.764 1.855

90.269 75.433 54.629 55.352

310.023 256.914 189.236 177.505

−1.834 −1.765 −1.717 −1.645

4.684 4.644 4.575 4.522

4.611 4.571 4.503 4.451

12

13

14

15

In this work, δν12 has linear temperature functionality when we use the volume fraction as a variable in the equation. Therefore, the value of the parameter δν12 can be calculated using δν12 = −1.21532 + 0.005023T

for corn oil + n‐heptane (19)

δν12 = −1.20303 + 0.006103T

for corn oil + n‐octane (20)

δν12 = −1.01595 + 0.004819T

for corn oil + n‐nonane (21)

δν12 = −1.99543 + 0.008755T

for corn oil + n‐octane (22)

where T is in kelvis. A new curve fit is done using eqs 19−22 to obtain δg12 * and δg12 * . The deterioration of the curve fit is minimal, obtaining almost the same standard deviation, and all parameters are statistically valid. We have found that the temperature dependences of the parameters δg*12 and δg*21 are simple quadratic functions of temperature, * = −144.5830 + 0.982445T − 1.5735 × 10−3T 2 δg12 for corn oil + n‐heptane

(23)

* = −3.8217 + 0.022278T − 3.0257 × 10−5T 2 δg12 (24)

for corn oil + n‐octane

* = −62.9805 + 0.39415T − 5.9926 × 10−4T 2 δg12 for corn oil + n‐nonage ́ et al.25 correlation for Figure 6. Percentage deviations from Nava-Rios the corn oil blends kinematic viscosity as a function of temperature: ●, n-heptane; ○, n-octane; ▼, n-nonane; and △, n-decane. Plots: a, volume fraction; b, mole fraction.

(25)

* = −1.8074 + 0.013077T − 2.1264 × 10−5T 2 δg12 (26)

for corn oil + n‐decane

and * = 18.6742 − 0.082898T + 9.1799 × 10−6T 2 δg21

The parameter δν12 is statistically valid within a 95% ́ et al.25 proposed a linear confidence interval. Nava-Rios temperature dependence of this parameter for alcohol mixtures.

for corn oil + n‐heptane 2735

(27) DOI: 10.1021/acs.jced.7b00121 J. Chem. Eng. Data 2017, 62, 2726−2739


Article

́ et al.25 Correlation Using as Variable the Volume Fraction Table 11. Parameters and Deviations of the Nava-Rios T/K

δν12

δg12*

δg21*

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.2283 0.2499 0.2782 0.3013 0.3359 0.3583 0.3840 0.4340 0.4555 0.4658 0.4684 0.4840

8.1851 9.4156 8.9322 9.4712 8.5143 8.5791 8.4208 6.5724 6.8571 7.7728 8.7082 8.8280

2.6428 2.3708 2.2011 2.0563 1.7505 1.7431 1.5813 1.2606 1.1921 1.2339 1.2052 1.1580

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.5400 0.5796 0.6165 0.6488 0.6824 0.7124 0.7497 0.7902 0.8194 0.8259 0.8392 0.8776

0.1011 0.1131 0.1272 0.1472 0.1622 0.1815 0.1925 0.1987 0.2117 0.2528 0.276 0.2729

0.2970 0.3140 0.3296 0.3532 0.3712 0.3882 0.3837 0.3757 0.3808 0.4217 0.4239 0.4029

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.3747 0.4079 0.4395 0.4242 0.4568 0.4850 0.5129 0.5411 0.5681 0.5954 0.6172 0.6398

0.8912 0.905 0.9195 1.8756 1.8274 1.8082 1.8116 1.781 1.7745 1.7617 1.7083 1.7053

0.6817 0.6907 0.6999 0.8775 0.8647 0.8549 0.8442 0.8261 0.8024 0.7884 0.7630 0.7333

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.4822 0.5839 0.6348 0.6670 0.7030 0.7394 0.7971 0.8734 0.8719 0.9091 0.9645 0.9895

0.2751 0.1856 0.1789 0.1912 0.2008 0.2074 0.1921 0.1679 0.1998 0.2016 0.1819 0.1906

0.6005 0.4143 0.4021 0.4104 0.4228 0.4226 0.3953 0.3260 0.3913 0.3840 0.3528 0.3406

