Densities and Viscosities of Mixtures of Methyl Dodecanoate + Ethyl

Oct 18, 2018 - Correlations for the data of density and viscosity were proposed with maximum absolute relative deviations less than 0.04 and 5.8%, ...
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Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Densities and Viscosities of Mixtures of Methyl Dodecanoate + Ethyl Octanoate at Pressures up to 15 MPa Xiangyang Liu, Feng Yang, Tianwang Lai, Chenyang Zhu, and Maogang He*

J. Chem. Eng. Data Downloaded from pubs.acs.org by UNIV OF NEW ENGLAND on 10/20/18. For personal use only.

Key Laboratory of Thermal Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China ABSTRACT: Blending methyl ester biodiesel and ethyl ester biodiesel can improve the properties of biodiesel. The densities and viscosities of the mixtures of methyl dodecanoate plus ethyl octanoate with various compositions were reported at temperatures from 303.15 to 323.15 K and at pressures up to 15 MPa. Experimental data show that the densities and viscosities of the mixtures of methyl dodecanoate plus ethyl octanoate will increase when temperature decreases or pressure increases. Ethyl octanoate can effectively reduce the viscosity of methyl dodecanoate with a small change in density. Correlations for the data of density and viscosity were proposed with maximum absolute relative deviations less than 0.04 and 5.8%, respectively.

1. INTRODUCTION With the energy crisis and environmental pollution becoming increasingly serious, more and more attention has been paid to renewable energy,1−3 waste heat utilization,4−6 as well as environmental working fluid.7−10 With the lack of fossil fuels, there is an urgent need to seek substitutes which have similar properties to fossil fuels, allowing them to be used in existing engines. As a clean energy, biodiesel comprising fatty acid alkyl esters is a good choice.11 Viscosity and density are the two most important properties of biodiesel influencing the injection process.12,13 There is plenty of research about the densities and viscosities of biodiesel and fatty acid alkyl esters contained in biodiesel to provide information for design and application of biodiesel. Our group has reported the densities and viscosities of three ethyl esters (carbon numbers in fatty acid chain N are 7, 8, and 12) and one methyl ester (N is 12) from 303 to 353 K and up to 15 MPa.14,15 Dzida et al.16,17 have reported the experimental densites of two methyl esters (N are 14 and 12) and two ethyl esters (N are 8 and 10) at atmospheric pressure and the calculated results at elevated pressures. Habrioux et al.18,19 have reported the viscosities of two methyl esters and two ethyl esters (N are 14 and 10) from 293 to 353 K and up to 100 MPa. Feitosa et al.20 have reported the viscosities and densities of two biodiesel mixtures. Pratas et al.21,22 have reported density data and viscosity data of lots of fatty acid ethyl and methyl esters including saturated esters as well as unsaturated esters. Biodiesel can be obtained by transesterification of vegetable oils with different alcohols. The widely used alcohols are methanol and ethanol, producing methyl ester biodiesel and ethyl ester biodiesel, respectively. Methyl ester biodiesel has the advantages of rich feedstock source and low cost.23−25 Methyl ester also shows better performance in power and torque than ethyl ester. Ethyl ester biodiesel also has lots of © XXXX American Chemical Society

advantages over methyl ester biodiesel, such as lower cloud and pour point, better lubricity, and higher stability.26−28 Therefore, blending methyl ester biodiesel and ethyl ester biodiesel is an effective method to improve the performance of biodiesel in engines.26,29,30 However, there is rare research about the densities and viscosities of methyl ester biodiesel and ethyl ester biodiesel mixtures. Only Baroutian et al.30 reported the densities and viscosities of the mixtures of methyl ester biodiesel plus ethyl ester biodiesel from 293 to 358 K and at atmosphere pressure. In this work, the densities and viscosities of methyl dodecanoate (MDO) plus ethyl octanoate (EOC) mixtures with various compositions were determined. The experimental temperatures are from 303.15 to 323.15 K, and experimental pressures are from 0.1 to 15 MPa. The densities and viscosities of MDO plus EOC mixtures were correlated by functions of temperature, pressure, and mole fraction.

