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Liquid densities and excess molar volumes of ethanol + biodiesel binary system between the temperatures 273.15 K and 333.15 K
Journal of Molecular Liquids 204 (2015) 95–99
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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Liquid densities and excess molar volumes of ethanol + biodiesel binary system between the temperatures 273.15 K and 333.15 K István Barabás Department of Automotive Engineering and Transportation, Technical University of Cluj-Napoca, Romania, 103–105 Muncii Blvd., 400641 Cluj-Napoca, Romania
a r t i c l e
i n f o
Article history: Received 23 September 2014 Received in revised form 19 January 2015 Accepted 28 January 2015 Available online 29 January 2015 Keywords: Rapeseed oil biodiesel + ethanol mixtures Density Excess molar volume Thermal expansion coefficient Excess thermal expansion coefficient
a b s t r a c t The densities of ten binary mixtures of biodiesel made from rapeseed oil and ethanol have been measured for eight temperatures within the range between 273.15 K and 333.15 K, using an Anton Paar DMA 4500 M densimeter. The excess molar volume has been calculated from experimental densities. Variation of mixtures volumes was low, but measurable. It was observed that the excess molar volume was positive for all studied mixtures, due to increased physical interactions between fatty acid methyl esters and ethanol. Density variation was modeled by polynomial regression and the thermal expansion coefficient, as well as its excess value, were estimated. The excess molar volume and excess thermal expansion coefficient results were fitted to the Redlich–Kister type polynomial equation to obtain the regression coefficients and estimate the standard deviations and correlation coefficients between experimental and calculated results. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Population and number of vehicles growth, as well as the acute need for transportation, associated with scarcity of oil resources bring into focus the need to find viable alternatives for partial or total substitution of fossil fuels for automobiles. Alternative sources of energy for transportation are liquid fuels made from biomass, such as biodiesel and bioethanol, considered as strong candidates for substituting fossil fuels. Compared to fossil fuels, biofuels have a number of undeniable advantages: they reduce a country's fossil fuel dependency, they are renewable and environmentally friendly, are carbon neutral, their production supports emerging markets and expand labor markets in agriculture [1,2]. Biodiesel can be produced from various raw materials, such as vegetable oils, animal fat, and some algae species, [3] while bioethanol is made from sugar, starch or cellulose [4]. Biodiesel can substitute diesel fuel, while bioethanol is used as a substitute for petrol. Biodiesel has a high cetane number, wherefrom reduced solid particle and hydrocarbons emissions, but its volatility, calorific value and flow properties at low temperatures are inferior to those of diesel [5,6]. This means that the use of biodiesel at low temperatures can be problematic. However, ethanol has a low cetane number, is very volatile and has excellent flow properties at low temperature [5]. An efficient method of solving some drawbacks of biodiesel is blending it with substances which can compensate for their deficient
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http://dx.doi.org/10.1016/j.molliq.2015.01.048 0167-7322/© 2015 Elsevier B.V. All rights reserved.
properties. Using ethanol as an extender for biodiesel is one method which has received close attention in research lately, because the presence of ethanol in biodiesel compensates for some of its drawbacks: it reduces density and viscosity, [7] it improves volatility [8,9] and its flow properties at low temperatures [10]. Density is a very important fuel property because it influences production, transportation, and distribution processes as well as all processes that take place in the internal combustion engine. Knowing the density of fuels is necessary for: designing production and manufacturing facilities for fuels — reactors, tanks, and distillation units; finding the mass and volume flows through such facilities; establishing the appropriate size of transfer pumps, transfer and safety valves, etc. [11]. Density, together with vapor pressure, vapor diffusivity, surface tension, and liquid dynamic viscosity, influences fuel spray structure, combustion and emission characteristics, engine deposit formation, and engine behavior in cold weather conditions [12–15]. Developing reliable models for injection and combustion processes implies the accurate description of the thermo-physical characteristics of fuels, including their density [16]. The injection system of compression ignition engine (CIE) introduces discrete volumes of fuel in the combustion chamber, calculated by the electronic control unit, based, among others, on the functioning conditions of the engine [17] and the temperature of the fuel [18]. For this reason, knowing the precise density of fuel allows for accurate dosage and for a correct energy consumption, because density influences the mass of the injected fuel [19] and the heating value of the fuel is often given as energy content per unit mass [17]. Density influences the air/fuel mass ratio, [20] i.e. the quality of the air–fuel mixture.
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I. Barabás / Journal of Molecular Liquids 204 (2015) 95–99
Since 2002, in order to reduce pollution, the electronic control units of CIE can include a closed loop control for the quality of air–fuel mixtures, using pressure, temperature, wideband oxygen sensors, etc. In the case of these engines, knowing the exact density of the fuel becomes less important, since the quantity of fuel is calculated — together with the usual parameters — by taking into account the oxygen content of exhaust gases [21]. Excess molar volume of mixtures of pure esters and alcohols is the focus of many studies, but, to the best of our knowledge, molar excess values of biodiesel–ethanol mixtures have not been studied yet. The goals of our study are density estimation, excess molar volume estimation, thermal expansion coefficient of mixtures of biodiesel made from rapeseed oil and ethanol, as well as providing data for manufacturing processes, distribution, use, modeling and simulation in which these mixtures are involved.