AAD/%

MD/%

Corn oil + n-Heptane 0.271 0.635 0.347 0.965 0.388 1.175 0.454 1.405 0.689 1.992 0.650 1.766 0.800 1.946 0.965 2.275 1.114 2.643 1.062 2.397 1.041 2.208 1.118 2.373 Corn oil + n-Octane 1.515 3.969 1.476 3.740 1.476 3.670 1.406 3.336 1.382 3.178 1.346 3.072 1.350 2.990 1.295 3.040 1.271 2.672 1.291 2.547 1.253 2.332 1.304 2.428 Corn oil + n-Nonane 0.376 0.972 0.408 1.053 0.395 1.113 0.210 0.583 0.222 0.692 0.188 0.619 0.193 0.689 0.215 0.720 0.239 0.814 0.243 0.892 0.249 0.951 0.254 1.022 Corn oil + n-Decane 0.516 1.381 0.988 3.037 1.056 3.279 1.017 3.020 1.012 3.034 0.966 2.959 1.040 3.167 0.994 4.103 1.078 3.337 1.110 3.355 1.209 3.604 1.288 3.804

* = −9.4246 + 0.060124T − 9.1893 × 10−5T 2 δg21 for corn oil + n‐octane

RMSD

−9.13 4.33 8.21 9.80 1.39 1.21 1.33 1.51 1.63 1.43 1.28 1.29

× × × × × × × × × × × ×

10−6 10−4 10−4 10−4 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

1.25 1.29 1.04 1.12 1.58 1.44 1.73 2.22 2.35 2.28 2.20 2.24

× × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

9.88 1.02 8.20 8.87 1.25 1.14 1.37 1.75 1.86 1.80 1.74 1.77

× × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

5.62 4.86 4.39 3.74 3.32 2.97 2.72 2.48 2.16 1.93 1.77 1.71

× × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

6.85 6.13 5.75 5.08 4.64 4.23 3.98 3.61 3.29 3.17 2.92 2.90

× × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

5.41 4.85 4.55 4.02 3.67 3.34 3.15 2.85 2.60 2.51 2.31 2.29

× × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

1.57 1.51 1.37 6.47 6.57 5.29 5.23 5.23 5.48 5.48 5.39 5.36

× × × × × × × × × × × ×

10−3 10−3 10−3 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4

2.39 2.29 1.96 9.71 8.37 7.28 6.54 6.47 6.43 6.43 6.04 6.10

× × × × × × × × × × × ×

10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

1.89 1.81 1.55 7.68 6.61 5.76 5.17 5.12 5.09 5.09 4.78 4.82

× × × × × × × × × × × ×

10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

2.30 4.80 4.64 3.95 3.60 3.17 3.15 3.23 2.83 2.68 2.71 2.70

× × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

4.51 6.03 5.85 5.17 4.68 4.12 4.14 3.84 3.74 3.64 3.80 3.65

× × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

3.57 4.77 4.62 4.09 3.70 3.26 3.27 3.04 2.95 2.87 3.00 2.89

× × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

* = −0.5084 + 0.0080290T − 1.6261 × 10−5T 2 δg21 (28)

for corn oil + n‐decane

(30)

where T is the temperature in kelvin. Equation 17 together with eqs 18−30 correlates the kinematic viscosity data within an AAD and bias of (0.737, 1.367, 0.287, 1.046) % and (0.209, 0.428, 0.090, 0.327) % for the blends of corn oil with n-heptane,

* = −12.1713 + 0.081503T − 1.2780 × 10−4T 2 δg21 for corn oil + n‐nonane

σ

Bias/%

(29) 2736



Article

́ et al.25 Correlation Using as Variable the Mole Fraction Table 12. Parameters and Deviations of Nava-Rios δν12

T/K

δg12*

δg21*

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

9.9293 10.364 10.6776 10.8313 11.8607 11.4597 11.965 13.7489 14.0974 13.3687 12.9603 12.9887

48.767 34.6297 19.4345 14.532 5.3305 4.9888 2.7564 0.6238 0.4367 0.5746 0.6103 0.4711

2.5723 2.0291 1.7852 1.5510 1.1729 1.1714 0.9575 0.6689 0.5754 0.5875 0.5290 0.4752