2. EXPERIMENTAL SECTION Materials. The chemical supplier of MDO and EOC is Sigma-Aldrich. Their details are given in Table 1. The densities and viscosities of them measured by our group14,15 (the same samples were used in this work) and other groups31,32 were compared to check their purities. The mixture were prepared using an electronic balance (Sartorius BSA4202S), and the expanded uncertainty of the mole fraction is U(x) = 0.0001 (coverage factor k = 2). Experimental Method. The viscosities of MDO and EOC mixtures were measured using a capillary experimental system, Received: June 22, 2018 Accepted: October 8, 2018

A

DOI: 10.1021/acs.jced.8b00521 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 1. Characteristics of Chemicals Used in This Work

chemical name methyl dodecanoate ethyl octanoate

chemical supplier Sigma-Aldrich Sigma-Aldrich

mass fraction puritya

water content in mass fractionb

0.99 0.99

0.0006 0.0007

purification method none none

ρ/kg·m−3 (298 K, 0.1 MPa)

η/mPa·s (298 K, 0.1 MPa)

expt

expt

5

865 8624

lit 33

864.9 862.1534

15

2.79 1.4114

lit 2.789533 1.41134

a

As stated by the supplier, in mass fraction. bMeasured with a KLS701 Karl Fischer titrator provided by Zibo Kulun Analysis Instrument Co., Ltd.

water thermostat bath and measured by a platinum resistant thermometer (Fluke 5608). The expanded uncertainty of the measured temperature, pressure, and density is 0.02 K, 5 kPa, and 2 kg·m−3 (k = 2), respectively. The experimental system for density and viscosity measurement was calibrated using water in the experimental temperature and pressure range with maximum deviations of 1 kg·m−3 for density and 1% for viscosity.35

as shown in Figure 1. The details about the experimental system were described in our previous work.15 On the basis of

3. RESULTS AND DISCUSSION Density. The measured densities of MDO plus EOC mixtures are reported in Table 2. The temperature and pressure range of the experimental density data are from 303.15 to 323.15 K and from 0.1 to 15 MPa, respectively. Figure 2 is a plot of density against MDO mole fraction for MDO plus EOC mixtures from 0.1 to 15 MPa at 303.15 K. The densities of MDO and EOC were obtained from our earlier works.14,15 It can be found that the densities of the mixtures of MDO plus EOC increase with the increasing mole fraction of MDO; there is a positive correlation between pressure and density, but pressure has no significant effect on the slope of density against mole fraction at fixed temperature. Figure 3 is a plot of density against MDO mole fraction for the mixtures of MDO plus EOC at different temperatures when the pressure is 0.1 MPa. It can be observed that there is a negative correlation between the density and the temperature. Similar to pressure, temperature has no significant effect on the slope of density against mole fraction at fixed pressure. From Table 2, the 0.04−0.08% reduction of the density of the mixture of MDO plus EOC is found to be caused by 0.1 increment in the mole fraction of EOC, indicating that blending with EOC has no significant effect on the density of MDO. A correlation for density was proposed on the basis of the tendency of the densities of pure MDO and EOC14,15 as follows

Figure 1. Schematic diagram of the experimental system for viscosity and denstity measurements.

kinetic theory, if fluid is under laminar flow in a pipe, its viscosity can be given by η=

πρR4Δp 8qL

(1)

where L is the capillary length; R is the capillary inner radius; Δp is the pressure difference of fluid caused by capillary measured by a differential pressure transmitter (Rosemount 3051s); and q and ρ are the mass flow rate and the density of the fluid, respectively. In fact, there are some deviations between eq 1 and the real viscosity. In order to improve the accuracy of eq 1, it can be corrected to η=

nq πρR4Δp (1 + αΔT )3 − 8qL 8πL(1 + αΔT )

(2)

where α and n are the capillary expansion coefficient and the kinetic energy correction coefficient, respectively. n is usually considered to be 1.12;33,34 ΔT is the temperature difference of room and fluid. The system pressure was provided by a plunger-type pump (Scientific Systems 1500). Two pressure transmitters (Rosemount 3051s) were used to measure the pressure with an expanded uncertainty of 5 kPa (k = 2). The capillary is set inside the experimental cell whose temperature was controlled by a water thermostat bath and measured by a platinum resistant thermometer (Fluke 5608), and the expanded uncertainty of temperature measurement is 0.02 K (k = 2). The relative expanded uncertainty of viscosity Ur(η) is 3.0% including the random error. The densities of the mixtures of MDO and EOC were determined with a Siemens flowmeter (MASS 2100 DI 1.5 and MASS 6000) which could determine the density and flow rate simultaneously. The pressure was measured by a pressure transmitter (3051S). The temperature was controlled by a

ρ = D + ET + Fp

(3)

where ρ is density and D, E, and F are adjustable parameters. In order to extend eq 3 to a mixture, a mixing rule of density was used. The mixing rule is expressed as ρmix = x1ρ1 + x 2ρ2

