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Experimental Investigation and Modeling of Thermophysical Properties of Pure Methyl and Ethyl Esters at High Pressures Mohamed A. Aissa, Gorica R. Ivanis, Ivona R. Radovic, and Mirjana Lj Kijevcanin Energy Fuels, Just Accepted Manuscript • Publication Date (Web): 12 Jun 2017 Downloaded from http://pubs.acs.org on June 13, 2017

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Experimental Investigation and Modeling of Thermophysical Properties of Pure Methyl and Ethyl Esters at High Pressures

Mohamed A. Aissa, Gorica R. Ivaniš, Ivona R. Radović, and Mirjana Lj. Kijevčanin* Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, 11120, Belgrade, Serbia

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Abstract Densities, speeds of sound and refractive indices of methyl laurate, ethyl laurate, ethyl myristate and ethyl oleate in the temperature range 288.15 to 343.15 K and viscosities from 288.15 to 373.15 K were measured at atmospheric pressure. The measured properties were in good agreement with several available literature data, finding an overall absolute average percentage deviation, AAD, of 0.04%, 0.07%, 3 % and 0.1% for density, speed of sound, viscosity and refractive index, respectively. The densities of mentioned esters were also measured along 15 isotherms from 293.15 to 413.15 K and at pressures up to 60 MPa using Anton Paar DMA HP densimeter. Based on the literature data selected for comparison, in the studied ranges of temperature and pressure, the AADs of high pressure densities were 0.08 % for methyl laurate, 0.06 % for ethyl laurate and 0.05 % for ethyl myristate. The obtained density values were correlated through the modified Tammann-Tait equation with an AAD lower than 0.009% for all the studied esters. The adjusted parameters were used to calculate the isothermal compressibility, the isobaric thermal expansivity, the internal pressure and the difference in isobaric and isochoric heat capacities. It was found that methyl laurate has higher density, speed of sound and refractive index than ethyl laurate of the same fatty acid, while viscosities are slightly higher for the ethyl than those of the methyl laurate. The values of the isothermal compressibility and the isobaric thermal expansivity are slightly higher for ethyl laurate than for methyl.


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1. INTRODUCTION The transport sector has the largest share in oil consumption and is the major contributor of greenhouse gases emissions, such as carbon dioxide (CO2), nitrogen oxides (NOx), carbon monoxide (CO) and volatile organic compounds (VOCs) which affect the oxidation-reduction capacity of the atmosphere, as well as aerosols and particulate matter (PM) growth.1-4 These issues have challenged researchers to study the performance of diesel engine in order to meet the future rigorous emission standards. For this purpose, the research projects have generally been focused on some of promising engine technologies, e.g. advanced fuel injection system, combustion process and a new exhaust gas after treatment system.5 In spite of high level of achievements, further reduction of engine emissions and fuel consumption are the most important demands imposed on engines and these requirements have been increasingly stringent every year.3 Due to these growing concerns, many researchers have shifted their attention towards exploring different renewable energy sources. Among various fuel sources, biofuels have come into focus recently as alternative energy sources and strong contenders for reductions in environmental pollution. Biodiesel consists of long chain alkyl (methyl or ethyl) esters produced by transesterification of vegetable oils or other feed-stocks, largely comprised of triacylglycerols, with short-chain alcohol, such as methanol or ethanol, in the presence of a catalyst.6,7 Unlike diesel fuel, biodiesel consists of a limited number of components8 which enables to study the properties of each individual component and to predict thermophysical properties of biodiesels as a function of their fatty acid profile. The knowledge of thermophysical properties of pure components over large ranges of temperature and pressure is important for predicting the behavior of fuel injection and combustion systems in diesel engines where a precise amount of fuel must be delivered into the engine cylinder and mixed with air to achieve proper combustion.9 This operation is carried out under rapid variation of pressure and temperature, and is strongly affected by the fuel density and viscosity.10-12 Therefore, in order to achieve the correct fuel atomization and a complete combustion, proper values of density and viscosity are required, as well as of 3 ACS Paragon Plus Environment

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the speed of sound, which is related to the starting of diesel engine. A higher speed of sound and isentropic bulk modulus of biodiesel results in a quicker fuel pressure rise from the fuel pump towards the injectors which leads to earlier injection timing and, consequently, to a higher NOx emission.13-15 Ndiaye et al.16 studied the acoustic and thermodynamic properties of methyl myristate, ethyl myristate, and methyl palmitate at pressures up to 100 MPa along isotherms ranging from 293.15 to 403.15 K, methyl oleate and methyl linoleate17at pressures up to 200 MPa at the temperature range 283.15 to 393.15 K, methyl caprate and ethyl caprate18 at pressures up to 210 MPa along isotherms ranging from 283.15 to 403.15 K. Tat and Van Gerpen19 have reported speeds of sound and densities of methyl laurate at pressures up to 34.5 MPa within the temperature range 293.15-373.15 K. Moreover, Pratas et al.20 performed measurements for methyl laurate, methyl myristate and methyl oleate at pressures up to 45 MPa. Schedemann21 determined densities of methyl linoleate at temperatures between 278 and 367 K and pressures between 0.4 and 130 MPa, while Dzida et al.22 obtained densities of ethyl caprylate, ethyl caprate, ethyl myristate,23 as well as ethyl laurate23 from speed of sound measurements at pressures up to 100 MPa within the temperature limits 293.15 and 318.15 K. Recently, Zarska et al.24 obtained densities of

methyl caprylate, methyl caprate, methyl myristate and methyl laurate from speed of sound

measurements at pressures up to 100 MPa within the temperature limits 293.15- 318.15 K. In this work, experimental data on densities, speeds of sound and refractive indices of methyl laurate, ethyl laurate, ethyl myristate and ethyl oleate are reported at temperatures from 288.15 to 343.15 K and atmospheric pressure while the viscosities are obtained under the same pressure over the temperature range from 288.15 to 373.15 K, with temperature step of 5 K. Also, for the same samples, densities are reported along with the derived thermodynamic properties, such as the isothermal compressibility, κT, isobaric thermal expansivity, αp, the internal pressure, pint, and the difference in isobaric and isochoric heat capacities, cp – cv, in temperature interval 293.15 to 413.15 K and at pressures up to 60 MPa. Besides the attractiveness of the chosen compounds, the novelty of the presented data is in expansion of the


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measurement range for the investigated compounds, while, to the best of our knowledge, density measurements of ethyl oleate have never been investigated under high pressure. 2. EXPERIMENTAL SECTION 2.1. Materials. The methyl ester and all studied ethyl esters were supplied by Sigma-Aldrich. The chemicals were degassed and used without further purification. Details of chemicals are listed in Table 1. The purity of components was ascertained by comparison of the experimental densities, speeds of sound, viscosities and refractive indices with those reported in the open literature. The agreement of these two data sets were very good: for density data the deviations were mostly less than 0.60 kg⋅m-3, for sound velocity less than 0.65 m·s-1, for viscosity they were mainly around 0.05 mPa·s and the experimental refractive indices differ from literature values less than 0.006, for all studied substances (Table 2). 2.2. Measurement Procedure. Experimental measurements of density, ρ, and speed of sound, u, were performed with an Anton Paar DSA 5000 M at atmospheric pressure, while refractive index, nD, and viscosity, η, were measured using an automatic Anton Paar RXA 156 refractometer and Stabinger SVM3000/G2 viscometer, respectively. The procedures for measuring on mentioned viscometer and refractometer have been described in previous publications,36,