2. Experimental Ethanol was provided by S.C. Nordic S.A. Biodiesel was produced from rapeseed oil by the Research Institute for Analytical Instrumentation from Cluj-Napoca. Ethanol purity is 99.3% w/w. Esters' content of biodiesel is 97.7% w/w, while water content is 183 mg·kg−1. From the two constituents, ten binary mixtures were prepared by weight dosing, using a Mettler AE 163 type analytical balance with a precision of ± 1 × 10−5 g, consequently the uncertainty in the mole fractions is ±5 × 10−5. Sample composition was chosen so that it covered the range of molar concentration between 0 and 1 with steps of about 0.1. After mixing, the samples were kept for ten days in dark glass bottles, filled to 95% of the volume and tightly closed. As expected, no components separation was observed during this period. The fatty acid methyl ester (FAME) composition profile of biodiesels used in this work was determined by gas chromatography with an HP 6890 series gas chromatography system equipped with a flame ionization detector and automated split injector. Before measuring densities, the samples have been thoroughly mixed and degassed by using an Elmasonic S 50 R type ultrasonic unit. Densities of the pure liquids and mixtures were measured at atmospheric pressure and at (273.15, 283.15, 288.15, 293.15, 303.15, 313.15, 323.15 and 333.15) K by using an Anton Paar DMA 4500 M equipped with vibrating U-tube and provided with automatic viscosity correction. The maximum value of temperature was limited by the relatively low boiling point of bioethanol. The precision of measured densities was 1 × 10− 5 g·cm− 3 and uncertainty of the measurements was estimated to be ±5 × 10−5 g·cm−3. The temperature in the measuring cell was regulated with Peltier elements and was measured via two integrated Pt 100 platinum resistance thermometers with a precision of ±0.01 K. Before each series of measurements, the densimeter was calibrated at atmospheric pressure using double distilled and degassed water and dried air. The density data for water and dried air were taken from DMA 4500 M Instruction Manual. The cell for density measurement was washed with solvent at a temperature of 333.15 K and air dried at a temperature of 363.15 K before each fuel sample. In order to wet the inner walls of the U-tube, before measurements, 20 cm3 of the samples was passed through the density cell. The measurement cell was refilled with a fuel sample before every measurement was taken. In order to ensure maximum accuracy, each measurement was done three times and average of the three values was calculated.
3. Results and discussion Excess molar volume VE of binary biodiesel–ethanol mixtures was calculated for the entire range of concentrations and temperatures
Table 1 Fatty acid methyl ester concentration profiles of RME analyzed by gas chromatography. Fatty acid methyl ester
CAS number
% w/w
Methyl decanoate (C10:0) Methyl dodecanoate (C12:0) Methyl tetradecanoate (C14:0) Methyl hexadecanoate (C16:0) Methyl octadecanoate (C18:0) Methyl eicosanoate (C20:0) Methyl docosanoate (C22:0) Methyl hexadec-9-enoate (C16:1) Methyl (Z)-octadec-9-enoate (C18:1) Methyl cis-11-eicosenoate (C20:1) Methyl (Z)-13-docosenoate (C22:1) Methyl (Z,Z)-octadeca-9,12-dienoate (C18:2) Methyl (Z,Z,Z)-octadeca-9,12,15-trienoate (C18:3)
110-42-9 111-82-0 124-10-7 112-39-0 112-61-8 1120-28-1 929-77-1 1120-25-8 112-62-9 2390-09-2 1120-34-9 112-63-0 301-00-8
0.02 0.03 0.82 3.81 1.75 0.56 1.13 0.12 58.41 0.68 0.21 21.25 11.21
studied with the formula: E
V ¼
2 X
−1 −1 ; xi Mi ρ −ρi
ð1Þ
i¼1
where xi is the mole fraction of the component i (i = 1 for ethanol, i = 2 for biodiesel), Mi is the molecular weights, expressed in g·mol−1, and ρ and ρi represent mixture density and component density, respectively, in g·cm−3. The molar quantities used for calculations in this paper are based on data published by IUPAC [22]. Table 1 reports the methyl ester compositions of the biodiesel (RME) used in this study. Molecular weight of biodiesel, M2, was calculated with the formula [23]. M2 ¼
X
x jM j;
ð2Þ
j
where xj is the mole fraction component j, and Mj is the molecular weight of component j. The molecular weight of RME used in this paper is calculated with Eq. (2) is 295.26 g·mol−1. The thermal expansion coefficient for atmospheric pressure is given by the formula [24]:
α¼V
−1
ð∂V=∂T Þp ;
ð3Þ
where V is the volume and (∂V/∂T)p is the temperature variation ratio for atmospheric pressure. Taking into account the relation of volume
Table 2 Coefficients and precision of polynomial regression. x1
c0/g·cm−3
104 c1/g·cm−3·T−1
107 c2/g·cm−3·T−2
R
102 SD
0 0.12025 0.18657 0.27735 0.41781 0.50609 0.60683 0.71334 0.80786 0.90452 0.95107 1
1.31537 0.31892 −0.13282 −0.97034 −1.40845 −1.87967 −2.53586 −3.41613 −4.51692 −5.88794 −7.35090 −8.61472
−8.07445 −7.56664 −7.36064 −6.94577 −6.78120 −6.59032 −6.30430 −5.91772 −5.43407 −4.83032 −4.11437 −3.52179
1.10648 1.09825 1.09423 1.08658 1.08100 1.07694 1.06957 1.05816 1.04371 1.02132 1.00071 0.97548
1.00000 0.99995 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
0.22327 1.04200 0.24597 0.52723 0.45762 0.45660 0.59862 9.85563 1.25498 2.11268 1.56606 2.39012
I. Barabás / Journal of Molecular Liquids 204 (2015) 95–99
and density, thermal expansion coefficient can also be expressed by the formula: [24] −1
α ¼ −ρ
ð∂ρ=∂T Þp :
ð4Þ
In the range between 273.15 K and 333.15 K, density variation by temperature is described by a quadratic function [24].
97
2
ρ ¼ c0 þ c1 T þ c2 T ;
ð5Þ
where ρ/g·cm−3 is the density, T/K is the temperature, c0, c1 and c2 are parameters of polynomial regressions. Constants of Eq. (5) were determined based on experimental data by polynomial regression, using the least-square method are given in Table 2.