(4)

where x1 and x2 are the mole fractions of compounds 1 and 2 in the mixture and ρ1, ρ2, and ρmix are the densities of compound 1, compound 2, and the mixture, respectively. By combination of eq 3 with eq 4, a correlation for the density of the mixture of MDO and EOC was proposed as follows ρ(x , T , p) = A 0 + B0 x + C0T + D0p + E0xT + F0xp (5)

where A0, B0, C0, D0, E0, and F0 are fitting parameters; x is the mole fraction of MDO; T is the temperature (K); p is the B

DOI: 10.1021/acs.jced.8b00521 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 2. Densities (ρ) and Viscosities (η) of the Mixtures of MDO plus EOC from T = (303.15 to 323.15) K at p = (0.1 to 15) MPaa T/K

p/MPa

ρ/kg·m−3

η/mPa·s

T/K

b

303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15 303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15 303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15

x = 0.9000 0.10 862 2.99 863 6.06 865 8.99 868 12.03 869 14.98 871 0.10 853 3.07 855 6.09 857 9.01 859 12.07 860 15.05 862 0.10 844 3.02 846 6.08 849 8.98 850 12.00 852 14.96 854 x = 0.6001 0.10 860 2.99 862 6.02 864 9.05 866 12.01 867 14.94 869 0.10 852 2.95 853 6.00 855 9.00 857 11.91 859 15.01 861 0.10 843 2.98 845 6.04 847 9.03 849 11.96 850 14.96 852 x = 0.3001 0.10 859 2.96 861 6.08 863 8.98 864 12.00 866 15.07 867 0.10 851 2.99 852 5.96 854 9.03 855 11.98 857 15.02 859 0.10 842 2.94 844 6.02 845 9.07 847 11.99 849 15.02 850

2.32 2.40 2.48 2.56 2.64 2.70 1.95 2.03 2.09 2.15 2.22 2.28 1.61 1.65 1.70 1.75 1.79 1.85

303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15

1.96 2.05 2.12 2.19 2.24 2.30 1.65 1.71 1.76 1.81 1.87 1.92 1.33 1.38 1.42 1.46 1.50 1.55

303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15

1.61 1.66 1.71 1.78 1.83 1.88 1.39 1.43 1.48 1.52 1.57 1.62 1.13 1.18 1.22 1.26 1.29 1.33

303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15

ρ/kg·m−3

p/MPa

x = 0.8001 0.10 861 3.00 863 5.98 865 8.95 867 11.96 869 14.97 870 0.10 852 2.96 854 5.99 856 9.03 858 12.01 860 14.97 862 0.10 844 3.04 846 6.01 848 8.98 850 11.99 852 14.97 853 x = 0.4999 0.10 860 2.94 862 6.00 863 9.09 865 12.02 867 15.04 868 0.10 851 3.04 853 6.10 855 9.05 857 12.02 858 15.04 860 0.10 843 3.01 844 6.03 846 9.07 848 11.97 850 15.04 851 x = 0.1999 0.10 859 2.98 860 6.03 862 8.98 863 12.02 865 15.07 867 0.10 850 2.98 852 6.00 854 8.90 855 12.01 856 15.05 858 0.10 842 2.93 843 6.06 845 9.14 847 12.02 848 14.99 850

η/mPa·s

T/K

2.19 2.28 2.37 2.44 2.50 2.56 1.85 1.93 1.99 2.06 2.11 2.16 1.51 1.57 1.61 1.67 1.72 1.76

303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15

1.82 1.90 1.96 2.02 2.08 2.13 1.55 1.59 1.65 1.70 1.74 1.79 1.26 1.31 1.35 1.39 1.43 1.48

303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15

1.52 1.56 1.60 1.66 1.70 1.75 1.31 1.34 1.38 1.42 1.47 1.51 1.09 1.11 1.15 1.19 1.22 1.26

303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15

p/MPa

ρ/kg·m−3

x = 0.6999 0.10 861 3.08 862 6.04 864 9.04 866 11.96 868 14.97 870 0.10 852 2.97 854 5.99 856 8.96 858 12.09 860 14.98 861 0.10 844 2.96 845 6.03 847 8.93 849 12.06 851 14.98 853 x = 0.4000 0.10 860 2.98 861 6.10 863 8.99 865 12.04 866 15.08 868 0.10 851 3.03 853 6.05 854 9.01 856 11.95 858 15.09 859 0.10 843 3.02 844 6.08 846 9.09 847 11.90 849 15.01 851 x = 0.1000 0.10 859 2.96 860 6.01 861 9.03 863 11.98 864 15.02 866 0.10 850 2.98 851 6.00 853 8.90 855 12.01 856 15.05 858 0.10 841 2.93 843 6.06 844 9.04 846 12.02 847 14.99 849

