Viscosities of Fatty Acid Methyl and Ethyl Esters under High Pressure

Article pubs.acs.org/jced

Viscosities of Fatty Acid Methyl and Ethyl Esters under High Pressure: Methyl Myristate and Ethyl Myristate Matthieu Habrioux, Jean-Patrick Bazile, Guillaume Galliero, and Jean Luc Daridon* Laboratoire des Fluides Complexes et leurs Réservoirs, UMR 5150, Université de Pau, BP 1155, 64013 Pau Cedex, France ABSTRACT: Viscosity have been measured in ethyl myristate (C16H32O2) and methyl myristate (C15H30O2) at pressures up to 100 MPa along isotherms ranging from 293.15 to 403.15 K. The measurements were carried out by using a falling-body viscometer as well as a quartz crystal resonator viscometer. A comparison made between both sets of data reveals a good agreement with the different viscometers. Based on the data provided, high pressure correlations are proposed to represent viscosity in terms of density and temperature within the expanded experimental uncertainty. In addition a scaling method is given to relate the viscosity to a single thermodynamic quantity.

1. INTRODUCTION Biodiesels are promising fuels for use in compression ignition engines. While retaining comparable capacities of petroleumderived fuel regarding the heat of combustion and ignition delay time (cetane number), these substances exhibit additional environmental benefits. The use of biodiesel instead of fossil fuels results in a reduction of unburned hydrocarbons, carbon monoxide, and particulate matter. Sulfur dioxide exhausts from diesel engines are also substantially reduced as biodiesels do not contain any sulfur. Consequently, replacing either totally or partially petrodiesel with biodiesel has the potential to reduce the overall emissions of gases to the atmosphere and therefore improves air quality if engines are specially designed and optimized for working with biodiesels. The performances of compression ignition engines are mainly influenced by the way fuel is injected and atomized in the combustion chamber. An efficient injection leads to a fine spray and a good atomization that result in a more effective mixing of air and fuel and consequently to a more complete combustion. Fuel properties play a critical role in the spray characteristics and atomization process,1,2 and it is consequently essential to know the thermophysical properties of biofuels to adapt engines for working efficiently with biodiesels. Among all of the liquid properties, viscosity is the most important property that affects atomization.3,4 It acts on the spray pattern as well as on droplet size distribution in the spray. Viscosity also influences the flow within nozzle as well as the output flow rate. In addition, viscosity affects lubrication and leakage within the moving parts of the pump and injectors. Therefore, optimization of the formulation of biodiesels requires an accurate knowledge of biodiesel viscosity over a wide range of pressure as fuel injection can be carried out at fuel pressures up to 200 MPa in modern direct injection system. This property can be measured for each biodiesel or © XXXX American Chemical Society

evaluated from ester composition by using correlations and mixing rules5−7 when properties of pure esters are known. However, these predictive methods are so far limited to atmospheric pressure conditions as only few works have been dedicated to the measurement of biodiesels and fatty acid alkyl ester viscosities under high pressure. To address this limitation, we have initiated8 a measurement program of viscosity of pure fatty acid methyl (and ethyl) ester coming from the transesterification of fatty acids of chain length containing from 10 to 20 carbons. The present work aims at reporting experimental data of viscosity of liquid methyl myristate and ethyl myristate measured at pressures from atmospheric to 100 MPa and temperatures ranging from 293 to 353 K using two different techniques. The former method relies on the falling body principle in which viscosity is directly related to the time taken for a sinker to fall freely inside a vertical cylinder containing the liquid sample. The latter is based on thickness shear mode (TSM) quartz resonator technique which relates the electrical response of a quartz crystal resonator fully immersed in a liquid to the viscous friction at the interface between the liquid and the quartz.

2. EXPERIMENTAL SECTION 2.1. Materials. Table 1 provides the sample descriptions of methyl myristate (tetradecanoic acid, methyl ester, CAS: 12410-7, molar mass: 242.40 g·mol−1) and ethyl myristate (tetradecanoic acid, ethyl ester, CAS: 124-06-1, molar mass: 256.42 g·mol−1) studied in the present work. The source and Received: July 17, 2015 Accepted: December 21, 2015