Table 3 Values of ρ, α, VE and αE for mixture of x1(ethanol) + (1 − x1)RME at temperatures from 273.15 K to 333.15 K and atmospheric pressure. ρa/g·cm−3
103 α/K−1
VE/cm3·mol−1
105 αE/K−1
x1
ρ/g·cm−3
103 α/K−1
VE/cm3·mol−1
105 αE/K−1
273.15 K 0 0.12025 0.18657 0.27735 0.41781 0.50609
0.89574 0.89395 0.89218 0.88961 0.88626 0.88290
0.82121 0.82694 0.83315 0.84035 0.85197 0.86275
0 0.07096 0.09826 0.12027 0.13248 0.12583
0 0.54573 0.77057 1.16260 1.43619 1.52246
0.60683 0.71334 0.80786 0.90452 0.95107 1
0.87845 0.87103 0.86158 0.84545 0.83348 0.81501
0.87536 0.89365 0.91711 0.95179 0.97545 1.00956
0.10675 0.08579 0.05811 0.03540 0.01453 0
1.49402 1.59513 1.57296 1.20138 0.91701 0
283.15 K 0 0.12025 0.18657 0.27735 0.41781 0.50609
0.88840 0.88656 0.88474 0.88213 0.87870 0.87526
0.82503 0.83311 0.84046 0.84968 0.86250 0.87457
0 0.08210 0.11706 0.13930 0.15840 0.15669
0 0.675261 0.965838 1.32143 1.77708 1.88382
0.60683 0.71334 0.80786 0.90452 0.95107 1
0.87074 0.86322 0.85363 0.83734 0.82527 0.80669
0.88894 0.90965 0.93624 0.97507 1.00297 1.04133
0.13556 0.11000 0.08027 0.04891 0.02266 0
1.87762 1.97374 1.94630 1.52366 1.12466 0
288.15 K 0 0.12025 0.18657 0.27735 0.41781 0.50609
0.88474 0.88287 0.88102 0.87838 0.87490 0.87143
0.82696 0.83623 0.84416 0.85441 0.86786 0.88057
0 0.08978 0.12878 0.15303 0.17684 0.17413
0 0.74128 1.06027 1.53845 1.95083 2.06801
0.60683 0.71334 0.80786 0.90452 0.95107 1
0.86686 0.85928 0.84962 0.83325 0.82112 0.80247
0.89584 0.91780 0.94597 0.98692 1.01699 1.05754
0.15378 0.12569 0.09313 0.05549 0.02648 0
2.13805 2.11172 2.10660 1.79263 1.24560 0
293.15 K 0 0.12025 0.18657 0.27735 0.41781 0.50609
0.88108 0.87918 0.87731 0.87462 0.87111 0.86759
0.82890 0.83938 0.84788 0.85919 0.87325 0.88664
0 0.09664 0.13686 0.16885 0.19172 0.19244
0 0.80750 1.15498 1.67588 2.12509 2.25274
0.60683 0.71334 0.80786 0.90452 0.95107 1
0.86297 0.85533 0.84559 0.82912 0.81692 0.79821
0.90282 0.92603 0.95582 0.99894 1.03121 1.07398
0.17230 0.14097 0.10627 0.06340 0.03175 0
2.32904 2.45027 2.26746 1.92205 1.35687 0
303.15 K 0 0.12025 0.18657 0.27735 0.41781 0.50609
0.87379 0.87180 0.86987 0.86710 0.86348 0.85988
0.83280 0.84575 0.85543 0.86888 0.88423 0.89896
0 0.11818 0.16729 0.20626 0.23753 0.23743
0 0.94228 1.34776 1.95559 2.47978 2.61173
0.60683 0.71334 0.80786 0.90452 0.95107 1
0.85515 0.84737 0.83747 0.82078 0.80843 0.78955
0.91701 0.94279 0.97588 1.02344 1.06023 1.10758
0.21685 0.17842 0.13565 0.08028 0.04199 0
2.75776 2.79421 2.71592 2.12615 1.58334 0
313.15 K 0 0.12025 0.18657 0.27735 0.41781 0.50609
0.86653 0.86443 0.86242 0.85955 0.85583 0.85213
0.83674 0.85223 0.86313 0.87877 0.89542 0.91155
0 0.14705 0.20882 0.25778 0.29117 0.29200
0 1.07915 1.54353 2.13965 2.83999 3.01058
0.60683 0.71334 0.80786 0.90452 0.95107 1
0.84729 0.83935 0.82925 0.81232 0.79978 0.78072
0.93150 0.95994 0.99644 1.04859 1.09008 1.14217
0.26748 0.22093 0.17123 0.09960 0.05523 0
3.18254 3.15428 3.11043 2.43499 1.81333 0
323.15 K 0 0.12025 0.18657 0.27735 0.41781 0.50609
0.85929 0.85707 0.85498 0.85199 0.84816 0.84434
0.84073 0.85880 0.87095 0.88885 0.90684 0.92441
0 0.18001 0.25202 0.31526 0.35063 0.35461
0 1.21820 1.74241 2.52823 3.20592 3.39849
0.60683 0.71334 0.80786 0.90452 0.95107 1
0.83937 0.83126 0.82094 0.80374 0.79099 0.77171
0.94633 0.97750 1.01754 1.07444 1.12078 1.17784
0.32690 0.26919 0.21105 0.12105 0.06954 0
3.51359 3.52071 3.51121 2.74874 2.04698 0
333.15 K 0 0.12025 0.18657 0.27735 0.41781 0.50609
0.85208 0.84971 0.84753 0.84441 0.84045 0.83652
0.84476 0.86549 0.87892 0.89913 0.91851 0.93754
0 0.22085 0.30702 0.38477 0.42383 0.42510
0 1.35391 1.93652 2.70988 3.66307 3.77709
0.60683 0.71334 0.80786 0.90452 0.95107 1
0.83140 0.82310 0.81254 0.79505 0.78205 0.76254
0.96150 0.99549 1.03917 1.10099 1.15239 1.21459
0.39495 0.32452 0.25602 0.14392 0.08610 0
3.90501 3.87738 3.90237 3.05496 2.27502 0
x1 b
a b
Uncertainty in density = ±0.00005 g·cm−3. Uncertainty in temperature = ±0.01 K.