η/mPa·s 2.08 2.15 2.24 2.31 2.38 2.44 1.75 1.82 1.89 1.93 1.99 2.03 1.42 1.45 1.50 1.56 1.60 1.65 1.71 1.75 1.82 1.88 1.94 2.00 1.46 1.52 1.56 1.59 1.63 1.69 1.19 1.24 1.29 1.32 1.36 1.40 1.41 1.46 1.51 1.55 1.59 1.64 1.22 1.25 1.29 1.33 1.37 1.41 1.03 1.04 1.08 1.11 1.14 1.18

Expanded uncertainties U are U(T) = 0.02 K, U(p) = 5 kPa, U(ρ) = 2 kg·m−3, U(x) = 0.0001; relative expanded uncertainty Ur is Ur(η) = 0.03. The level of confidence is 0.95 (k = 2). bx is the mole fraction of MDO. a

C

DOI: 10.1021/acs.jced.8b00521 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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jij n ρ cal − ρ exp AARD = jjj∑ i exp i jj ρi k i=1 MARD = Max

Article

zyz zz/n zz z {

(7)

ρical − ρiexp ρiexp

(8)

Figure 4 shows RDs of eq 5 from the experimental densities of the mixtures of MDO and EOC at different pressures and

Figure 2. Densities of the mixtures of MDO plus EOC at 303.15 K: ◇, 0.1 MPa; □, 3 MPa; ●, 6 MPa; ▲, 9 MPa; ◆, 12 MPa; ■, 15 MPa. The lines are the calculated results of eq 5.

Figure 4. Deviations of eq 5 from the densities of the mixtures of MDO plus EOC: ◇, 0.1 MPa; □, 3 MPa; ●, 6 MPa; ▲, 9 MPa; ◆, 12 MPa; ■, 15 MPa.

temperatures. MARD and AARD of eq 5 from experimental densities, which are lower than 0.040% and 0.013%, respectively. The density data of the mixtures are also correlated by the Tait equation36 ρ(T , p) = (a + bT )/[1 − A ln((p + B(T ))/(p0 + B(T )))] (9)

Figure 3. Densities of the mixtures of MDO plus EOC at 0.1 MPa: ■, 303.15 K; ◆, 313.15 K; ▲, 323.15 K. The lines are the calculated results of eq 5.

B(T ) = c1 + c 2(T /100)

where a, b, A, c1, and c2 are adjustable coefficients and p0 = 0.1 MPa. The coefficients at each composition are listed in Table 4. MARD and AARD of the Tait equation from all experimental densities are 0.037 and 0.011%, respectively. The results show that eq 5 has the same level of accuracy as the Tait equation. Viscosity. The viscosities of MDO plus EOC mixtures are reported in Table 2. The viscosities of MDO plus EOC mixtures at pressures of 0.1, 3, 6, 9, 12, and 15 MPa and at a temperature of 303.15 K were also plotted against MDO mole

pressure (MPa); and ρ is the density (kg·m−3) of mixture. The parameters were determined using density data in this work and provided in Table 3. To evaluate the accuracy of eq 5, three deviations were defined as follows RD =

ρical − ρiexp ρiexp

(10)

(6)

Table 3. Coefficients and Deviations of eq 5 and eq 11 parameter

value

unit

parameter

value

unit

A0 B0 C0 D0 E0 F0 AARD MARD

1119 −1.277 −0.8601 0.4856 0.01618 0.1798 0.013% 0.040%

kg·m−3 kg·m−3 kg·m−3·K−1 kg·m−3·MPa−1 kg·m−3·K−1 kg·m−3·MPa−1

A1 B1 C1 D1 E1 F1 AARD MARD

6.950 8.610 −0.01869 0.01165 −0.02445 0.01168 1.40% 5.81%

mPa·s mPa·s mPa·s·K−1 mPa·s·MPa−1 mPa·s·K−1 mPa·s·MPa−1

D

DOI: 10.1021/acs.jced.8b00521 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 4. Coefficients and Deviations of the Tait Equation xa

0.9000

0.8001

0.6999

0.6001

0.4999

0.4000

0.3001

0.1999

0.1000

a b A c1 c2 AARD (%) MARD (%)

1119 −0.848 0.1048 207.4 −23.44 0.018 0.037

1117 −0.845 0.0639 102.5 −7.20 0.011 0.023

1116 −0.842 0.1126 98.37 16.05 0.013 0.026

1117 −0.846 0.1446 234.8 −10.95 0.011 0.023

1120 −0.857 0.0477 96.96 −10.46 0.011 0.025

1118 −0.851 0.7501 1296.6 −42.26 0.007 0.018

1117 −0.852 0.1879 308.0 −5.373 0.008 0.020

1116 −0.849 −0.1815 −288.8 −5.650 0.010 0.028

1119 −0.859 0.5655 1195 −77.02 0.013 0.034

a

x is the mole fraction of MDO.

fraction in Figure 5. The viscosities of the mixture of MDO and EOC are observed to increase when the MDO mole

Figure 6. Viscosities of the mixtures of MDO plus EOC at 0.1 MPa: ▲, 303.15 K; ◆, 313.15 K; ■, 323.15 K. The lines are a guide for the eye.