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

57.6282 51.5882 47.0107 42.2931 38.4713 35.3759 33.4600 31.6438 29.5293 27.2383 25.6855 25.1824

6.410 1.600 3.550 8.300 1.743 3.437 5.783 9.541 1.623 2.939 4.507 5.783

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

4.9153 4.8872 4.8152 4.2651 4.2692 4.2297 4.2156 4.2208 4.2440 4.2527 4.2461 4.2748

0.2917 0.2846 0.2902 1.1355 1.0466 1.0092 0.9696 0.8845 0.8088 0.7563 0.6761 0.6102

0.4822 0.5019 0.5266 0.6556 0.6645 0.6719 0.6723 0.6615 0.6403 0.6327 0.6092 0.5754

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

3.5136 4.3873 4.5154 4.4537 4.4191 4.4069 4.6091 5.0020 4.6791 4.7414 4.9844 5.0485

0.0715 0.0202 0.0171 0.0187 0.0200 0.0206 0.0158 0.0103 0.0149 0.0139 0.0099 0.0094

0.4957 0.3030 0.2953 0.3060 0.3218 0.3271 0.3029 0.2440 0.3001 0.2919 0.2600 0.2422

× × × × × × × × × × × ×

10−11 10−10 10−10 10−10 10−9 10−9 10−9 10−9 10−8 10−8 10−8 10−8

0.0210 0.0257 0.0298 0.0361 0.0423 0.0483 0.0510 0.0544 0.0595 0.0679 0.0705 0.0689

AAD/%

MD/%

σ

Bias/%

Corn oil + n-Heptane 0.384 1.749 0.550 2.063 0.637 2.446 0.728 2.652 0.929 3.130 0.894 2.937 1.017 3.076 1.103 3.208 1.243 3.589 1.211 3.414 1.188 3.209 1.256 3.373 Corn oil + n-Octane 2.080 6.151 1.983 5.878 1.960 5.696 1.850 5.437 1.800 5.257 1.758 5.013 1.731 4.892 1.640 4.449 1.597 4.464 1.632 4.770 1.597 4.468 1.606 4.504 Corn oil + n-Nonane 0.290 0.697 0.317 0.755 0.297 0.788 0.184 0.518 0.191 0.612 0.153 0.515 0.155 0.577 0.173 0.597 0.191 0.675 0.191 0.743 0.189 0.771 0.185 0.815 Corn oil + n-Decane 0.480 1.250 0.798 2.485 0.863 2.742 0.830 2.502 0.833 2.555 0.786 2.470 0.847 2.661 0.740 3.411 0.889 2.870 0.921 2.903 1.005 3.136 1.084 3.355