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I. Barabás / Journal of Molecular Liquids 204 (2015) 95–99
Table 4 Coefficients Ai, R and SD of the Redlich–Kister type equation for VE. Temperature/K
A0
A1
A2
R
103 SD
273.15 283.15 288.15 293.15 303.15 313.15 323.15 333.15
0.50137 0.61438 0.68763 0.75839 0.94144 1.15799 1.40518 1.69404
−0.20908 −0.18363 −0.17819 −0.16221 −0.16760 −0.20588 −0.23950 −0.30746
0.03729 0.06609 0.07408 0.08461 0.11292 0.18997 0.25494 0.34541
0.99923 0.99908 0.99927 0.99955 0.99969 0.99972 0.99970 0.99968
2.11506 2.76221 2.72137 2.33811 2.40308 2.80434 3.52132 4.38648
The correlation coefficient R and the standard deviations SD reported in this table were computed by applying the following equations: R¼
n X
" # n n X 2 X 2 1=2 exptli −exptl calci −calc = exptli −exptl calci −calc ;
i¼1
i¼1
i¼1
ð6Þ SD ¼
" n X
#1=2 2
ðcalci −exptli Þ =ðn−mÞ
;
ð7Þ
i¼1
where exptli and calci are the experimental and calculated values, respectively, exptl and calc are the average values of the measured and calculated values, respectively, n is the number of experimental values and m is the numbers of model parameters. Variation ratio (∂ρ/∂T)p was determined by deriving Eq. (5). The excess thermal expansion coefficient αE can be calculated using the formula: [24] X E α ¼ α− ϕi α i
ð8Þ
i
where ϕi is volume fraction of component i. The values of ρ, α, VE and αE are given in Table 3. Variation of molar excess volume and thermal expansion coefficient were modeled by Redlich–Kister type polynomial equation: E
Fig. 1. Plot of the excess molar volume of x1(ethanol) + (1 − x1)RME at the local atmospheric pressure against mole fraction of ethanol.
E
V or ¼ α x1 x2
p X
k
Ak ðx1 −x2 Þ ¼ x1 ð1−x1 Þ
k¼0
p X
Fig. 1 shows excess molar volume variation, while Fig. 2 shows the variation of excess expansion coefficient by temperature as well as by molecular concentration of ethanol in the mixture. Symbols represent calculated values, while solid lines show polynomial variations. The excess molar volume is positive all along the concentration and temperature range. The same trend was observed for mixtures of ethanol and pure esters [25–27]. The fact that excess molar volume is positive indicates the reduction of intermolecular associations (hydrogen bonds in ethanol, dipole–dipole interactions in methyl esters), the presence of repulsive forces due to the electronic charges of both ethanol and esters, the declustering of ethanol in the presence of esters, and the domination of steric hindrance in the ester molecules [27]. This effect is not compensated by a reduction in excess volume due to space redistribution of molecules, facilitated by an important difference of dimensions between the molecules of the two components. 4. Conclusions
k
Ak ð2x1 −1Þ ;
ð9Þ
k¼0
where Ak, k = 0…p are coefficients whose values were calculated by the least-square method. The p order of the polynomial described by Eq. (9) was optimized by applying the F-test. We established that p = 2 for the VE and p = 4 for αE provides sufficient accuracy for modeling these two quantities. The values obtained for coefficients from Eq. (9), with the SD and the R are given in Table 4 for VE and in Table 5 for αE. It can be seen that the Redlich–Kister type polynomial equation represents the excess molar volume and excess expansion coefficient accurately, which is indicated by a low SD and by the R ~ 1.
An Anton Paar DMA 4500 M densimeter was used to measure the densities of ten binary mixtures of ethanol and rapeseed oil biodiesel in the range of 273.15 K to 333.15 K and at atmospheric pressure. As expected, mixtures' density decreases by temperature as well as by ethanol concentration. The Redlich–Kister type polynomial equation provides a good description for the excess molar volumes and excess expansion coefficients. Excess molar volume is positive all along the concentration range, increases with the increase of temperature and has its maximum value in the range of 0.40 to 0.44 of ethanol concentration (11…13% v/v ethanol in biodiesel). The highest value of excess molar volume, 0.42 cm3·mol− 1, was observed at a temperature of 333.15 K and a concentration of ethanol of 0.42, representing 0.21% of the theoretical one. The excess thermal expansion
Table 5 Coefficients Ai, R and SD of the Redlich–Kister type equation for αE. Temperature/K
104 A0
105 A1
105 A2
104 A3
104 A4
R
107 SD
273.15 283.15 288.15 293.15 303.15 313.15 323.15 333.15
0.61289 0.75837 0.83252 0.90688 1.05825 1.21197 1.36813 1.52054
1.20749 1.49409 1.64018 1.78669 2.08490 2.38775 2.69541 2.99569
1.69663 2.09933 2.30459 2.51045 2.92946 3.35499 3.78728 4.20914
0.73220 0.90599 0.99457 1.08341 1.26424 1.44788 1.63444 1.81651
0.64908 0.80314 0.88167 0.96042 1.12072 1.28351 1.4489 1.61031
0.99753 0.99880 0.99897 0.99841 0.99858 0.99858 0.99891 0.99879
5.33720 4.84151 4.66189 6.42909 6.89925 7.80613 7.76258 9.06294
I. Barabás / Journal of Molecular Liquids 204 (2015) 95–99 [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] Fig. 2. Plot of the excess thermal expansion coefficient of x1(ethanol) + (1 − x1)RME at the local atmospheric pressure against mole fraction of ethanol.