37

while handling DSA 5000 M is pretty

much the same as for DMA 5000, that has also been previously explained.36,37The expanded uncertainties of the density, U(ρ), viscosity, U(η), refractive index, U(nD), and speed of sound measurements, U(u), with a confidence level of 95% (coverage factor, k =2), were estimated to be 0.09 kg·m-3, 0.004 mPa·s, 5·10-5 and 0.1 m·s-1, respectively. High pressure density measurements were carried out using an Anton Paar DMA HP digital vibrating tube densimeter over the temperature, T, range 293.15-413.15 K at pressures, p, up to 60 MPa. Each selected temperature was controlled by an integrated Peltier thermostat with the stability of ±0.05 K. The required pressure was generated and controlled with a Pressure Generator model 50-6-15, High Pressure Equipment Co, using acetone as the hydraulic fluid, and was measured with a pressure transducer WIKA


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S-10, Alexander Wiegand GmbH & Co, with an expanded uncertainty of 0.05 MPa, confidence level of 95% (coverage factor, k = 2). DMA HP facility is connected with DMA 5000 densimeter as a reading device, which evaluates the oscillation period of the measuring cell filled with a sample.37 AP SoftPrint software program (a Microsoft Excel Add-In) was used to read out and transfer the measured values from DMA 5000 to a PC. Before running each experiment, all samples were degassed by Branson 3210 ultrasound bath for at least 15 min at room temperature. All measurements were performed starting at 0.1 MPa and pressure was increased along an isotherm up to a maximum of 60 MPa. The system was returned to 0.1 MPa after a sequence of measurements in order to equilibrate and reperform measurement at the initial state point. After completing an isotherm, the set point temperature was changed for the next set of measurements increasing to a maximum of 413.15 K. Detailed description of the experimental setup and measuring procedure for high pressure density has been discussed in our previous publication38 and the apparatus is schematically shown in Figure S1 in the supplementary material to this paper. For accurate and reliable data, it was necessary to calibrate precisely an Anton Paar DMA HP high pressure vibrating tube densimeter. This required the use of calibration fluids with known densities in the wide ranges of temperature and pressure. Therefore, the classical calibration method with one reference fluid was performed according to the procedure described by Comuñas et al.39 which is the modification of the procedure previously proposed by Lagourette et al.40 and described in details in a previous publication.38 The chosen calibration fluids were water at temperatures under 373.15 K and n-decane and water at temperatures higher than 373.15 K. The calibration procedure also includes data for vacuum so the measured densities of esters are in the range of the reference fluids (Tables 2 and 3).38 The density correction due to viscosity of the sample was estimated according to the information received from the supplier Anton Paar and it was less than 0.07 kg·m-3. Taking into account the uncertainties of pressure, temperature, the error in the period of oscillation measurements, the densities of the reference 6 ACS Paragon Plus Environment

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ﬂuids and the damping effects on the vibrating tube, the overall combined expanded uncertainty with conﬁdence level 95% (coverage factor k = 2) of the reported density values, Uc(ρ), was estimated to be 0.8 kg·m-3 in the temperature range 293.15–363.15 K and 2.0 kg·m-3 at temperatures 373.15–413.15 K. 3. RESULTS AND DISCUSSION 3.1. Measured Physical Properties. Densities, speeds of sound and refractive indices of methyl and ethyl esters were measured at atmospheric pressure and temperatures 288.15–343.15 K, while for the dynamic viscosities temperature range was 288.15–373.15 K. Obtained results are given in Tables 3 and 4, while some selected properties are shown in Figs. 1-3. The measured data of pure ethyl and methyl esters are compared with the available literature values. The absolute average percentage deviation and maximum percentage deviation are used to estimate the agreement between our and the literature values.38, 39 The absolute average percentage deviations between density values presented here and those obtained by Pratas et al.,25,41 at atmospheric pressure and at temperatures 288.15–343.15 K, were 0.06% (MD=0.07%), 0.04% (MD=0.05%), 0.02% (MD=0.03%), and 0.17% (MD=0.19%) for methyl laurate, ethyl laurate, ethyl myristate and ethyl oleate, respectively. The agreement of our density measurement at atmospheric pressure and those reported by Freitas et al.32over the temperature range 293.15–343.15 K are within absolute average percentage deviation of 0.01% (MD=0.015%), 0.02%(MD=0.027%) and 0.008% (MD=0.02%) for ethyl laurate, ethyl myristate and ethyl oleate, respectively. The values obtained in this work for methyl laurate and ethyl myristate were compared with literature data 26, 33 obtained at 298.15 K, finding an AAD% of 0.005% and 0.015%, respectively. For speed of sound, the agreement of our results at atmospheric pressure and those reported in literature27,32 over the temperature range 288.15–343.15 K are 0.047% (MD=0.07%), 0.025% (MD=0.04%), 0.039% (MD=0.06%) and 0.16 (MD=0.17%) for methyl laurate, ethyl laurate, ethyl myristate and ethyl oleate, respectively. The values obtained here for methyl laurate were compared with data reported by Zarska et al.24 from 298.15 to 318.15 K at atmospheric pressure yielding an AAD of 7 ACS Paragon Plus Environment

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0.07% (MD=0.14%). The results of Ndiaye et al.16 show absolute average percentage deviation from our measurements for ethyl myristate of 0.12% (MD= 0.22%) at temperature range 293.15-343.15 K, while speeds of sound of ethyl laurate and ethyl myristate obtained by Dzida et al.23 at temperature range 293.15-318.15 K deviate from our experimental work by 0.06% (MD=0.1%) and 0.04% (MD=0.08%), respectively. Regarding viscosity, the absolute average percentage deviation between viscosities presented here and those obtained by25 were 1.6 % (MD=2.19%), 1.1 % (MD=1.46%), 1.2 % (MD=1.96%) and 6.2 % (MD=7.26%) for methyl laurate, ethyl laurate, ethyl myristate and ethyl oleate, respectively, over the temperature range 288.15–363.15 K at atmospheric pressure. Concerning refractive index, the values obtained in this work for methyl laurate were compared with data obtained by Althouse et al.28 from 293.15 to 318.15 K and with literature values26,29-31obtained at 298.15K yielding an AAD of 0.015 % (MD=0.037%) and 0.01% (MD=0.014%), respectively. The absolute average deviation between our and literature value33 for ethyl laurate is 0.45% at 298.15K. The AADs between our and data obtained by Shigley et al.34 are 0.014% (MD=0.028%) and 0.013% (MD=0.029%) over temperature range 293.15–313.15 K for ethyl laurate and ethyl myristate, respectively. Otin et al.35 obtained refractive index of ethyl oleate which deviates from ours with ADD= 0.032% at 298.15 K. Densities and speeds of sound at atmospheric pressure decrease linearly with temperature increase (Figs. 1-2) and differences between the mentioned properties of the studied esters are almost temperature independent. The ranked increase in density was found to be: ethyl myristate < ethyl laurate < methyl laurate < ethyl oleate while speed of sound increases in the following order: ethyl laurate < methyl laurate < ethyl myristate < ethyl oleate (Table 3) in the examined temperature interval. The comparison between methyl and ethyl laurate shows that methyl laurate has higher density and speed of sound than ethyl laurate of the same fatty acid, at atmospheric pressure. Concerning the dependences of viscosities on temperature, it decreases exponentially with temperature elevation, as expected (Fig. 3). The order of increasing viscosity at atmospheric pressure is: methyl laurate 8 ACS Paragon Plus Environment