Figure 5. Viscosities of the mixtures of MDO plus EOC at 303.15 K: ◇, 0.1 MPa; □, 3 MPa; ●, 6 MPa; ▲, 9 MPa; ◆, 12 MPa; ■, 15 MPa. The lines are a guide for the eye.

fraction increases, and the increase rate increases when the pressure increases. The pressure shows a positive correlation with the viscosity of MDO plus EOC mixture. It also can be found that the increase rate of the viscosities of the MDO plus EOC mixtures shows an apparent decease when the mole fractions of MDO are 0.8 and 0.9, especially at 15 MPa, which may be caused by the different strengths of intermolecular interaction at different mole compositions. Figure 6 shows the viscosities of the mixtures of MDO plus EOC at different mole fractions of MDO from 303.15 to 323.15 K when the pressure is 0.1 MPa. The viscosity of MDO plus EOC mixture at fixed pressure decreases with increasing temperature, while its increase rate has the same trend. From Table 4, 4−11% reduction of the viscosity of MDO plus EOC mixture is found to be caused by 0.1 increment in the mole fraction of EOC, indicating that blending with EOC can effectively reduce the viscosity of MDO. There are many correlations for viscosity in the literature,37,38 but most of them are not easy to conduct. Inspired by eq 5, a simple correlation was proposed as follows

Figure 7. Deviations of eq 11 from the viscosities of the mixture of MDO plus EOC: ◇, 0.1 MPa; □, 3 MPa; ●, 6 MPa; ▲, 9 MPa; ◆, 12 MPa; ■, 15 MPa.

present correlation at different pressures and temperatures. The AARD and MARD were calculated to be 1.4 and 5.8%, respectively, which indicates a good accuracy of the present correlation. Derived Volumetric Properties. From density data, two important derived volumetric properties which are isothermal compressibility and isobaric thermal expansivity can be calculated. Isothermal compressibility kT (Pa−1) is expressed as

η(x , T , p) = A1 + B1 x + C1T + D1p + E1xT + Fxp 1 (11)

1 ji ∂v zy k T = − jjj zzz v jk ∂p z{ T

where A1, B1, C1, D1, E1, and F1 are fitting parameters; x is the mole fraction of MDO; T is the temperature (K); p is the pressure (MPa); and η is the viscosity (mPa·s) of a mixture. The parameters were determined using viscosity data in this work and provided in Table 3. Figure 7 shows RDs of the

(12) −1

Isobaric thermal expansivity αv (K ) is expressed as E

DOI: 10.1021/acs.jced.8b00521 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 5. Isobaric Thermal Expansivity (αv) and Isothermal Compressibility (kT) of the Mixtures of MDO plus EOC from T = (303.15 to 323.15) K at p = (0.1 to 15) MPa 10−3αv/K−1 T/K

p/MPa

eq 5

10−3kT/MPa−1

Tait

RD/%

eq 5

Tait

RD/%

a

x = 0.9000 303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15 x = 0.8001 303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15 x = 0.6999 303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15

0.10 2.99 6.06 8.99 12.03 14.98 0.10 3.07 6.09 9.01 12.07 15.05 0.10 3.02 6.08 8.98 12.00 14.96

0.980 0.979 0.976 0.974 0.972 0.970 0.990 0.988 0.985 0.984 0.982 0.979 1.000 0.998 0.995 0.993 0.991 0.989

0.984 0.980 0.975 0.969 0.965 0.961 0.994 0.989 0.984 0.979 0.975 0.970 1.004 0.999 0.993 0.988 0.983 0.979

0.41 0.12 −0.16 −0.43 −0.69 −0.94 0.41 0.11 −0.18 −0.46 −0.72 −0.98 0.41 0.11 −0.19 −0.48 −0.75 −1.01

0.750 0.749 0.747 0.745 0.744 0.742 0.758 0.757 0.754 0.753 0.751 0.750 0.766 0.764 0.762 0.760 0.759 0.757

0.737 0.736 0.734 0.733 0.731 0.729 0.750 0.748 0.746 0.745 0.743 0.741 0.763 0.761 0.759 0.757 0.756 0.754