A

DOI: 10.1021/acs.jced.5b00612 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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viscosity under high pressure is based on an oscillating quartz crystal working in the thickness shear mode. The apparatus has been described previously in detail.14 Its heart is a highly polished AT-cut quartz disk supplied by International Crystal Manufacturing Co. (Oklahoma City, Oklahoma, USA). It has a fundamental resonance frequency of 2 MHz and a blank diameter of 25.4 mm. Its electrodes were formed by vacuum evaporation of an adhesive layer of titanium of 10 nm thickness followed by a 100 nm thick layer of gold. To achieve measurements up to 100 MPa, the entire quartz resonator is immersed in the liquid located within a high pressure cell. This vessel is made up of a stainless steel autoclave cylinder closed at one end by a plug fitted with two electrical pin contacts used to hold the quartz crystal resonator into the cell. The external parts of pin contacts are connected to an Agilent E5071C network analyzer that measured the complex refection coefficient, S11 at the quartz contacts, and allows recording the conductance spectra of the resonator. The quartz resonator is excited not only at its fundamental frequency but at its odd harmonics ranging from 3 to 15. The resonance frequency f n and bandwidths Γn of each overtone n are determined by noting the maximum and the half-width at half-maximum (bandwidth) of the peak. For every temperatures, experiments started with a scan of the quartz crystal in vacuum in order to evaluate the properties of the unload quartz f 0,n Γ0,n. Measurement were then carried out with the resonator fully immersed in liquid. In this configuration, the oscillation of the quartz surface generates a laminar flow15 in liquid, which causes a decreases in resonance frequency (Δf n = f n − f 0,n) as well as an increase in dissipation (ΔΓn = Γn − Γ0,n) related to the square root of the density viscosity product. Although both properties are related to viscous damping, only dissipation was used to determine viscosity of methyl or ethyl myristate. In this method, viscosity is related to quartz crystal resonator measurements by using the working equation:14

Table 1. Details of the Chemicals Used in This Study chemical name

source

mole fraction puritya

ethyl myristate methyl myristate decane

Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich

0.99 0.99 0.994

a

Purity determined by the supplier by gas chromatography (GC). No further purification was applied.

purity of decane (CAS: 124-18-5) used to validate calibration in the falling body technique is also presented in Table 1. 2.2. Falling Body Viscometer. Viscosity measurements have been carried out by two different techniques to crosscheck the reliability of the data. The first one is based on a falling body technique. The basic principle of this method is the measurement of the falling time of a sinker through the studied liquid enclosed inside a vertical tube of known length. This method has been considered owing to the simplicity of its working equation that directly related the viscosity of the liquid to the falling time t, the difference in density between the sinker and liquid: η = K (ρS − ρL )t

(1)

The proportionality coefficient K is a parameter independent of pressure and specific of the instrument. It accounts for the geometrical dimensions of the apparatus. Its value is determined by calibration for each considered temperature using a self-reference method considering measurements performed at atmospheric pressure with a Ubbelohde tube connected to an automatic AVS350 Schott gerate analyzer. Prior to measurements with fatty acid methyl esters, the validity of the calibration was checked with a liquid of known viscosity and density. Decane was considered for such calibration using the viscosity data reported by Huber et al.9 Central to the apparatus is a high-pressure cylindrical cell described previously in detail.10 It contains an open cylindrical tube placed vertically and concentrically inside the cell in such a way that both its internal and external faces are surrounded by the pressurized fluid. The aim of this configuration is to reduce the deformation of the tube so as to maintain constant its internal diameter and keep valid the working equation whatever the pressure applied to the fluid. Two coils separated from each other by a distance of 150 mm were wrapped around the outer face of the cell for detecting presence of the sinker by a change of their inductance and thus measuring the fall time. The pressure of the liquid is raised by means of an external pump, and its value is measured with an HBM-P3M pressure gauge with a standard uncertainty of 0.2 MPa at the maximum pressure. Both the viscometer and the pump are thermoregulated by an external circulating fluid. The temperature of the viscometer is regulated by an external circulating fluid and is measured with a Pt100 with a standard uncertainty of 0.05 K in the temperature range investigated. Although the apparatus can operate up to 200 MPa, measurements have been limited to 100 MPa because of crystallization of these components under high pressure in this range of pressure.11 Density values have been taken from data given by Ndiaye et al.12 for both components. Taking into account the standard uncertainties in time, density, temperature, pressure, and calibration, the expanded uncertainty calculated by the root-sum-of-squares method13 with (k = 2) is estimated to be 0.02 η in the pressure range investigated. Quartz Crystal Resonator Viscometer. The second experimental technique used for the measurement of liquid

⎞2 πZq 2 ⎛ cexp ηL = ⎜ ⎟ 4ρL f0 3 ⎝ 1 + R interface ⎠

(2)

where f 0 is the fundamental resonance frequency of the unloaded quartz crystal, Zq is the acoustic impedance of AT-cut quartz, and cexp stands for the ratio:

cexp =

ΔΓn n

(3)