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< ethyl laurate < ethyl myristate < ethyl oleate (Table 4). The obtained viscosities are slightly higher for the ethyl esters than those of the methyl ester. The dependences of refractive indices of the studied components (Table 4) at atmospheric pressure decrease linearly with temperature increase (Fig. S2), indicating that refractive index of the methyl laurate is slightly higher than ethyl laurate and is almost temperature independent for all studied esters. Combining densities and speeds of sound enables to determine the isentropic bulk modulus, βS, (Table 5) or the isentropic compressibility, κS. For pure compounds, it can be calculated at each temperature using the following relation: 42, 43

βS =

1

κS

= ρu2 (1)

The knowledge of the isentropic bulk modulus enables calculation of the intermolecular free length (Table 5):

Lf = K j ⋅ κS =

Kj

βS

(2)

where Kj denotes temperature dependent Jacobson’s constant.44-46 Jacobson44 gave values of the constant at a few temperatures in the range 273.15-323.15 K that were correlated and its dependence on temperature is presented as: 47

K j = (93.875 + 0.375⋅T ) ⋅10−8

(3)

The trend of speed of sound and density is found to decrease as temperature increases. Hence, a corresponding increase in the isentropic compressibility and a decrease in isentropic bulk modulus with temperature is observed (Table 5, Fig. S3). The intermolecular free length behaves similar as the isentropic compressibility - it increases linearly when temperature rises at atmospheric pressure. The differences in the isentropic bulk modulus between studied esters are almost the same at all examined temperatures. On the basis of literature,

48,49

the isentropic bulk modulus is related to the free space 9

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between molecules. As it can be seen from Table 5, the intermolecular free length decreases when temperature drops while the isentropic bulk modulus increases. It means that the isentropic compressibility decreases under the same conditions, which is expected due to less free space to be consumed during compression. The ranked increase in the isentropic bulk modulus of the studied components along the temperature range is the same as for speed of sound and it was found to be ethyl laurate < methyl laurate < ethyl myristate < ethyl oleate (Table 5). A higher speed of sound and isentropic bulk modulus of biodiesel compared to diesel fuel results in a quicker fuel pressure rise from the fuel pump towards the injectors which leads to earlier injection timing and, consequently, to a higher NOx emission.13-15 The Vogel-Fulcher-Tammann (VFT) model was used in correlation of measured viscosity data as a function of temperature: ln η = A +

B T −C

(4)

where A, B and C are the fitting parameters obtained by linearization of the Eq. (4) along with an optimization algorithm based on the least square method. The obtained model parameters, together with the values of comparison criteria, are presented in Table 6. Obtained values of the absolute average percentage deviation, AAD, the percentage maximum deviation, MD, the average percentage deviation, Bias, and the standard deviation, σ,

39,40,50

are pretty low which justifies the application of this model in

viscosity modeling. Densities of the same compounds were also carried out at pressures up to 60 MPa and at temperatures ranging from 293.15 to 413.15 K. Comparison of densities at the atmospheric pressure obtained using DSA 5000 M densimeter and those measured by means of DMA HP densimeter shows a good agreement, the absolute average percentage deviation is less than 0.01% (about 0.08 kg·m-3) for all of the examined samples (Fig. S4). This confirms the accuracy of the measurement procedure and the validity of the selected calibration method for DMA HP densimeter. Densities of the pure components measured in this 10 ACS Paragon Plus Environment

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study (Table 7) are also compared with those reported in open literature. An absolute average percentage deviation, together with the maximum percentage deviation, is used to estimate the level of agreement between measured and literature values. In some cases, it was necessary to interpolate the literature values in order to obtain the data that correspond to a certain pressures and temperature considered in this study. Experimental high pressure densities for studied esters were compared to data published by various authors under different temperature and pressure conditions and the obtained absolute average percentage deviations were less than 0.08% (MD=0.22%) for methyl laurate (Fig. 4a) over the temperature range (293.15-373.15) K, 0.06% (MD=0.11%) for ethyl laurate (Fig. 4b) at temperatures ranging from 293.15 to 318.15 K and 0.05% (MD=0.10%) for ethyl myristate (Fig. 4c) along 12 isotherm ranging from 293.15 to 393.15K. The experimental results are presented in Table 7 and shown graphically in Figs. S5 and S6. Fig. S5 shows measured densities of the pure compounds as a function of pressure at different temperatures and the variation of density versus pressure is almost linear, which is more noticeable at low temperatures. Each of the pure components showed an increase in density when pressure rises and decrease in density with temperature elevation (Fig. S6), as expected due to the compression of molecules and reduction of molecular vibration. 3.2. High Pressure Density Correlation. To make the present results easily usable for engineering and design purposes, the modified Tammann-Tait51 equation was applied to correlate the experimental high pressure density data and also to calculate various derived properties. It is one of the simplest empirical equations and widely used 20, 52-54 as a common method to correlate liquid density data over a broad pressure and temperature range:

ρ (T , p) =

ρ ref (T , p)  B(T) + p  1 − C ⋅ ln  ref   B(T) + p 

(5)


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where ρref denotes density of the sample at reference pressure, pref=0.1MPa, and it depends on temperature, as well as B(T), while C is temperature independent parameter. ρref and B(T) could be expressed as a function of temperature by considering a second-order polynomial form: 2

i ρ ref (T , p) = ∑ aT i i =0

(6)

2

i B(T ) = ∑bT i i =0

(7)

and ai, bi and C are adjustable parameters. For each component, parameters ai of Eq. (6) were first determined in a simultaneous non-linear optimization for atmospheric density data by applying the Marquardt algorithm in order to minimize the absolute average deviation between the measured and correlated values. In the next step, parameters bi and C of Eqs. (5) and (7) were adjusted using the same optimization procedure for the entire data set, except densities at atmospheric pressure, pertaining to a given pure component. For the purpose of verifying the quality of density data modeling, the absolute average percentage deviation, the percentage maximum deviation, the average percentage deviation and the standard deviation of experimental data from those obtained by applying optimized parameters of the modified Tammann-Tait equation were calculated. The optimized values for the parameters of Eqs. (5)-(7) are given in Table 8 along with the corresponding values of the comparison criteria. 3.3. Derived Thermodynamic Properties. Based on the statistical indicators it can be concluded that modified Tammann-Tait equation gave an excellent data correlation for pure components of methyl and ethyl esters as shown in Table 8. Hence, very important properties can be derived from measured densities since most of thermophysical properties are linked together by thermodynamic relations. These properties are partial derivatives of the density as a function of pressure or temperature. The effect of pressure on density can be described by the isothermal compressibility, κT, which can be expressed as follows:55,56


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κT = −

1  ∂Vm  1  ∂ρ   ∂ ln ρ    =   =  Vm  ∂p T ρ  ∂p T  ∂p T

(8)

Isothermal compressibility can be calculated by incorporating equation (5) into (8) as follows:55

  ρ (T , p )  C κT =   ref   B(T ) + p  ρ (T , p) 

(9)

The effect of temperature on density can be best described by the isobaric thermal expansivity, αp, which can be defined as:55,56

αp = −

1  ∂Vm  1  ∂ρ   ∂ ln ρ  = −   = −    Vm  ∂T  p ρ  ∂T  p  ∂T  p

(10)