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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Liquid densities and excess molar volumes of ethanol + biodiesel binary system between the temperatures 273.15 K and 333.15 K István Barabás Department of Automotive Engineering and Transportation, Technical University of Cluj-Napoca, Romania, 103–105 Muncii Blvd., 400641 Cluj-Napoca, Romania
a r t i c l e
i n f o
Article history: Received 23 September 2014 Received in revised form 19 January 2015 Accepted 28 January 2015 Available online 29 January 2015 Keywords: Rapeseed oil biodiesel + ethanol mixtures Density Excess molar volume Thermal expansion coefficient Excess thermal expansion coefficient
a b s t r a c t The densities of ten binary mixtures of biodiesel made from rapeseed oil and ethanol have been measured for eight temperatures within the range between 273.15 K and 333.15 K, using an Anton Paar DMA 4500 M densimeter. The excess molar volume has been calculated from experimental densities. Variation of mixtures volumes was low, but measurable. It was observed that the excess molar volume was positive for all studied mixtures, due to increased physical interactions between fatty acid methyl esters and ethanol. Density variation was modeled by polynomial regression and the thermal expansion coefficient, as well as its excess value, were estimated. The excess molar volume and excess thermal expansion coefficient results were fitted to the Redlich–Kister type polynomial equation to obtain the regression coefficients and estimate the standard deviations and correlation coefficients between experimental and calculated results. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Population and number of vehicles growth, as well as the acute need for transportation, associated with scarcity of oil resources bring into focus the need to find viable alternatives for partial or total substitution of fossil fuels for automobiles. Alternative sources of energy for transportation are liquid fuels made from biomass, such as biodiesel and bioethanol, considered as strong candidates for substituting fossil fuels. Compared to fossil fuels, biofuels have a number of undeniable advantages: they reduce a country's fossil fuel dependency, they are renewable and environmentally friendly, are carbon neutral, their production supports emerging markets and expand labor markets in agriculture [1,2]. Biodiesel can be produced from various raw materials, such as vegetable oils, animal fat, and some algae species, [3] while bioethanol is made from sugar, starch or cellulose [4]. Biodiesel can substitute diesel fuel, while bioethanol is used as a substitute for petrol. Biodiesel has a high cetane number, wherefrom reduced solid particle and hydrocarbons emissions, but its volatility, calorific value and flow properties at low temperatures are inferior to those of diesel [5,6]. This means that the use of biodiesel at low temperatures can be problematic. However, ethanol has a low cetane number, is very volatile and has excellent flow properties at low temperature [5]. An efficient method of solving some drawbacks of biodiesel is blending it with substances which can compensate for their deficient
E-mail address: [email protected].
http://dx.doi.org/10.1016/j.molliq.2015.01.048 0167-7322/© 2015 Elsevier B.V. All rights reserved.
properties. Using ethanol as an extender for biodiesel is one method which has received close attention in research lately, because the presence of ethanol in biodiesel compensates for some of its drawbacks: it reduces density and viscosity, [7] it improves volatility [8,9] and its flow properties at low temperatures [10]. Density is a very important fuel property because it influences production, transportation, and distribution processes as well as all processes that take place in the internal combustion engine. Knowing the density of fuels is necessary for: designing production and manufacturing facilities for fuels — reactors, tanks, and distillation units; finding the mass and volume flows through such facilities; establishing the appropriate size of transfer pumps, transfer and safety valves, etc. [11]. Density, together with vapor pressure, vapor diffusivity, surface tension, and liquid dynamic viscosity, influences fuel spray structure, combustion and emission characteristics, engine deposit formation, and engine behavior in cold weather conditions [12–15]. Developing reliable models for injection and combustion processes implies the accurate description of the thermo-physical characteristics of fuels, including their density [16]. The injection system of compression ignition engine (CIE) introduces discrete volumes of fuel in the combustion chamber, calculated by the electronic control unit, based, among others, on the functioning conditions of the engine [17] and the temperature of the fuel [18]. For this reason, knowing the precise density of fuel allows for accurate dosage and for a correct energy consumption, because density influences the mass of the injected fuel [19] and the heating value of the fuel is often given as energy content per unit mass [17]. Density influences the air/fuel mass ratio, [20] i.e. the quality of the air–fuel mixture.
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I. Barabás / Journal of Molecular Liquids 204 (2015) 95–99
Since 2002, in order to reduce pollution, the electronic control units of CIE can include a closed loop control for the quality of air–fuel mixtures, using pressure, temperature, wideband oxygen sensors, etc. In the case of these engines, knowing the exact density of the fuel becomes less important, since the quantity of fuel is calculated — together with the usual parameters — by taking into account the oxygen content of exhaust gases [21]. Excess molar volume of mixtures of pure esters and alcohols is the focus of many studies, but, to the best of our knowledge, molar excess values of biodiesel–ethanol mixtures have not been studied yet. The goals of our study are density estimation, excess molar volume estimation, thermal expansion coefficient of mixtures of biodiesel made from rapeseed oil and ethanol, as well as providing data for manufacturing processes, distribution, use, modeling and simulation in which these mixtures are involved.