This property is theoretically independent of n16 and can be determined from measurements of any overtone apart from fundamental. The average of the third, fifth, and seventh was considered here to evaluate its value. Moreover, for each condition of pressure and temperature and for each harmonic, measurements were repeated 5 times leading to an average of 15 experimental measurements. ρL is the density of the investigated liquid. Its values have been also taken from data given by Ndiaye et al.12 for both components. Finally, Rinterface is a pressure independent coefficient related to the quality of the outer electrode surface. It is specific of each quartz crystal resonator and must be calibrated for each temperature. This calibration was done at atmospheric pressure for each temperature by self-reference considering measurements performed at atmospheric pressure using a Ubbelohde viscometer. The pressure is produced by a high pressure volumetric pump and measured by using a pressure gauge (Hotting Baldwin Messtechnik MVD 2510) fixed on the circuit B



Article

Table 2. Experimental Values of Viscosity ηFB Measured with Falling Body Viscometers at Temperatures T and Pressures p for the Liquid Methyl Myristate and Ethyl Myristatea

a

p/MPa

T/K

η/mPa·s

T/K

0.1013 20 40 60 80 100

303.15 303.15 303.15 303.15 303.15 303.15

3.51 4.43 5.51

313.15 313.15 313.15 313.15 313.15 313.15

0.1013 20 40 60 80 100

293.15 293.15 293.15 293.15 293.15 293.15

4.73 6.10 7.68

313.15 313.15 313.15 313.15 313.15 313.15

η/mPa·s Methyl Myristate 2.80 3.50 4.31 5.24 6.31 7.54 Ethyl Myristate 2.96 3.74 4.64 5.67 6.86 8.23

T/K

η/mPa·s

T/K

η/mPa·s

333.15 333.15 333.15 333.15 333.15 333.15

1.91 2.37 2.89 3.47 4.11 4.82

353.15 353.15 353.15 353.15 353.15 353.15

1.40 1.72 2.08 2.47 2.90 3.38

333.15 333.15 333.15 333.15 333.15 333.15

2.03 2.53 3.09 3.73 4.46 5.27

353.15 353.15 353.15 353.15 353.15 353.15

1.48 1.83 2.22 2.66 3.16 3.71

Standard uncertainties u are u(T) = 0.05 K, u(p) = 0.2 MPa, and the expanded uncertainties Uc (level of confidence = 0.95) is Uc(η) = 0.02η.

Table 3. Experimental Values of Viscosity ηQCR Measured with Quartz Crystal Resonator at Temperatures T and Pressures p for the Liquid Methyl Myristate and Ethyl Myristatea p/MPa

a

T/K

η/mPa·s

η/mPa·s

T/K

0.1013 10 20 30 40 50 60 70 80 90 100

303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15

3.51 3.95 4.45 4.95 5.53 6.11 6.79

313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15

0.1013 10 20 30 40 50 60 70 80 90 100

293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15

4.73 5.36 6.08 6.83 7.68

313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15

Methyl Myristate 2.80 3.15 3.50 3.91 4.33 4.79 5.26 5.74 6.29

Ethyl Myristate 2.96 3.34 3.71 4.15 4.63 5.10 5.67 6.22 6.89 7.56 8.14

T/K

η/mPa·s

T/K

η/mPa·s

333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15

1.91 2.14 2.37 2.61 2.88 3.16 3.46 3.76 4.08 4.46 4.81

353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15

1.40 1.57 1.74 1.92 2.11 2.29 2.50 2.71 2.92 3.14 3.40

333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15

2.03 2.30 2.54 2.82 3.13 3.44 3.76 4.08 4.48 4.86 5.25

353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15

1.48 1.65 1.84 2.03 2.24 2.44 2.66 2.91 3.14 3.41 3.66

Standard uncertainties u are u(T) = 0.1 K, u(p) = 0.02 MPa, and the expanded uncertainties Uc (level of confidence = 0.95) are Uc(η) = 0.02η.

3. RESULTS AND DISCUSSION

linking the pump to the measurement cell. It is calibrated in the full pressure scale with a standard uncertainty of 0.02 MPa. The temperature of the liquid is controlled by entirely immersing the cell in a thermoregulated bath (Huber CC410) filled with silicone oil, and the temperature is measured into the fluid with a standard uncertainty of 0.1 K by a platinum probe (Pt100, 1.2 mm diameter) housed in a metal finger. The expanded uncertainty (k = 2) in viscosity measurements including standard uncertainties due to density, temperature, pressure, and calibration was estimated by the root-sum-of-squares method13 to be 0.02 η up to 100 MPa.