−1.73 −1.77 −1.78 −1.71 −1.72 −1.76 −1.06 −1.11 −1.06 −1.10 −1.11 −1.09 −0.40 −0.41 −0.39 −0.39 −0.38 −0.40

0.10 3.00 5.98 8.95 11.96 14.97 0.10 2.96 5.99 9.03 12.01 14.97 0.10 3.04 6.01 8.98 11.99 14.97

0.983 0.981 0.979 0.977 0.974 0.973 0.993 0.991 0.988 0.986 0.984 0.982 1.003 1.000 0.998 0.996 0.994 0.992

0.982 0.979 0.975 0.972 0.969 0.967 0.992 0.988 0.985 0.982 0.979 0.976 1.001 0.998 0.995 0.992 0.989 0.986

−0.14 −0.24 −0.34 −0.42 −0.50 −0.58 −0.14 −0.24 −0.34 −0.43 −0.51 −0.58 −0.14 −0.24 −0.34 −0.43 −0.51 −0.58

0.731 0.729 0.727 0.726 0.724 0.723 0.738 0.736 0.734 0.733 0.731 0.730 0.745 0.743 0.742 0.740 0.739 0.737

0.733 0.732 0.730 0.728 0.727 0.725 0.739 0.738 0.736 0.734 0.733 0.731 0.746 0.744 0.742 0.741 0.739 0.737

0.37 0.34 0.36 0.36 0.37 0.36 0.20 0.18 0.21 0.21 0.19 0.20 0.04 0.06 0.02 0.07 0.03 0.05

0.10 3.08 6.04 9.04 11.96 14.97 0.10 2.97 5.99 8.96 12.09 14.98 0.10 2.96 6.03 8.93 12.06 14.98

0.986 0.984 0.982 0.979 0.977 0.975 0.995 0.993 0.991 0.989 0.987 0.985 1.005 1.004 1.001 0.999 0.997 0.995

0.978 0.980 0.981 0.982 0.983 0.984 0.988 0.989 0.990 0.992 0.992 0.993 0.998 0.999 1.000 1.001 1.002 1.003

−0.74 −0.40 −0.07 0.26 0.58 0.89 −0.74 −0.41 −0.08 0.24 0.55 0.85 −0.74 −0.42 −0.10 0.21 0.52 0.81

0.711 0.709 0.708 0.706 0.705 0.703 0.718 0.716 0.714 0.713 0.712 0.710 0.725 0.723 0.722 0.720 0.719 0.717

0.719 0.717 0.715 0.714 0.712 0.711 0.711 0.727 0.726 0.724 0.723 0.721 0.735 0.733 0.732 0.730 0.729 0.727

1.13 1.10 1.11 1.14 1.09 1.10 −0.91 1.59 1.61 1.56 1.58 1.58 1.38 1.38 1.38 1.38 1.39 1.39

F

DOI: 10.1021/acs.jced.8b00521 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 5. continued 10−3αv/K−1 T/K x = 0.6000 303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15 x = 0.4999 303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15 x = 0.4000 303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15

10−3kT/MPa−1

p/MPa

eq 5

Tait

RD/%

eq 5

Tait

RD/%

0.10 2.99 6.02 9.05 12.01 14.94 0.10 2.95 6.00 9.00 11.91 15.01 0.10 2.98 6.04 9.03 11.96 14.96

0.988 0.986 0.984 0.982 0.980 0.978 0.998 0.996 0.994 0.992 0.990 0.988 1.008 1.006 1.004 1.002 1.000 0.998

0.984 0.982 0.979 0.977 0.975 0.973 0.994 0.992 0.989 0.987 0.985 0.982 1.004 1.001 0.999 0.997 0.995 0.992

−0.43 −0.46 −0.48 −0.50 −0.52 −0.54 −0.43 −0.46 −0.48 −0.50 −0.52 −0.54 −0.43 −0.46 −0.48 −0.50 −0.52 −0.53

0.690 0.689 0.688 0.686 0.685 0.684 0.697 0.696 0.695 0.693 0.692 0.690 0.705 0.703 0.701 0.700 0.699 0.697

0.699 0.698 0.696 0.695 0.693 0.692 0.703 0.701 0.700 0.699 0.697 0.696 0.707 0.705 0.704 0.702 0.701 0.699

1.26 1.22 1.26 1.25 1.25 1.23 0.80 0.77 0.77 0.80 0.79 0.79 0.30 0.33 0.32 0.31 0.30 0.32

0.10 2.94 6.00 9.09 12.02 15.04 0.10 3.04 6.10 9.05 12.02 15.04 0.10 3.01 6.03 9.07 11.97 15.04