The following expression is derived from the modified Tait-Tammann Eq. (5) and Eq. (10):55

 ρ ref ' (T , p)  α P = −  ref −  ρ (T , p ) 

B′(T )( p ref − p) ( B(T ) + p)( B(T) + p ref )  B(T ) + p  1 − C ⋅ ln B(T ) + p ref   

C⋅

(11)

where ρref’(T, p) and B’(T) are derivatives with respect to T of the parameters ρref(T, p) and B(T) of Eq. (5), respectively: 2

i −1 ρ (T , p) = ∑ibT i ref '

i =0

(12)

2

i −1 B′(T ) = ∑ibT i i =0

(13)

The thermal pressure coefficient, γ, and the internal pressure, pint, provide a great deal of information about the nature of the liquid state and they can be calculated by the following thermodynamic relationships:56

γ=

αp κT

(14)


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Tα P  ∂U   ∂P  pint =  −p  =T   − p = Tγ − p = κT  ∂V T  ∂T  ρ

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(15)

where U refers to an internal energy and V is volume of the sample. Another important parameter for the investigation of the thermodynamic properties of methyl and ethyl esters is the difference between the specific heat capacity at constant pressure, cp, and the specific heat capacity at constant volume, cv, and it can be calculated using the following equation:56

( ∂p / ∂T )ρ 2

c p = cv + T

ρ 2 (∂p / ∂T )T

(16)

Coupling Eqs. (8) and (10) with Eq. (16) leads to the following expression of mentioned property:

α p2T c p − cv = ρκ T

(17)

The knowledge of the isothermal and isentropic compressibility, as well as the isobaric thermal expansivity, allows determination of the specific heat capacity at constant pressure:

α 2pT cp = ρ (κ T − κ S )

(18)

which further leads to calculation of the isochoric heat capacity that can be difficult to measure. The resulting values of the isothermal compressibility, the isobaric thermal expansivity, the internal pressure and the difference between the specific heat capacity at constant pressure and the specific heat capacity at constant volume for all examined components, at the temperature and pressure ranges investigated in this study, were calculated using the modified Tammann–Tait equation parameters and given in the supplementary material (Tables S1–S4). Additionally, some selected derived properties are shown in Figs. 5-6 and S7. The dependence of the isobaric molar heat capacity on temperature at atmospheric pressure is presented in Fig. 7 and the calculated values of molar heat capacities at constant pressure and at constant volume are given in Table S5 in the supplementary material.


Page 15 of 41

1 2 1 3 4 2 5 6 3 7 8 9 4 10 11 5 12 13 6 14 15 16 7 17 18 8 19 20 9 21 22 23 24 10 25 26 27 11 28 29 30 12 31 32 13 33 34 35 14 36 37 15 38 39 16 40 41 42 17 43 44 18 45 46 19 47 48 49 20 50 51 21 52 53 22 54 55 56 23 57 58 24 59 60

Energy & Fuels

The isothermal compressibilities of the studied components increase with the increasing temperature at a constant pressure and decrease when pressure rises along the isotherms (Fig. 5), as expected, and thus, the trends with temperature and pressure are the opposite of those for the density (Figs. S5 and S6). The obtained values are slightly higher for ethyl than for methyl laurate but differences are very small though growing with increasing temperature. In terms of isobaric thermal expansivity variation with pressure, the obtained values decrease with increasing pressure up to 60 MPa at a constant temperature. As it can be seen from Fig. 6, the isotherms of the isobaric thermal expansivity for all the studied components show a clear intersection point at the pressure of about 40 MPa for methyl and ethyl myristate, 45 MPa for ethyl laurate, and around 35 MPa

 ∂α  for ethyl oleate. This point obeys to the condition  p  = 0 , meaning that the isobaric thermal  ∂T  p expansivity of the examined esters is temperature independent at those pressures. At the pressures lower than those at intersection points, all the studied components show increase in thermal expansivity with temperature elevation, while their values decrease as the temperature rises at pressures higher than those of intersection points. The obtained isobaric thermal expansivity values of ethyl laurate are higher than those of methyl laurate. A larger isobaric thermal expansivity causes a larger engine power loss due to fuel heating.20,50 With regard to the internal pressure of the studied esters, it decreases with temperature elevation at constant pressure (Tables S1-S4). On the other hand, its dependence on pressure is a bit more complex. The internal pressure of methyl laurate increases monotonically as pressure rises along all isotherms. For the ethyl esters internal pressure is almost constant or slightly decreases at temperatures below 323.15 K while above 323.15 K it starts to increase with pressure rise along isotherms (Fig. S7). The pressure influence is most pronounced at the highest isotherm (413.15 K) for all compounds. The difference between the specific heat capacity at constant pressure and at constant volume decreases with both temperature and pressure increase (Tables S1-S4). Both isobaric and isochoric molar heat 15 ACS Paragon Plus Environment

Energy & Fuels

1 2 1 3 4 2 5 6 3 7 8 9 4 10 11 5 12 13 6 14 15 16 7 17 18 8 19 20 9 21 22 23 10 24 25 11 26 27 28 12 29 30 13 31 32 14 33 34 35 15 36 37 16 38 39 17 40 41 42 18 43 44 19 45 46 20 47 48 49 21 50 51 22 52 53 54 23 55 56 24 57 58 59 60

Page 16 of 41

capacity, increase with temperature rise at atmospheric pressure and the values (Table S5) of ethyl esters are higher than those methyl laurate (Fig. 7).

4. CONCLUSION Density, viscosity, speed of sound and refractive index of the methyl and ethyl esters were reported at various temperatures and atmospheric pressure. The absolute average percentage deviations between measured and several literature values were within 0.008-0.17%, 0.01-0.2%, 1-6 %, 0.01-0.03% for density, speed of sound, viscosity and refractive index data, respectively. Also, densities of mentioned esters were reported along with the derived thermodynamic properties at pressures up to 60 MPa over the temperature range from 293.15-413.15 K. The measured densities were in good agreement with available literature data, finding an overall ADDs of 0.08%, 0.06%, 0.05% for methyl laurate, ethyl laurate and ethyl myristate, respectively. The modified Tammann-Tait equation correlates well the high-pressure density data of all studied esters with an ADD lower than 0.009%. Results show that methyl laurate has slightly higher density, speed of sound and refractive index than ethyl laurate of the same fatty acid, while viscosities are higher for the ethyl than those of the methyl laurate. Regarding (ρ, p, T) data, densities of the examined esters increase with pressure rise and decrease as temperature increases, as expected. The dependence of the isothermal compressibility on temperature and pressure is opposite to that of the density. The isobaric thermal expansivity behaves similar to the isothermal compressibility at pressure lower than at the one of the isotherms intersection point. At pressures higher than the mentioned, αp still decrease with increase in pressure along isotherms but it increase as temperature drops at constant pressure. The isobaric thermal expansivity is temperature independent at pressures of 40 MPa for methyl laurate and ethyl myristate, 45 MPa for ethyl laurate and 35 MPa for ethyl oleate. The values of the isothermal compressibility and the isobaric thermal expansivity are slightly higher for ethyl than for methyl laurate. The isobaric and isochoric molar heat capacities rise


Page 17 of 41

when temperature increases at atmospheric pressure and their value of ethyl esters are higher than those of methyl laurate.