The experiments were performed at temperature from 293.15 to 353.15 K and pressures up to 100 MPa. For lower temperatures, measurements were limited in pressure due to the conditions of crystallization. The viscosities measured every 10 MPa steps with the falling body viscometer are reported in Table 2, whereas Table 3 lists the viscosities measured with quartz crystal resonator. Data given for atmospheric pressure correspond to the measurement performed with Ubbelohde tube and used for calibration of quartz crystal resonators. These data at 0.1 MPa were fitted as a function of temperature by using a Vogel−Fulcher−Tammann17−19 like equation: C


Journal of Chemical & Engineering Data ⎡ η0,VFT = A exp⎢ ⎣

Article

B ⎤ ⎥ T − C⎦

(4)

whereas high pressure measurements were correlated as a function of both temperature T and relative pressure Δp = p − patm with the following equation: ⎛ ⎞ η ⎟ ln⎜⎜ ⎟ = DΔp + (E0 + E1T ) ⎝ η0,VFT ⎠ ⎛ Δp + F + FT + F T 2 ⎞ 0 1 2 ⎟ ln⎜ 2 + F T ⎝ F0 + FT ⎠ 1 2

Figure 1. Relative differences Δη/η = {η(cal) − η(exp)}/ η(exp) of the values η(cal) obtained from eqs 4−5 from experimental viscosities η(exp) as a function of pressure at T = 333.15 K. Red ▲, methyl myristate measured with falling body viscometer; red ○, methyl myristate measured with quartz crystal resonator viscometer; blue ◆, ethyl myristate measured with falling body viscometer; blue □, ethyl myristate measured with quartz crystal resonator viscometer.

(5)

After evaluating A, B, and C parameters based on a least-squares method, the six coefficients of eq 5 were estimated using experimental data measured by both techniques by minimizing the following objective function: 2 ⎛ ⎛ η ⎞ ⎛ η ⎞ ⎞ i ,exp ⎟ − ln⎜ i ⎟ ⎟ OF = ∑ ⎜ln⎜⎜ ⎟ ⎜η ⎟ ⎟ ⎜ η ⎝ ⎝ 0,VFT ⎠calc ⎠ 0,VFT ⎠ i ⎝ Nexp

Table 5. Deviations with Previous Reported Measurements at Atmospheric Pressure

(6)

Bonhorst et al.20 Gros and Feuge21 Gouw et al.22 Knothe and Steidley23 Ceriani et al.24 Pratas et al.25

Table 4. Parameters of eqs 1 to 3 for Methyl Myristate and Ethyl Myristate from 293.15 to 353.15 K and for Pressure Range 0.1−100 MPa and Relative Deviations Δη/η in Average (AD%), Absolute Average (AAD%), and Maximum Deviation (MD%) parameters

methyl myristate

ethyl myristate

A B C D E0 E1 F0 F1 F2 deviations with falling body values AD% AAD% MD% deviations with QCR values AD% AAD% MD%

7.414721 × 10−2 6.187846 × 102 1.426800 × 102 4.233497 × 10−3 4.651365 −1.178048 × 10−2 −1.145322 × 103 8.953038 −1.564810 × 10−2

5.966512 × 10−2 7.276455 × 102 1.267624 × 102 1.722290 × 10−4 9.872496 −2.249951 × 10−2 −3.740299 × 103 5.043750 −9.906750 × 10−3

0.1 0.3 1.0

0.06 0.3 1.5

−0.01 0.2 0.8

0.05 0.4 1.2

T/K range

reference

The values of the nine coefficients determined in this way are listed in Table 4 along with the average deviation, the average

Shigley et al.26 Gros and Feuge27 Knothe and Steidley28 Pratas et al.29

Methyl Myristate 293−333 348 293−343 313 293−343 293−353 Ethyl Myristate 308−368 348 313 283−353

AAD%

MD%

0.8 1.4 1.4 0.5 2.7 1.6

1.6 1.4 2.0 0.5 6.3 2.0

0.4 2.9 0.6 0.9

0.7 2.9 0.6 1.4

available at higher pressures. It can be observed that data are in good agreement with previous measurements. The maximum error observed is smaller than 2% with the exception of data reported by Ceriani et al.24 for methyl myristate that presents a maximum deviation higher than 6% and data of Gros and Feuge21 that deviate of 2.9% at maximum. It was previously observed8 that the reduced viscosity of methyl (and ethyl) decanoate can be related to a single thermodynamic quantity defined by the product of temperature and volume raised to the power of γ, an exponent related to the relative contribution of T and V. This scheme, named thermodynamic scaling,27−29 has been extended to methyl (and ethyl) myristate. For that purpose, the reduced viscosity was calculated. It is defined by