RMSD

1.37 1.86 2.48 2.66 3.14 2.94 3.08 3.23 3.38 3.13 2.88 2.87

× × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

1.14 1.46 1.51 1.59 1.91 1.79 1.97 2.24 2.33 2.30 2.21 2.22

× × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

8.98 1.15 1.19 1.26 1.51 1.41 1.56 1.77 1.84 1.82 1.75 1.76

× × × × × × × × × × × ×

10−3 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

1.41 1.22 1.10 9.60 8.57 7.69 6.96 6.18 5.46 5.07 4.70 4.40

× × × × × × × × × × × ×

10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

8.59 7.64 7.06 6.28 5.70 5.19 4.79 4.28 3.88 3.77 3.48 3.32

× × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

6.79 6.04 5.58 4.96 4.51 4.10 3.79 3.38 3.07 2.98 2.75 2.63

× × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

1.67 1.72 1.53 8.87 8.52 6.56 6.29 6.24 6.40 6.29 5.94 5.75

× × × × × × × × × × × ×

10−3 10−3 10−3 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4 10−4

1.73 1.70 1.42 7.93 6.54 5.54 4.81 4.69 4.58 4.44 4.08 4.02

× × × × × × × × × × × ×

10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

1.37 1.34 1.12 6.27 5.17 4.38 3.80 3.71 3.62 3.51 3.23 3.17

× × × × × × × × × × × ×

10−2 10−2 10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

2.53 5.54 5.42 4.62 4.22 3.67 3.65 3.44 3.32 3.17 3.24 3.23

× × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3

4.05 4.83 4.69 4.14 3.74 3.25 3.26 2.94 2.95 2.89 3.05 2.90

× × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

3.20 3.82 3.71 3.27 2.96 2.57 2.58 2.32 2.34 2.29 2.41 2.29

× × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

Table 13. Correlative Capability of Eqs 17−30 Blends Corn Corn Corn Corn

oil oil oil oil

+ + + +


AAD/% 0.737 1.367 0.287 1.046

MD/%

σ

Bias/%

2.649 4.322 0.925 3.798

2.09 4.28 8.99 3.27

2737

× × × ×

−1

10 10−1 10−2 10−1

1.52 3.79 1.49 3.76

× × × ×

RMSD −2

10 10−2 10−2 10−2

1.45 3.63 1.43 3.60

× × × ×

10−2 10−2 10−2 10−2



■

n-octane, n-nonane, and n-decane, respectively. Table 13 shows a summary of the deviations using these equations. Figure 7

REFERENCES

(1) Demirbas, A. Biodiesel: A Realistic Fuel Alternative for Diesel Engines; Springer-Verlag: London, UK, 2008. (2) Singh, S.; Singh, D. Biodiesel Production through the Use of Different Sources and Characterization of Oils and their Esters as the Substitute of Diesel: A Review. Renewable Sustainable Energy Rev. 2010, 14, 200−216. (3) Demirbas, A. Relationships Derived from Physical Properties of Vegetable Oil and Biodiesel Fuels. Fuel 2008, 87, 1743−1748. (4) Esteban, B.; Riba, J.-R.; Baquero, G.; Rius, A.; Puig, R. Temperature Dependence of Density and Viscosity of Vegetable Oils. Biomass Bioenergy 2012, 42, 164−171. (5) Lapuerta, M.; García-Contreras, R.; Campos-Fernández, J.; Dorado, M. P. Stability, Lubricity, Viscosity, and Cold-Flow Properties of Alcohol−Diesel Blends. Energy Fuels 2010, 24, 4497−4502. (6) Mesquita, F.; Feitosa, F.; Do Carmo, F.; de Santiago-Aguiar, R.; de Sant’Ana, H. Viscosities and Viscosity Deviations of Binary Mixtures of Biodiesel+ Petrodiesel (or n-Hexadecane) at Different Temperatures. Braz. J. Chem. Eng. 2012, 29, 653−664. (7) Leung, D. Y.; Wu, X.; Leung, M. A Review on Biodiesel Production Using Catalyzed Transesterification. Appl. Energy 2010, 87, 1083−1095. (8) González, C.; Resa, J. M.; Ruiz, A.; Gutiérrez, J. I. Densities of Mixtures Containing n-Alkanes with Sunflower Seed Oil at Different Temperatures. J. Chem. Eng. Data 1996, 41, 796−798. (9) González, C.; Resa, J. M.; Ruiz, A.; Gutiérrez, J. I. Excess Molar Volumes of Mixtures of Hexane + Natural Oils from 298.15 to 313.15 K. J. Chem. Eng. Data 1997, 42, 339−341. (10) Kuksis, A.; Beveridge, J. Composition of Molecular Distillates of Corn Oil: Isolation and Identification of Sterol Esters. J. Lipid Res. 1960, 1, 311−320. (11) Anton, P. Instruction Manual: DMA 4500/DMA 5000 Density/ Specific Gravity/Concentration Meter; Anton Paar: Graz, Austria, 2005. (12) Spieweck, F.; Bettin, H. Review: Ü bersicht: Bestimmung der Dichte von Festkörpern und Flüssigkeiten. Tech. Mess. 1992, 59, 285− 292. (13) Orge, B.; Iglesias, M.; Rodriguez, A.; Canosa, J.; Tojo, J. Mixing Properties of (Methanol, Ethanol, or 1-Propanol) with (n-Pentane, nHexane, n-Heptane and n-Octane) at 298.15 K. Fluid Phase Equilib. 1997, 133, 213−227. (14) Sagdeev, D.; Fomina, M.; Mukhamedzyanov, G. K.; Abdulagatov, I. Experimental Study of the Density and Viscosity of n-Heptane at Temperatures from 298 to 470 K and Pressure up to 245 MPa. Int. J. Thermophys. 2013, 34, 1−33. (15) Landaverde-Cortes, D. C.; Iglesias-Silva, G. A.; Ramos-Estrada, M.; Hall, K. R. Densities and Viscosities of MTBE + Nonane or Decane at P = 0.1 MPa from (273.15 to 363.15) K. J. Chem. Eng. Data 2008, 53, 288−292. (16) Feitosa, F. X.; Caetano, A. C. R.; Cidade, T. B.; de Sant’Ana, H. B. Viscosity and Density of Binary Mixtures of Ethyl Alcohol with nAlkanes (C6, C8, and C10). J. Chem. Eng. Data 2009, 54, 2957−2963. (17) Abramovic, H.; Klofutar, C. The Temperature Dependence of Dynamic Viscosity for Some Vegetable Oils. Acta Chim. Slov. 1998, 45, 69−77. (18) Noureddini, H.; Teoh, B. C.; Clements, L. D. Densities of vegetable oils and fatty acids. J. Am. Oil Chem. Soc. 1992, 69, 1184− 1188. (19) Benjumea, P.; Agudelo, J.; Agudelo, A. Basic Properties of Palm Oil Biodiesel−Diesel Blends. Fuel 2008, 87, 2069−2075. (20) Moradi, G.; Karami, B.; Mohadesi, M. Densities and Kinematic Viscosities in Biodiesel−Diesel Blends at Various Temperatures. J. Chem. Eng. Data 2013, 58, 99−105. (21) Andrade, E. d. C. The Viscosity of Liquids. Nature 1930, 125, 309−10. (22) Tat, M. E.; Van Gerpen, J. H. The Kinematic Viscosity of Biodiesel and Its Blends with Diesel Fuel. J. Am. Oil Chem. Soc. 1999, 76, 1511−1513.