0.991 0.989 0.987 0.985 0.983 0.981 1.001 0.999 0.996 0.995 0.993 0.991 1.011 1.009 1.007 1.004 1.002 1.001

0.997 0.992 0.988 0.984 0.980 0.977 1.007 1.002 0.998 0.994 0.990 0.986 1.017 1.012 1.008 1.003 1.000 0.996

0.59 0.35 0.13 −0.07 −0.25 −0.42 0.59 0.35 0.12 −0.09 −0.27 −0.44 0.59 0.34 0.11 −0.10 −0.29 −0.47

0.670 0.669 0.668 0.666 0.665 0.664 0.677 0.676 0.674 0.673 0.672 0.670 0.684 0.683 0.681 0.680 0.678 0.677

0.664 0.662 0.661 0.660 0.658 0.657 0.673 0.672 0.671 0.669 0.668 0.667 0.684 0.682 0.681 0.679 0.678 0.677

−1.01 −1.04 −1.03 −1.01 −1.01 −1.03 −0.55 −0.55 −0.54 −0.55 −0.57 −0.54 −0.07 −0.10 −0.08 −0.06 −0.06 −0.09

0.10 2.98 6.10 8.99 12.04 15.08 0.10 3.03 6.05 9.01 11.95 15.09 0.10 3.02 6.08 9.09 11.90 15.01

0.993 0.991 0.989 0.988 0.986 0.984 1.003 1.001 0.999 0.997 0.995 0.994 1.013 1.011 1.009 1.008 1.006 1.004

0.990 0.989 0.987 0.985 0.983 0.982 1.000 0.999 0.997 0.995 0.993 0.991 1.010 1.009 1.007 1.005 1.003 1.001

−0.29 −0.28 −0.27 −0.25 −0.24 −0.23 −0.29 −0.28 −0.26 −0.25 −0.24 −0.22 −0.29 −0.28 −0.26 −0.25 −0.24 −0.22

0.650 0.649 0.648 0.647 0.645 0.644 0.657 0.656 0.654 0.653 0.652 0.650 0.663 0.662 0.661 0.660 0.658 0.657

0.644 0.643 0.642 0.640 0.639 0.638 0.646 0.645 0.644 0.643 0.641 0.640 0.649 0.647 0.646 0.645 0.644 0.642

−0.99 −0.98 −0.97 −0.97 −0.98 −0.98 −1.58 −1.60 −1.60 −1.60 −1.60 −1.59 −2.24 −2.22 −2.22 −2.24 −2.23 −2.22

G

DOI: 10.1021/acs.jced.8b00521 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 5. continued 10−3αv/K−1 T/K x = 0.3001 303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15 x = 0.1999 303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15 x = 0.1000 303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15

10−3kT/MPa−1

p/MPa

eq 5

Tait

RD/%

eq 5

Tait

RD/%

0.10 2.96 6.08 8.98 12.00 15.07 0.10 2.99 5.96 9.03 11.98 15.02 0.10 2.94 6.02 9.07 11.99 15.02

0.996 0.994 0.992 0.990 0.988 0.987 1.006 1.004 1.002 1.000 0.998 0.996 1.016 1.014 1.012 1.010 1.008 1.007

0.992 0.990 0.989 0.987 0.986 0.985 1.002 1.000 0.999 0.997 0.996 0.995 1.012 1.010 1.009 1.007 1.006 1.005

−0.44 −0.39 −0.34 −0.30 −0.250 −0.20 −0.44 −0.39 −0.34 −0.30 −0.25 −0.20 −0.44 −0.39 −0.34 −0.29 −0.25 −0.20

0.630 0.629 0.628 0.627 0.626 0.624 0.637 0.635 0.634 0.633 0.632 0.631 0.643 0.642 0.641 0.639 0.638 0.637

0.634 0.633 0.632 0.630 0.629 0.628 0.635 0.634 0.633 0.632 0.630 0.629 0.636 0.635 0.634 0.633 0.632 0.630

0.59 0.61 0.60 0.59 0.60 0.59 −0.23 −0.23 −0.22 −0.24 −0.22 −0.22 −1.03 −1.03 −1.06 −1.03 −1.04 −1.04

0.10 2.98 6.03 8.98 12.02 15.07 0.10 2.98 6.00 8.90 12.01 15.05 0.10 2.93 6.06 9.14 12.02 14.99

0.999 0.997 0.995 0.993 0.991 0.989 1.008 1.007 1.005 1.003 1.001 0.999 1.019 1.017 1.015 1.013 1.012 1.009

0.989 0.988 0.987 0.987 0.986 0.985 0.998 0.998 0.997 0.996 0.996 0.995 1.009 1.008 1.007 1.006 1.006 1.005