⎛ MN 2 ⎞1/6 η* = η⎜ 4 A 3 ⎟ ⎝ ρ (RT ) ⎠

absolute deviation and the maximum deviation with experimental data of both components. It can be noted from this table that the maximum deviation does not exceed the experimental error of both techniques (2%). Moreover, the plot in Figure 1 of deviation versus pressure at a fixed temperature shows that the deviations do not increase systematically with pressure whatever the technique used (quartz crystal resonator or falling body). This result highlights the consistency between both techniques. In order to confirm the reliability of the measurements, they were compared with data previously reported in the literature for the same components.20−26 However, this comparison reported in Table 5 was limited to atmospheric pressure as no data are

(7)

−1

where M (kg·mol ) correspond to the molar mass and NA (mol−1) to Avogadro’s constant. The density values needed for the estimation of η* were determined from speed of sound measurements reported by Ndiaye et al.12 The γ exponent was then determined for each components by plotting η* as a function of ργ/T and by estimating the value for which all measurements overlap in a single curve as can be seen in Figure 2. The optimal γ value is obtained by minimizing the difference between the experimental data and the values calculated by the following function: D



Article

that the deviations do not increase systematically with pressure at a fixed temperature (333.15 K). The maximum deviation observed never exceeds experimental error showing the performance of the scaling approach to correlate data within the experimental range with only three adjustable parameters.

4. CONCLUSIONS Viscosity measurements for methyl myristate and ethyl myristate are reported in this work over a temperature range between 303.15 and 353.15 K with pressure ranging from atmosphere to 100 MPa. The data were obtained by two independent techniques: falling body and quartz crystal resonator. Correlations proposed for representing data as a function of temperature and pressure correlate data within their experimental expanded uncertainties. Finally, a thermodynamic scaling method was given for representing viscosity measurements in terms of density and temperature within their experimental expanded uncertainties. This procedure allows correlating viscosity measurements viscosity with only three parameters. These data and correlations make a contribution to set up a common database integrating all thermophysical properties of pure fatty acid methyl (and ethyl) ester needed for designing injection systems in compression ignition engines.

Figure 2. Reduced viscosity η* versus ργ/T. △, methyl myristate measured with falling body viscosimeter; red ▲, methyl myristate measured with falling body viscometer; ○, methyl myristate measured with quartz crystal resonator viscometer; blue ◆, ethyl myristate measured with falling body viscometer; □: ethyl myristate measured with quartz crystal resonator viscometer.

ργ 1 T = a0 + a1 γ + a 2 η* ρ T

(8)

where the parameters a0, a1, and a2 are adjusted for each γ value. The optimal γ values obtained in this way are listed in Table 6 as well as the parameters a0, a1, and a2. The deviations

■

Table 6. Parameters of eq 8 for Methyl Myristate and Ethyl Myristate from 293.15 to 353.15 K and for Pressure Range 0.1−100 MPa and Relative Deviations Δη/η in Average (AD %), Absolute Average (AAD%), and Maximum Deviation (MD%) parameters γ a0 a1 a2 AD% AAD% MD%

methyl myristate

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

ethyl myristate

The authors declare no competing financial interest.

4.55 4.42 −1.017665 × 10−1 −1.037047 × 10−1 6.746280 × 109 2.711940 × 109 4.080590 × 10−13 1.032880 × 10−12 Deviations with Experimental Values 0.1 0.1 0.4 0.4 1.2 1.9

■

REFERENCES

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added in Table 6 show a good agreement between experimental and calculated viscosities despite the limited number of parameters (3). Moreover, it can be observed from Figure 3

Figure 3. Relative differences Δη/η = {η(cal) − η(exp)}/ η(exp) of the values η(cal) obtained from the thermodynamic scaling (eq 8) from experimental viscosities η(exp) as a function of pressure at T = 333.15 K. Red ▲, methyl myristate measured with falling body viscometer; red ○, methyl myristate measured with quartz crystal resonator viscometer; blue ◆, ethyl myristate measured with falling body viscometer; blue □, ethyl myristate measured with quartz crystal resonator viscometer. E



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Viscosities of Fatty Acid Methyl and Ethyl Esters under High Pressure

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