́ et al.25 Figure 7. Percentage deviations from the Nava-Rios generalized correlation (eqs 17−30) for the corn oil blends kinematic viscosity as a function of temperature: ●, n-heptane; ○, n-octane; ▼, n-nonane; and △, n-decane.

shows the percentage deviation of the generalized Nava-Rios et al. equation when correlating the kinematic viscosity. As can be seen in Figures 5 and 6, a minimal deterioration is obtained when the parameters are expressed as functions of temperature. This is an indication that it is possible to include temperature effects in the Nava-Rios et al. correlation, and a generalization is possible for homologous families.

4. CONCLUSIONS We have measured the densities and viscosities of corn oil blends with n-alkanes (n-heptane, n-octane, n-nonane, and ndecane) from (288.15 to 343.15) K at atmospheric pressure. The composition interval has been selected, such as the viscosity of the fuel, and it can be similar to that of commercial diesel. Empirical correlations based upon the Andrade equation have been used to correlate the dynamic viscosity of these blends. However, the Nava Rios et al. equation can correlate adequately the kinematic viscosity when the mole fraction is replaced by the volume fraction. The adjustable constants can be expressed as simple polynomials of temperature with a small deteriorating of the fit. This generalized equation correlates the dynamic viscosity within (0.737, 1.367, 0.287, 1.046) % for the corn oil blends with n-heptane, n-octane, n-nonane, and ndecane, respectively.

■

Article

AUTHOR INFORMATION

Corresponding Author

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

Gustavo A. Iglesias-Silva: 0000-0001-7260-2308 Funding

The authors want to thank Consejo Nacional de Ciencia y Tecnologiá (CONACyT) for providing financial support for this work through project CB-2012-177920. Notes

The authors declare no competing financial interest. 2738



Article

(23) Yilmaz, N. Temperature-Dependent Viscosity Correlations of Vegetable Oils and Biofuel−Diesel Mixtures. Biomass Bioenergy 2011, 35, 2936−2938. (24) Grunberg, L.; Nissan, A. H. Mixture Law for Viscosity. Nature 1949, 164, 799−800. (25) Nava-Ríos, G. E.; Iglesias-Silva, G. A.; Estrada-Baltazar, A.; Hall, K. R.; Atilhan, M. A New Equation to Correlate Liquid Kinematic Viscosities of Multicomponent Mixtures. Fluid Phase Equilib. 2012, 329, 8−21.

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K at 0.1 MPa - American Chemical Society

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