880

-3

860

ρ / kg·m

1 2 1 3 4 2 5 6 3 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 4 34 35 5 36 37 6 38 39 7 40 41 8 42 43 9 44 45 10 46 47 11 48 12 49 50 13 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

840

820

800 280

300

320

340

T/K

Figure 1. Density, ρ, of: () methyl laurate, () ethyl laurate, () ethyl myristate and () ethyl oleate at atmospheric pressure.


Energy & Fuels

1450 1400 1350

u / m·s-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 1 27 28 2 29 30 3 31 32 4 33 34 5 35 36 6 37 38 7 39 40 8 41 42 9 43 44 10 45 46 11 47 48 12 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 41

1300 1250 1200 1150 280

300

320

340

T/K

Figure 2. Speed of sound, u, of: () methyl laurate, () ethyl laurate, () ethyl myristate and () ethyl oleate at atmospheric pressure.


Page 19 of 41

8

6

η / mPa·s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 1 27 28 2 29 30 3 31 32 4 33 34 5 35 36 6 37 38 7 39 40 8 41 42 9 43 44 10 45 46 11 47 48 12 49 50 13 51 52 14 53 54 15 55 56 16 57 58 59 60

Energy & Fuels

4

2

0 280

300

320

340

360

380

T/K

Figure 3. Dynamic viscosity, η, of: () methyl laurate, () ethyl laurate, () ethyl myristate and () ethyl oleate at atmospheric pressure.


Energy & Fuels

0.25 0.20 0.10

0.15 (ρlit-ρexp) / ρlit×100 / %

(ρlit-ρexp) / ρlit×100 / %

0.10 0.05 0.00

0.05

-0.05 0.00

-0.10

0

0

20

40

20

40

60

p / MPa

60

p / MPa

a)

b)

0.15

0.10 (ρlit-ρexp) / ρlit×100 / %

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 41

0.05

0.00

-0.05

-0.10 0

20

40

60

p / MPa

c) Figure 4. Comparison of the experimental densities with literature data for a) methyl laurate with () Tat and Van Gerpen19, () Pratas et al. 20 and () Zarska et al.,24 b) ethyl laurate with () Dzida et al.23 and c) ethyl myristate with () Ndiaye et al.16 and () Dzida et al.23 1 2 3 4 5 6 20 ACS Paragon Plus Environment

2.0

1.8

1.8

1.6

1.6

1.4

1.4

-1 kT / GPa

2.0

1.2 1.0

1.2 1.0

0.8

0.8

0.6

0.6

0.4

0.4

0

10

20

30

40

50

60

30

b)

1.8

1.8

1.6

1.6

1.4

1.4

1.2 1.0

0.6

0.6 0.4

30

40

50

60

50

60

40

50

60

1.0 0.8

0.4

40

1.2

0.8

20

20

a)

2.0

10

10

p / MPa

2.0

0

0

p / MPa

-1 kT / GPa

-1 kT / GPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

-1 kT / GPa

Page 21 of 41

0

10

20

30

p / MPa

p / MPa

c)

d)

Figure 5. The isothermal compressibility, κT, vs. pressure, p, for: a) methyl laurate, b) ethyl laurate, c) ethyl myristate and d) ethyl oleate at () 293.15 K, () 303.15 K, () 313.15 K, () 323.15 K,() 333.15 K, () 343.15 K, (►) 353.15 K, () 363.15 K, () 373.15 K, ( ) 393.15 K and ( ) 413.15 K. 1 2 3 4 5 6 7 8 21 ACS Paragon Plus Environment

Energy & Fuels

1.1

1.0

1.0

0.9

0.9 -3

αp / 10 K

-3

ap / 10 K

-1

-1

1.1

0.8

0.7

0.8

0.7

0

10

20

30

40

50

0.6

60

0

10

20

30

p / MPa

p / MPa

a)

b) 1.1

1.0

1.0

0.9

0.9

-3 -1 K

1.1

αp / 10

-3 -1 K

0.6

αp / 10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 1 36 37 2 38 39 3 40 41 4 42 43 5 44 45 6 46 47 7 48 49 8 50 51 9 52 53 10 54 55 56 57 58 59 60

Page 22 of 41

0.8

40

50

60

40

50

60

0.8

0.7

0.7

0.6

0.6 0

10

20

30

40

50

60

0

10

20

30

p / MPa

p / MPa

c) d) Figure 6. The isobaric thermal expansivity, αp, of a) methyl laurate, b) ethyl laurate, c) ethyl myristate and d) ethyl oleate at () 293.15 K,() 313.15 K, () 333.15 K, (▼)353.15 K, () 373.15 K, () 393.15 K and () 413.15 K.


Page 23 of 41

800 750 700

cp,m / J·mol-1·K-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 1 28 29 2 30 3 31 32 4 33 34 5 35 36 6 37 38 7 39 8 40 41 9 42 43 10 44 45 11 46 12 47 48 13 49 50 14 51 52 15 53 54 16 55 17 56 57 18 58 59 60

Energy & Fuels

650 600 550 500 450 300

320

340

T/K

Figure 7. Isobaric molar heat capacity, Cp,m, of: () methyl laurate, () ethyl laurate, () ethyl myristate and () ethyl oleate at atmospheric pressure.


Energy & Fuels

1 2 1 3 4 5 6 7 8 9 10 11 12 13 14 2 15 16 3 17 18 4 19 20 5 21 6 22 23 7 24 25 8 26 27 9 28 10 29 30 11 31 32 12 33 34 13 35 36 14 37 15 38 39 16 40 41 17 42 43 18 44 19 45 46 20 47 48 21 49 50 22 51 52 23 53 24 54 55 25 56 57 58 59 60

Page 24 of 41

Table 1. Sample information. Chemical name

CAS

Supplier

Purity mass

Purification

fraction

method

Methyl laurate

11-82-0

Sigma–Aldrich

≤ 0.995

None

Ethyl laurate

106-33-2

Sigma–Aldrich

≤ 0.98

None

Ethyl myristate

124-06-1

Sigma–Aldrich

≤ 0.99

None

Ethyl oleate

111-62-6

Sigma–Aldrich

Ph. EUR

None


Page 25 of 41

1 2 1 3 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 3 34 35 4 36 37 5 38 39 6 40 41 7 42 43 8 44 45 9 46 47 10 48 49 11 50 51 12 52 53 13 54 55 14 56 57 58 59 60

Energy & Fuels

Table 2. Comparison of experimental densities, ρ, speeds of sound, u, viscosities, η, and refractive indices, nD, with literature data at atmospheric pressure ρ/kg·m-3 exp. lit.