2. Experimental Ethanol was provided by S.C. Nordic S.A. Biodiesel was produced from rapeseed oil by the Research Institute for Analytical Instrumentation from Cluj-Napoca. Ethanol purity is 99.3% w/w. Esters' content of biodiesel is 97.7% w/w, while water content is 183 mg·kg−1. From the two constituents, ten binary mixtures were prepared by weight dosing, using a Mettler AE 163 type analytical balance with a precision of ± 1 × 10−5 g, consequently the uncertainty in the mole fractions is ±5 × 10−5. Sample composition was chosen so that it covered the range of molar concentration between 0 and 1 with steps of about 0.1. After mixing, the samples were kept for ten days in dark glass bottles, filled to 95% of the volume and tightly closed. As expected, no components separation was observed during this period. The fatty acid methyl ester (FAME) composition profile of biodiesels used in this work was determined by gas chromatography with an HP 6890 series gas chromatography system equipped with a flame ionization detector and automated split injector. Before measuring densities, the samples have been thoroughly mixed and degassed by using an Elmasonic S 50 R type ultrasonic unit. Densities of the pure liquids and mixtures were measured at atmospheric pressure and at (273.15, 283.15, 288.15, 293.15, 303.15, 313.15, 323.15 and 333.15) K by using an Anton Paar DMA 4500 M equipped with vibrating U-tube and provided with automatic viscosity correction. The maximum value of temperature was limited by the relatively low boiling point of bioethanol. The precision of measured densities was 1 × 10− 5 g·cm− 3 and uncertainty of the measurements was estimated to be ±5 × 10−5 g·cm−3. The temperature in the measuring cell was regulated with Peltier elements and was measured via two integrated Pt 100 platinum resistance thermometers with a precision of ±0.01 K. Before each series of measurements, the densimeter was calibrated at atmospheric pressure using double distilled and degassed water and dried air. The density data for water and dried air were taken from DMA 4500 M Instruction Manual. The cell for density measurement was washed with solvent at a temperature of 333.15 K and air dried at a temperature of 363.15 K before each fuel sample. In order to wet the inner walls of the U-tube, before measurements, 20 cm3 of the samples was passed through the density cell. The measurement cell was refilled with a fuel sample before every measurement was taken. In order to ensure maximum accuracy, each measurement was done three times and average of the three values was calculated.
3. Results and discussion Excess molar volume VE of binary biodiesel–ethanol mixtures was calculated for the entire range of concentrations and temperatures
Table 1 Fatty acid methyl ester concentration profiles of RME analyzed by gas chromatography. Fatty acid methyl ester
CAS number
% w/w
Methyl decanoate (C10:0) Methyl dodecanoate (C12:0) Methyl tetradecanoate (C14:0) Methyl hexadecanoate (C16:0) Methyl octadecanoate (C18:0) Methyl eicosanoate (C20:0) Methyl docosanoate (C22:0) Methyl hexadec-9-enoate (C16:1) Methyl (Z)-octadec-9-enoate (C18:1) Methyl cis-11-eicosenoate (C20:1) Methyl (Z)-13-docosenoate (C22:1) Methyl (Z,Z)-octadeca-9,12-dienoate (C18:2) Methyl (Z,Z,Z)-octadeca-9,12,15-trienoate (C18:3)
110-42-9 111-82-0 124-10-7 112-39-0 112-61-8 1120-28-1 929-77-1 1120-25-8 112-62-9 2390-09-2 1120-34-9 112-63-0 301-00-8
0.02 0.03 0.82 3.81 1.75 0.56 1.13 0.12 58.41 0.68 0.21 21.25 11.21
studied with the formula: E
V ¼
2 X
−1 −1 ; xi Mi ρ −ρi
ð1Þ
i¼1
where xi is the mole fraction of the component i (i = 1 for ethanol, i = 2 for biodiesel), Mi is the molecular weights, expressed in g·mol−1, and ρ and ρi represent mixture density and component density, respectively, in g·cm−3. The molar quantities used for calculations in this paper are based on data published by IUPAC [22]. Table 1 reports the methyl ester compositions of the biodiesel (RME) used in this study. Molecular weight of biodiesel, M2, was calculated with the formula [23]. M2 ¼
X
x jM j;
ð2Þ
j
where xj is the mole fraction component j, and Mj is the molecular weight of component j. The molecular weight of RME used in this paper is calculated with Eq. (2) is 295.26 g·mol−1. The thermal expansion coefficient for atmospheric pressure is given by the formula [24]:
α¼V
−1
ð∂V=∂T Þp ;
ð3Þ
where V is the volume and (∂V/∂T)p is the temperature variation ratio for atmospheric pressure. Taking into account the relation of volume
Table 2 Coefficients and precision of polynomial regression. x1
c0/g·cm−3
104 c1/g·cm−3·T−1
107 c2/g·cm−3·T−2
R
102 SD
0 0.12025 0.18657 0.27735 0.41781 0.50609 0.60683 0.71334 0.80786 0.90452 0.95107 1
1.31537 0.31892 −0.13282 −0.97034 −1.40845 −1.87967 −2.53586 −3.41613 −4.51692 −5.88794 −7.35090 −8.61472
−8.07445 −7.56664 −7.36064 −6.94577 −6.78120 −6.59032 −6.30430 −5.91772 −5.43407 −4.83032 −4.11437 −3.52179
1.10648 1.09825 1.09423 1.08658 1.08100 1.07694 1.06957 1.05816 1.04371 1.02132 1.00071 0.97548
1.00000 0.99995 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000
0.22327 1.04200 0.24597 0.52723 0.45762 0.45660 0.59862 9.85563 1.25498 2.11268 1.56606 2.39012
I. Barabás / Journal of Molecular Liquids 204 (2015) 95–99
and density, thermal expansion coefficient can also be expressed by the formula: [24] −1
α ¼ −ρ
ð∂ρ=∂T Þp :
ð4Þ
In the range between 273.15 K and 333.15 K, density variation by temperature is described by a quadratic function [24].
97
2
ρ ¼ c0 þ c1 T þ c2 T ;
ð5Þ
where ρ/g·cm−3 is the density, T/K is the temperature, c0, c1 and c2 are parameters of polynomial regressions. Constants of Eq. (5) were determined based on experimental data by polynomial regression, using the least-square method are given in Table 2.