−0.98 −0.88 −0.77 −0.66 −0.54 −0.42 −0.99 −0.88 −0.77 −0.66 −0.54 −0.43 −0.99 −0.88 −0.77 −0.66 −0.55 −0.43

0.610 0.609 0.608 0.607 0.606 0.605 0.616 0.615 0.614 0.613 0.612 0.611 0.622 0.621 0.620 0.619 0.618 0.617

0.614 0.613 0.612 0.611 0.610 0.608 0.613 0.612 0.611 0.610 0.608 0.607 0.612 0.611 0.610 0.608 0.607 0.606

0.63 0.62 0.62 0.63 0.63 0.64 −0.55 −0.54 −0.53 −0.55 −0.56 −0.56 −1.74 −1.75 −1.75 −1.72 −1.75 −1.73

0.10 2.96 6.01 9.03 11.98 15.02 0.10 2.98 6.00 8.90 12.01 15.05 0.10 2.93 6.06 9.04 12.02 14.99

1.001 1.000 0.998 0.996 0.994 0.992 1.011 1.009 1.008 1.006 1.004 1.002 1.022 1.020 1.018 1.016 1.014 1.013

1.001 0.999 0.996 0.994 0.991 0.989 1.011 1.009 1.006 1.003 1.001 0.999 1.021 1.019 1.016 1.014 1.011 1.009

−0.03 −0.10 −0.16 −0.22 −0.29 −0.35 −0.03 −0.10 −0.16 −0.22 −0.29 −0.35 −0.03 −0.10 −0.16 −0.22 −0.29 −0.35

0.590 0.589 0.588 0.587 0.586 0.585 0.596 0.595 0.594 0.593 0.592 0.591 0.602 0.601 0.600 0.599 0.598 0.597

0.589 0.588 0.587 0.586 0.585 0.584 0.594 0.593 0.592 0.591 0.589 0.588 0.598 0.597 0.596 0.595 0.594 0.593

−0.17 −0.20 −0.21 −0.19 −0.20 −0.19 −0.38 −0.39 −0.37 −0.35 −0.36 −0.38 −0.59 −0.60 −0.61 −0.59 −0.59 −0.61

a

x is the mole fraction of MDO.

H

DOI: 10.1021/acs.jced.8b00521 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data αv =

1 ji ∂v zy jj zz v k ∂T { p

Article

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(13)

The isothermal compressibility and isobaric thermal expansivity of the mixtures of MDO and EOC calculated by eq 5 and the Tait equation were reported in Table 5. The AARD and MARD of eq 5 from the Tait equation for isothermal compressibility are 0.40 and 0.84%, respectively, and those for isobaric thermal expansivity are 1.01 and 2.24%, respectively. The isothermal compressibility and isobaric thermal expansivity of the mixtures of MDO and EOC are observed to increase when the temperature increases and the pressure decreases. The isothermal compressibility of the mixture of MDO and EOC has a small change with the increase of MDO mole fraction, while the isobaric thermal expansivity of the mixture of MDO and EOC has a significant increase as the MDO mole fraction decreases.

4. CONCLUSION New data of the densities and viscosities of the mixtures of MDO plus EOC at temperatures from 303.15 to 323.15 K and pressures up to 15 MPa were reported in this work. The experimental data show that the densities and viscosities of the mixtures of MDO plus EOC increase with the increasing pressure and decrease with the increasing temperature. The viscosity of MDO can be significantly reduced by adding EOC, while the density of MDO has a small change, indicating that it is a useful way to decrease the viscosity of methyl ester biodiesel by mixing methyl ester biodiesel with ethyl ester biodiesel. Correlations were proposed for the densities and viscosities of the mixtures of MDO plus EOC. Comparison results show that they agree well with experimental data. In addition, the isothermal compressibility and isobaric thermal expansivity of the mixtures of MDO plus EOC were calculated from the correlation for density.

■

AUTHOR INFORMATION

Corresponding Author

*Phone: +86-29-8266-3863. Fax: +86-29-8266-3863. E-mail: [email protected]. ORCID

Maogang He: 0000-0002-2364-2140 Funding

The support provided by National Natural Science Foundation of China (No. 51506172), the National Basic Research Program of China (No. 2015CB251502), the Science and Technology Research Project of Shaanxi Province, China (No. 2016GY-145), and Youth talent lifting project of Shaanxi Association for Science and Technology (No. 20180401) for the completion of the present work is acknowledged. Notes

The authors declare no competing financial interest.

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DOI: 10.1021/acs.jced.8b00521 J. Chem. Eng. Data XXXX, XXX, XXX−XXX