Component

T/K

Methyl laurate

298.15

865.23

303.15 308.15

861.30 857.37

298.15

858.15

303.15

854.26

308.15

850.36

298.15

856.97

303.15

853.19

308.15

849.41

298.15

865.23

303.15

861.60

308.15

857.97

Ethyl laurate

Ethyl myristate

Ethyl oleate

865.8025 865.2726 861.8025 857.90 25 858.5025 858.2532 858.1933 854.6025 854.3532 850.7025 850.4532 857.2025 857.1832 857.1033 853.4025 853.3932 849.6025 849.6232 866.9025 865.2432 863.2025 861.6232 859.5025 858.0032

η/mPa·s

u/m·s-1

nD

exp.

lit.

exp.

lit.

exp.

lit. 1.429826 1.431128 1.430129,30 1.430231 1.429028 1.427028

1332.90

1332.2627

2.7861

2.823725

1.4300

1314.36 1295.97

1313.78 27 1295.4427

2.4974 2.2535

2.535625 2.289325

1.4279 1.4258

1320.91

1321.0032

2.9862

3.015225

1.4294

1.422933 1.429534

1302.49

1302.6532

2.6777

2.707325

1.4273

1.427534

1284.26

1284.4832

2.4139

2.445525

1.4252

1.425534

1342.85

1342.6032

4.1452

4.188025

1.4340

1.433533 1.434034

1324.66

1324.3432

3.6726

3.720725

1.4319

1.432134

1306.64

1306.2332

3.2828

3.327825

1.4299

1.430234

1376.24

1378.5432

5.6740

6.023625

1.4481

1.448635

1358.43

1360.6732

4.9989

5.309425

1.4461

1340.81

1342.9832

4.4351

4.715625

1.4441


Energy & Fuels

1 2 1 3 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 3 22 4 23 5 24 25 6 26 7 27 8 28 9 29 10 30 11 31 32 12 33 13 34 14 35 15 36 16 37 17 38 18 39 40 19 41 20 42 21 43 22 44 23 45 24 46 25 47 26 48 49 27 50 28 51 29 52 30 53 31 54 32 55 56 57 58 59 60

Page 26 of 41

Table 3. Density, ρ, and speed of sound, u, of the examined methyl and ethyl esters at atmospheric pressure Methyl laurate ρ a/ ub/m·s-1 kg·m-3 288.15 873.09 1370.51 293.15 869.16 1351.62 298.15 865.23 1332.90 303.15 861.30 1314.36 308.15 857.37 1295.97 313.15 853.44 1277.76 318.15 849.51 1259.70 323.15 845.57 1241.81 328.15 841.63 1224.07 333.15 837.69 1206.49 338.15 833.74 1189.08 343.15 829.79 1171.91 a U(ρ)=0.09 kg·m−3 b U(u)=0.1 m·s-1 T/K

Ethyl laurate ρ a/ ub/m·s-1 kg·m-3 865.96 1358.22 862.05 1339.53 858.15 1321.00 854.26 1302.65 850.36 1284.48 846.46 1266.49 842.56 1248.62 838.66 1230.94 834.75 1213.41 830.84 1196.05 826.92 1178.87 823.00 1161.91

Ethyl myristate ρ a/ ub/m·s-1 kg·m-3 864.55 1379.84 860.76 1361.25 856.97 1342.85 853.19 1324.66 849.41 1306.64 845.64 1288.82 841.86 1271.14 838.08 1253.64 834.31 1236.31 830.53 1219.15 826.75 1202.18 822.96 1185.44

Ethyl oleate ρ a/ ub/m·s-1 kg·m-3 872.51 1412.32 868.87 1394.15 865.23 1376.17 861.60 1358.36 857.97 1340.73 854.34 1323.26 850.72 1305.94 847.09 1288.81 843.47 1271.83 839.84 1255.01 836.22 1238.38 832.59 1221.99


Page 27 of 41

1 2 1 3 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 3 27 4 28 5 29 6 30 31 7 32 8 33 9 34 35 10 36 11 37 12 38 39 13 40 14 41 42 15 43 16 44 17 45 46 18 47 19 48 20 49 50 21 51 22 52 23 53 54 24 55 56 57 58 59 60

Energy & Fuels

Table 4. Dynamic viscosity, η, and refractive index, nD, of the examined methyl and ethyl esters at atmospheric pressure Methyl laurate n Db ηa/mPa·s 288.15 3.545 1.43418 293.15 3.110 1.43208 298.15 2.786 1.42997 303.15 2.497 1.42786 308.15 2.254 1.42575 313.15 2.048 1.42362 318.15 1.865 1.42148 323.15 1.698 1.41943 328.15 1.562 1.41735 333.15 1.442 1.41525 338.15 1.340 1.41319 343.15 1.247 1.41104 348.15 1.165 353.15 1.089 358.15 1.020 363.15 0.958 368.15 0.901 373.15 0.855 a U(η) = 0.004 mPa·s b U(nD)= 5·10-5 T/K

Ethyl laurate n Db ηa/mPa·s 3.814 1.43363 3.342 1.43152 2.986 1.42942 2.678 1.42731 2.414 1.42520 2.191 1.42310 1.995 1.42096 1.827 1.41887 1.680 1.41680 1.549 1.41469 1.436 1.41262 1.335 1.41052 1.244 1.162 1.088 1.020 0.958 0.906

Ethyl myristate n Db ηa/mPa·s 5.421 1.43815 4.685 1.43608 4.145 1.43400 3.673 1.43192 3.283 1.42986 2.936 1.42778 2.666 1.42573 2.422 1.42366 2.212 1.42161 2.015 1.41957 1.867 1.41752 1.726 1.41550 1.600 1.487 1.386 1.294 1.211 1.143

Ethyl oleate n Db ηa/mPa·s 7.522 1.45221 6.430 1.45017 5.674 1.44814 4.999 1.44611 4.435 1.44409 3.928 1.44206 3.563 1.44005 3.222 1.43802 2.929 1.43602 2.650 1.43398 2.454 1.43201 2.259 1.43001 2.087 1.935 1.799 1.676 1.566 1.471


Energy & Fuels

1 2 1 3 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 3 21 4 22 5 23 6 24 7 25 8 26 9 27 10 28 29 11 30 12 31 13 32 14 33 15 34 16 35 17 36 37 18 38 19 39 20 40 21 41 22 42 23 43 24 44 25 45 46 26 47 27 48 28 49 29 50 30 51 31 52 32 53 54 33 55 34 56 35 57 36 58 59 60

Page 28 of 41

Table 5. The isentropic bulk modulus, βS, and the intermolecular free length, Lf, of the examined methyl and ethyl esters at atmospheric pressure 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

Methyl laurate βS / MPa Lf / 10-12 m 1640.00 1.5768 1587.88 1.6174 1537.20 1.6589 1487.95 1.7015 1440.02 1.7452 1393.44 1.7901 1348.10 1.8361 1304.04 1.8832 1261.20 1219.55 1179.06 1139.89

Ethyl laurate βS / MPa Lf / 10-12 m 1597.58 1.5976 1546.88 1.6387 1497.56 1.6807 1449.63 1.7239 1403.03 1.7681 1357.77 1.8134 1313.67 1.8600 1270.84 1.9077 1229.19 1188.72 1149.42 1111.35

Ethyl myristate βS / MPa Lf / 10-12 m 1646.2 1.57385 1595.08 1.61371 1545.40 1.65453 1497.17 1.69629 1450.27 1.73907 1404.72 1.78286 1360.36 1.82777 1317.26 1.87377 1275.35 1234.63 1195.08 1156.76

Ethyl oleate βS / MPa Lf / 10-12 m 1740.45 1.5306 1688.86 1.5683 1638.69 1.6067 1589.83 1.6461 1542.32 1.6864 1496.05 1.7276 1450.99 1.7698 1407.18 1.8129 1364.53 1323.01 1282.68 1243.60


Page 29 of 41

1 2 1 3 4 5 6 7 8 9 10 11 12 13 2 14 15 16 3 17 18 19 4 20 21 22 23 24 5 25 6 26 7 27 8 28 9 29 10 30 11 31 12 32 13 33 14 34 15 35 16 36 37 17 38 18 39 40 19 41 42 20 43 44 21 45 46 22 47 23 48 49 50 24 51 52 25 53 54 26 55 27 56 57 28 58 59 60