Table 3 Values of ρ, α, VE and αE for mixture of x1(ethanol) + (1 − x1)RME at temperatures from 273.15 K to 333.15 K and atmospheric pressure. ρa/g·cm−3
103 α/K−1
VE/cm3·mol−1
105 αE/K−1
x1
ρ/g·cm−3
103 α/K−1
VE/cm3·mol−1
105 αE/K−1
273.15 K 0 0.12025 0.18657 0.27735 0.41781 0.50609
0.89574 0.89395 0.89218 0.88961 0.88626 0.88290
0.82121 0.82694 0.83315 0.84035 0.85197 0.86275
0 0.07096 0.09826 0.12027 0.13248 0.12583
0 0.54573 0.77057 1.16260 1.43619 1.52246
0.60683 0.71334 0.80786 0.90452 0.95107 1
0.87845 0.87103 0.86158 0.84545 0.83348 0.81501
0.87536 0.89365 0.91711 0.95179 0.97545 1.00956
0.10675 0.08579 0.05811 0.03540 0.01453 0
1.49402 1.59513 1.57296 1.20138 0.91701 0
283.15 K 0 0.12025 0.18657 0.27735 0.41781 0.50609
0.88840 0.88656 0.88474 0.88213 0.87870 0.87526
0.82503 0.83311 0.84046 0.84968 0.86250 0.87457
0 0.08210 0.11706 0.13930 0.15840 0.15669
0 0.675261 0.965838 1.32143 1.77708 1.88382
0.60683 0.71334 0.80786 0.90452 0.95107 1
0.87074 0.86322 0.85363 0.83734 0.82527 0.80669
0.88894 0.90965 0.93624 0.97507 1.00297 1.04133
0.13556 0.11000 0.08027 0.04891 0.02266 0
1.87762 1.97374 1.94630 1.52366 1.12466 0
288.15 K 0 0.12025 0.18657 0.27735 0.41781 0.50609
0.88474 0.88287 0.88102 0.87838 0.87490 0.87143
0.82696 0.83623 0.84416 0.85441 0.86786 0.88057
0 0.08978 0.12878 0.15303 0.17684 0.17413
0 0.74128 1.06027 1.53845 1.95083 2.06801
0.60683 0.71334 0.80786 0.90452 0.95107 1
0.86686 0.85928 0.84962 0.83325 0.82112 0.80247
0.89584 0.91780 0.94597 0.98692 1.01699 1.05754
0.15378 0.12569 0.09313 0.05549 0.02648 0
2.13805 2.11172 2.10660 1.79263 1.24560 0
293.15 K 0 0.12025 0.18657 0.27735 0.41781 0.50609
0.88108 0.87918 0.87731 0.87462 0.87111 0.86759
0.82890 0.83938 0.84788 0.85919 0.87325 0.88664
0 0.09664 0.13686 0.16885 0.19172 0.19244
0 0.80750 1.15498 1.67588 2.12509 2.25274
0.60683 0.71334 0.80786 0.90452 0.95107 1
0.86297 0.85533 0.84559 0.82912 0.81692 0.79821
0.90282 0.92603 0.95582 0.99894 1.03121 1.07398
0.17230 0.14097 0.10627 0.06340 0.03175 0
2.32904 2.45027 2.26746 1.92205 1.35687 0
303.15 K 0 0.12025 0.18657 0.27735 0.41781 0.50609
0.87379 0.87180 0.86987 0.86710 0.86348 0.85988
0.83280 0.84575 0.85543 0.86888 0.88423 0.89896
0 0.11818 0.16729 0.20626 0.23753 0.23743
0 0.94228 1.34776 1.95559 2.47978 2.61173
0.60683 0.71334 0.80786 0.90452 0.95107 1
0.85515 0.84737 0.83747 0.82078 0.80843 0.78955
0.91701 0.94279 0.97588 1.02344 1.06023 1.10758
0.21685 0.17842 0.13565 0.08028 0.04199 0
2.75776 2.79421 2.71592 2.12615 1.58334 0
313.15 K 0 0.12025 0.18657 0.27735 0.41781 0.50609
0.86653 0.86443 0.86242 0.85955 0.85583 0.85213
0.83674 0.85223 0.86313 0.87877 0.89542 0.91155
0 0.14705 0.20882 0.25778 0.29117 0.29200
0 1.07915 1.54353 2.13965 2.83999 3.01058
0.60683 0.71334 0.80786 0.90452 0.95107 1
0.84729 0.83935 0.82925 0.81232 0.79978 0.78072
0.93150 0.95994 0.99644 1.04859 1.09008 1.14217
0.26748 0.22093 0.17123 0.09960 0.05523 0
3.18254 3.15428 3.11043 2.43499 1.81333 0
323.15 K 0 0.12025 0.18657 0.27735 0.41781 0.50609
0.85929 0.85707 0.85498 0.85199 0.84816 0.84434
0.84073 0.85880 0.87095 0.88885 0.90684 0.92441
0 0.18001 0.25202 0.31526 0.35063 0.35461
0 1.21820 1.74241 2.52823 3.20592 3.39849
0.60683 0.71334 0.80786 0.90452 0.95107 1
0.83937 0.83126 0.82094 0.80374 0.79099 0.77171
0.94633 0.97750 1.01754 1.07444 1.12078 1.17784
0.32690 0.26919 0.21105 0.12105 0.06954 0
3.51359 3.52071 3.51121 2.74874 2.04698 0
333.15 K 0 0.12025 0.18657 0.27735 0.41781 0.50609
0.85208 0.84971 0.84753 0.84441 0.84045 0.83652
0.84476 0.86549 0.87892 0.89913 0.91851 0.93754
0 0.22085 0.30702 0.38477 0.42383 0.42510
0 1.35391 1.93652 2.70988 3.66307 3.77709
0.60683 0.71334 0.80786 0.90452 0.95107 1
0.83140 0.82310 0.81254 0.79505 0.78205 0.76254
0.96150 0.99549 1.03917 1.10099 1.15239 1.21459
0.39495 0.32452 0.25602 0.14392 0.08610 0
3.90501 3.87738 3.90237 3.05496 2.27502 0
x1 b
a b
Uncertainty in density = ±0.00005 g·cm−3. Uncertainty in temperature = ±0.01 K.