Energy & Fuels

Table 6. The parameters of the Vogel-Fulcher-Tammann (VFT) model

a

A B/K C/K

Methyl laurate -2.937778 699.1822 121.6821

Ethyl laurate -3.012537 753.4941 114.7339

Ethyl myristate -2.803554 723.2488 126.9956

Ethyl oleate -2.593533 718.8809 132.0481

AADa / % MDb / % Biasc / % σ d / mPa·s

0.199 0.530 -0.0002 0.006

0.193 0.627 -0.0004 0.008

0.236 0.593 -0.0003 0.011

0.309 0.785 -0.0007 0.020

AAD =

100 N ηiexp − ηical ∑ N i =1 ηiexp

 η exp − η cal MD = max 100 i exp i  ηi  exp N 100 ηi −ηical c Bias = ∑ N i =1 ηiexp b

N

d

σ=

∑ (η i =1

exp i

− ηical )

  , i=1,N 

2

N −m


Energy & Fuels

1 2 1 3 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 41

Table 7. Density of the examined methyl and ethyl esters at temperatures 293.15 to 413.15 K and pressures 0.1 to 60 MPa Methyl laurate

ρa/kg·m-3 Ethyl laurate

Ethyl myristate

Ethyl oleate

b

T /K 293.15

pc/MPa 0.1 1 5 10 15 20 25 30 35 40 45 50 55 60

869.1 869.7 872.2 875.3 878.3 881.3 884.1 886.8 889.5 892.1 894.5 896.9 899.3 901.5

861.9 862.5 865.1 868.2 871.3 874.2 877.1 879.9 882.6 885.2 887.7 890.1 892.4 894.7

860.8 861.3 863.8 866.8 869.8 872.6 875.4 878.1 880.7 883.2 885.7 888.0

868.8 869.3 871.7 874.6 877.4 880.1 882.8 885.4 887.9 890.3 892.6 894.9 897.1 899.2

857.0 857.5 860.1 863.1 866.2 869.1 871.9 874.7 877.3 879.9 882.4 884.8 887.2 889.4

865.2 865.7 868.1 871.1 873.9 876.7 879.4 882.1 884.6 887.1 889.5 891.9 894.1 896.3

853.2 853.8 856.3 859.5 862.6 865.6 868.5 871.3 874.0

861.5 862.1 864.6 867.6 870.5 873.3 876.1 878.8 881.4

298.15 0.1 1 5 10 15 20 25 30 35 40 45 50 55 60

865.2 865.8 868.4 871.5 874.6 877.6 880.5 883.3 886.0 888.7 891.2 893.7 896.1 898.4

858.0 858.6 861.3 864.5 867.6 870.6 873.5 876.4 879.1 881.8 884.4 886.9 889.3 891.6 303.15

0.1 1 5 10 15 20 25 30 35

861.3 861.9 864.5 867.8 870.9 874.0 876.9 879.8 882.6

854.1 854.8 857.4 860.7 863.9 867.0 870.0 872.0 875.7


Page 31 of 41

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

40 45 50 55 60

885.3 887.9 890.4 892.8 895.2

878.4 881.1 883.6 886.1 888.4

876.6 879.2 881.7 884.0 886.3

883.9 886.4 888.8 891.1 893.3

849.4 850.0 852.6 855.9 859.0 862.1 865.0 867.9 870.7 873.4 876.0 878.5 880.9 883.2

857.9 858.5 861.0 864.1 867.1 870.0 872.8 875.5 878.2 880.8 883.3 885.7 888.0 890.3

845.6 846.2 848.9 852.3 855.5 858.6 861.6 864.6 867.4 870.1 872.8 875.3 877.8 880.2

854.3 854.9 857.4 860.6 863.6 866.6 869.5 872.3 875.0 877.6 880.2 882.6 885.0 887.3

841.8 842.5 845.2 848.6 851.9 855.1 858.2 861.2 864.1 866.9

850.6 851.2 853.9 857.1 860.2 863.3 866.2 869.1 871.8 874.5

308.15 0.1 1 5 10 15 20 25 30 35 40 45 50 55 60

857.3 858.0 860.7 864.0 867.2 870.3 873.4 876.3 879.1 881.9 884.5 887.1 889.6 892.0

850.2 850.9 853.6 857.0 860.2 863.4 866.5 869.4 872.3 875.1 877.8 880.4 882.9 885.3 313.15

0.1 1 5 10 15 20 25 30 35 40 45 50 55 60

853.4 854.0 856.8 860.2 863.5 866.7 869.8 872.8 875.7 878.5 881.2 883.8 886.3 888.8

846.3 847.0 849.8 853.2 856.6 859.8 863.0 866.0 868.9 871.8 874.5 877.1 879.7 882.1

0.1 1 5 10 15 20 25 30 35 40

849.5 850.1 853.0 856.4 859.8 863.1 866.3 869.3 872.3 875.2

842.4 843.1 846.0 849.5 852.9 856.2 859.4 862.5 865.5 868.4

318.15


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

45 50 55 60

877.9 880.6 883.1 885.6

871.2 873.9 876.5 878.9

Page 32 of 41

869.6 872.2 874.7 877.1

877.1 879.6 882.0 884.3

838.0 838.7 841.5 845.0 848.4 851.7 854.8 857.9 860.8 863.7 866.4 869.1 871.6 874.0

847.0 847.6 850.3 853.6 856.8 859.9 862.9 865.8 868.7 871.4 874.0 876.6 879.0 881.4

834.3 834.9 837.8 841.4 844.8 848.2 851.4 854.5 857.6 860.5 863.3 866.0 868.6 871.0

843.4 844.0 846.8 850.1 853.4 856.6 859.6 862.6 865.5 868.3 871.0 873.6 876.0 878.4

830.5 831.2 834.2 837.8 841.3 844.8 848.1 851.3 854.3 857.3 860.1

839.7 840.4 843.2 846.7 850.0 853.3 856.4 859.4 862.4 865.2 867.9

323.15 0.1 1 5 10 15 20 25 30 35 40 45 50 55 60

845.5 846.2 849.1 852.7 856.1 859.5 862.7 865.9 868.9 871.8 874.6 877.3 879.9 882.4

838.5 839.2 842.1 845.8 849.3 852.7 855.9 859.1 862.2 865.1 867.9 870.7 873.3 875.8 328.15

0.1 1 5 10 15 20 25 30 35 40 45 50 55 60

841.6 842.3 845.3 848.9 852.5 855.9 859.2 862.4 865.5 868.5 871.4 874.1 876.8 879.3

834.6 835.3 838.3 842.0 845.6 849.1 852.4 855.7 858.8 861.8 864.7 867.5 870.2 872.7 333.15

0.1 1 5 10 15 20 25 30 35 40 45

837.6 838.4 841.4 845.2 848.8 852.3 855.7 859.0 862.1 865.2 868.1

830.7 831.4 834.5 838.3 842.0 845.5 849.0 852.3 855.5 858.5 861.5


Page 33 of 41

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

50 55 60

870.9 873.6 876.2

864.3 867.0 869.6

0.1 1 5 10 15 20 25 30 35 40 45 50 55 60

829.8 830.5 833.8 837.7 841.5 845.2 848.7 852.1 855.4 858.6 861.6 864.5 867.3 869.9

822.8 823.6 826.9 830.9 834.7 838.4 842.0 845.5 848.8 852.0 855.1 858.0 860.8 863.4

0.1 1 5 10 15 20 25 30 35 40 45 50 55 60

821.8 822.6 826.0 830.2 834.2 838.0 841.7 845.3 848.7 852.0 855.2 858.2 861.0 863.8

815.0 815.7 819.2 823.4 827.5 831.4 835.1 838.7 842.2 845.5 848.7 851.7 854.6 857.3

862.9 865.5 868.0

870.5 873.1 875.5

822.9 823.6 826.8 830.6 834.3 837.9 841.3 844.7 847.9 850.9 853.9 856.7 859.4 862.0

832.5 833.2 836.1 839.7 843.2 846.6 849.9 853.0 856.1 859.0 861.9 864.6 867.2 869.7

815.3 816.1 819.4 823.4 827.3 831.0 834.6 838.1 841.4 844.6 847.7 850.6 853.4 856.1

825.2 826.0 829.1 832.8 836.5 840.0 843.4 846.7 849.9 852.9 855.8 858.7 861.3 863.9

807.7 808.5 812.0 816.2 820.3 824.2 828.0 831.6 835.0 838.4 841.5 844.5

817.9 818.7 822.0 825.9 829.7 833.4 837.0 840.4 843.7 846.9 849.9 852.8

343.15

353.15

363.15 0.1 1 5 10 15 20 25 30 35 40 45 50

813.8 814.7 818.3 822.6 826.9 830.9 834.8 838.5 842.1 845.5 848.8 851.9

807.2 808.0 811.6 816.0 820.2 824.3 828.2 832.0 835.6 839.1 842.3 845.5


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

55 60

854.8 857.6

848.5 851.3

Page 34 of 41

847.4 850.2

855.5 858.2

799.8 801.0 804.7 809.1 813.4 817.5 821.4 825.2 828.8 832.2 835.5 838.6 841.6 844.4

810.3 811.5 814.9 819.1 823.1 826.9 830.6 834.2 837.6 840.9 844.0 847.0 849.9 852.6

784.6 785.8 789.8 794.7 799.4 803.9 808.2 812.3 816.2 819.9 823.5 826.8 829.9 832.9

795.7 797.0 800.7 805.3 809.6 813.8 817.9 821.7 825.4 829.0 832.3 835.5 838.5 841.4

769.4 770.4 774.9 780.3 785.5 790.4 795.1 799.6 803.8 807.8 811.6 815.1 818.5

781.3 782.3 786.5 791.5 796.3 800.9 805.3 809.5 813.4 817.2 820.8 824.2 827.4

373.15 0.1 1 5 10 15 20 25 30 35 40 45 50 55 60

805.5 806.8 810.6 815.2 819.6 823.8 827.9 831.8 835.6 839.1 842.5 845.7 848.8 851.6

798.9 800.1 804.0 808.6 813.1 817.4 821.5 825.4 829.2 832.8 836.2 839.4 842.5 845.4 393.15

0.1 1 5 10 15 20 25 30 35 40 45 50 55 60

789.5 790.8 795.0 800.1 805.0 809.7 814.1 818.4 822.5 826.3 829.9 833.4 836.6 839.7

783.0 784.2 788.5 793.6 798.6 803.3 807.8 812.1 816.2 820.0 823.7 827.2 830.4 833.4

0.1 1 5 10 15 20 25 30 35 40 45 50 55

773.5 774.6 779.3 784.9 790.3 795.5 800.4 805.1 809.5 813.6 817.5 821.2 824.6

767.0 768.1 772.9 778.6 784.0 789.2 794.2 798.9 803.3 807.5 811.4 815.1 818.5

413.15


Page 35 of 41

1 2 3 1 4 2 5 3 6 4 7 5 8 6 9 10 7 11 8 12 9 13 10 14 11 15 12 16 13 17 14 18 19 15 20 16 21 17 22 18 23 19 24 20 25 21 26 27 22 28 23 29 24 30 25 31 26 32 27 33 28 34 29 35 36 30 37 31 38 32 39 33 40 34 41 35 42 36 43 44 37 45 38 46 39 47 40 48 41 49 42 50 43 51 44 52 53 45 54 46 55 47 56 57 58 59 60

Energy & Fuels

60

827.8

821.7

821.5

830.4

a

Uc(ρ)=0.8 kg·m-3 (293.15 K ≤ T≤ 363.15 K) and 2.0 kg·m-3 (373.15 K ≤ T≤ 413.15 K) b U(T)=0.01 K c U(p)=0.05 MPa


Energy & Fuels

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Page 36 of 41

Table 8. Adjusted parameters of the modified Tammann-Tait equation and comparison criteria for the pure methyl and ethyl esters at temperatures 293.15-413.15 K an at pressures up to 60 MPa

a

b

c

a0 /kg·m-3 a1 /kg·m·K-1 a2/kg·m·K-1 b0 /MPa b1/MPa·K-1 b2/MPa·K-1 c0

Methyl laurate 1087.571 -0.708585 -0.125189×10-3 416.885 -1.40329 0.125193×10-2 0.853160×10-1

Ethyl laurate 1080.429 -0.713001 -0.110470×10-3 430.642 -1.48335 0.136683×10-2 0.869263×10-1

Ethyl myristate 1075.998 -0.715480 -0.65×10-4 424.903 -1.43783 0. 130776×10-2 0.859578×10-1

Ethyl oleate 1078.913 -0.707806 -0.306115×10-4 431.568 -1.42771 0.127513×10-2 0.856932×10-1

AADa / % MDb / % Biasc / % σ d / kg·m-3

0.009 0.077 -0.004 0.113

0.009 0.084 -0.004 0.117

0.008 0.051 -0.003 0.091

0.006 0.055 -0.003 0.082

AAD =

100 N ρiexp − ρical ∑ ρ exp N i =1 i

 ρ exp − ρ cal MD = max 100 i exp i ρi 

100 N ρiexp − ρical Bias = ∑ N i=1 ρiexp N

d

  , i=1,N 

σ=

∑(ρ i =1

exp i

− ρ ical )

2

N −m


Page 37 of 41

1 2 1 3 4 2 5 6 3 7 8 9 4 10 11 5 12 13 6 14 15 16 7 17 18 8 19 20 9 21 22 23 10 24 25 11 26 27 28 12 29 30 13 31 32 14 33 34 15 35 36 37 16 38 39 17 40 41 18 42 43 44 19 45 46 20 47 48 21 49 50 51 22 52 53 23 54 55 56 24 57 58 25 59 60

Energy & Fuels

ASSOCIATED CONTENT

Supporting Information. The following files are available free of charge. Figures showing schematic diagram of the experimental system used for measuring densities at high pressure, dependence of the refractive index and the isentropic bulk modulus on temperature at atmospheric pressure, comparison between density values obtained using DSA 5000 M densimeter and those measured using DMA HP densimeter, dependence of the density on temperature and pressure as well as dependence of the internal pressure on pressure. Tables with values of the derived thermodynamic properties for all of the studied esters at temperatures 293.15-413.15 K and pressures up to 60 MPa and the isobaric and isochoric molar heat capacities at atmospheric pressure.

AUTHOR INFORMATION

Corresponding Author *

Tel: +381113370523. Fax: +381113370387.E-mail: [email protected].

ACKNOWLEDGMENT The authors gratefully acknowledge the financial support received from the Research Fund of Ministry of Education, Science and Technological Development (project No 172063) of the Republic of Serbia, and the Faculty of Technology and Metallurgy, University of Belgrade.


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