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I. Barabás / Journal of Molecular Liquids 204 (2015) 95–99
Table 4 Coefficients Ai, R and SD of the Redlich–Kister type equation for VE. Temperature/K
A0
A1
A2
R
103 SD
273.15 283.15 288.15 293.15 303.15 313.15 323.15 333.15
0.50137 0.61438 0.68763 0.75839 0.94144 1.15799 1.40518 1.69404
−0.20908 −0.18363 −0.17819 −0.16221 −0.16760 −0.20588 −0.23950 −0.30746
0.03729 0.06609 0.07408 0.08461 0.11292 0.18997 0.25494 0.34541
0.99923 0.99908 0.99927 0.99955 0.99969 0.99972 0.99970 0.99968
2.11506 2.76221 2.72137 2.33811 2.40308 2.80434 3.52132 4.38648
The correlation coefficient R and the standard deviations SD reported in this table were computed by applying the following equations: R¼
n X
" # n n X 2 X 2 1=2 exptli −exptl calci −calc = exptli −exptl calci −calc ;
i¼1
i¼1
i¼1
ð6Þ SD ¼
" n X
#1=2 2
ðcalci −exptli Þ =ðn−mÞ
;
ð7Þ
i¼1
where exptli and calci are the experimental and calculated values, respectively, exptl and calc are the average values of the measured and calculated values, respectively, n is the number of experimental values and m is the numbers of model parameters. Variation ratio (∂ρ/∂T)p was determined by deriving Eq. (5). The excess thermal expansion coefficient αE can be calculated using the formula: [24] X E α ¼ α− ϕi α i
ð8Þ
i
where ϕi is volume fraction of component i. The values of ρ, α, VE and αE are given in Table 3. Variation of molar excess volume and thermal expansion coefficient were modeled by Redlich–Kister type polynomial equation: E
Fig. 1. Plot of the excess molar volume of x1(ethanol) + (1 − x1)RME at the local atmospheric pressure against mole fraction of ethanol.
E
V or ¼ α x1 x2
p X
k
Ak ðx1 −x2 Þ ¼ x1 ð1−x1 Þ
k¼0
p X
Fig. 1 shows excess molar volume variation, while Fig. 2 shows the variation of excess expansion coefficient by temperature as well as by molecular concentration of ethanol in the mixture. Symbols represent calculated values, while solid lines show polynomial variations. The excess molar volume is positive all along the concentration and temperature range. The same trend was observed for mixtures of ethanol and pure esters [25–27]. The fact that excess molar volume is positive indicates the reduction of intermolecular associations (hydrogen bonds in ethanol, dipole–dipole interactions in methyl esters), the presence of repulsive forces due to the electronic charges of both ethanol and esters, the declustering of ethanol in the presence of esters, and the domination of steric hindrance in the ester molecules [27]. This effect is not compensated by a reduction in excess volume due to space redistribution of molecules, facilitated by an important difference of dimensions between the molecules of the two components. 4. Conclusions
k
Ak ð2x1 −1Þ ;
ð9Þ
k¼0
where Ak, k = 0…p are coefficients whose values were calculated by the least-square method. The p order of the polynomial described by Eq. (9) was optimized by applying the F-test. We established that p = 2 for the VE and p = 4 for αE provides sufficient accuracy for modeling these two quantities. The values obtained for coefficients from Eq. (9), with the SD and the R are given in Table 4 for VE and in Table 5 for αE. It can be seen that the Redlich–Kister type polynomial equation represents the excess molar volume and excess expansion coefficient accurately, which is indicated by a low SD and by the R ~ 1.
An Anton Paar DMA 4500 M densimeter was used to measure the densities of ten binary mixtures of ethanol and rapeseed oil biodiesel in the range of 273.15 K to 333.15 K and at atmospheric pressure. As expected, mixtures' density decreases by temperature as well as by ethanol concentration. The Redlich–Kister type polynomial equation provides a good description for the excess molar volumes and excess expansion coefficients. Excess molar volume is positive all along the concentration range, increases with the increase of temperature and has its maximum value in the range of 0.40 to 0.44 of ethanol concentration (11…13% v/v ethanol in biodiesel). The highest value of excess molar volume, 0.42 cm3·mol− 1, was observed at a temperature of 333.15 K and a concentration of ethanol of 0.42, representing 0.21% of the theoretical one. The excess thermal expansion
Table 5 Coefficients Ai, R and SD of the Redlich–Kister type equation for αE. Temperature/K
104 A0
105 A1
105 A2
104 A3
104 A4
R
107 SD
273.15 283.15 288.15 293.15 303.15 313.15 323.15 333.15
0.61289 0.75837 0.83252 0.90688 1.05825 1.21197 1.36813 1.52054
1.20749 1.49409 1.64018 1.78669 2.08490 2.38775 2.69541 2.99569
1.69663 2.09933 2.30459 2.51045 2.92946 3.35499 3.78728 4.20914
0.73220 0.90599 0.99457 1.08341 1.26424 1.44788 1.63444 1.81651
0.64908 0.80314 0.88167 0.96042 1.12072 1.28351 1.4489 1.61031
0.99753 0.99880 0.99897 0.99841 0.99858 0.99858 0.99891 0.99879
5.33720 4.84151 4.66189 6.42909 6.89925 7.80613 7.76258 9.06294
I. Barabás / Journal of Molecular Liquids 204 (2015) 95–99 [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] Fig. 2. Plot of the excess thermal expansion coefficient of x1(ethanol) + (1 − x1)RME at the local atmospheric pressure against mole fraction of ethanol.
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