Measurements of the Viscosity of Krytox GPL102 Oil in the

Jul 14, 2015 - (4) In these two cases there has not yet been a critical review of a body of data from a variety of laboratories. .... Figure 1. Percen...
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Measurements of the Viscosity of Krytox GPL102 Oil in the Temperature Range (282 to 364) K and up to 20 MPa Sofia K. Mylona,† Marc J. Assael,*,† Lefteris Karagiannidis,‡ Panagiotis D. Jannakoudakis,§ and William A. Wakeham∥ †

Laboratory of Thermophysical Properties & Environmental Processes, Chemical Engineering Department, Aristotle University, Thessaloniki 54636, Greece ‡ SIGMA Consultants Ltd., 2 Patriarchou Ioakeim Street, Thessaloniki 54622, Greece § Laboratory of Physical Chemistry, Chemistry Department, Aristotle University, Thessaloniki 54124, Greece ∥ Department of Chemical Engineering, Imperial College London, London, SW7 2BY, United Kingdom ABSTRACT: New measurements of the viscosity of a roundrobin sample of Krytox GPL102 oil are presented in the temperature range (282 to 364) K and up to 20 MPa. The measurements were performed in a vibrating-wire instrument with an uncertainty of 2 % (at the 95 % confidence level). The Newtonian behavior of Krytox GPL102 oil was confirmed by examining the relationship between shear stress and strain. Finally, a scheme based on considerations of the hard-sphere theory of the liquid state was employed successfully to correlate all of the present measurements within 2.5 % (at the 95 % confidence level).

1. INTRODUCTION Deeper drilling for hydrocarbon fuels has enhanced the need for reference values of the viscosity of liquids for the purpose of calibrating industrial viscometers. For this reason, the International Association for Transport Properties, IATP (former Subcommittee on Transport Properties of the International Union of Pure and Applied Chemistry), prompted by the work of late Dr. Anthony Goodwin, has instigated a project on the “Investigation of a New High-Viscosity Standard”. To date several studies have been performed within this project: (a) In 2008, di-isodecyl phthalate (DIDP, C6H4(COOC10H21)2) was proposed as an industrial standard reference liquid for the calibration of viscometers operating in the viscosity range (50 to 125) mPa·s at the temperatures of (293.15, 298.15, and 303.15) K with an uncertainty of ± 1 % (at the 95 % confidence level).1 The recommendation was based upon a critical review of measurements carried out in a number of laboratories explicitly for this purpose. (b) In 2013, a viscosity reference correlation for squalane, covering the viscosity range (3 to 118) mPa·s, and valid from (273 to 373) K at 0.1 MPa with an uncertainty of ± 1.5 % (at the 95 % confidence level), was proposed.2 This atmospheric pressure reference correlation, was subsequently extended in 2014, to pressures up to 200 MPa and temperatures up to 473 K.3 Again the correlation was based upon a critical review of experimental data. In an attempt to find other viscosity reference fluids in 2013 we reported atmospheric−pressure viscosity measurements on © XXXX American Chemical Society

two other moderately viscous liquids: bis(2-ethylhexyl) sebacate (DEHS), and bis(2-ethylhexyl) phthalate (DEHP). These fluids cover viscosities (3 to 31) mPa·s and (6 to 110) mPa·s with corresponding temperature ranges (284 to 358) K and (288 to 354) K, respectively.4 In these two cases there has not yet been a critical review of a body of data from a variety of laboratories. Another possible candidate liquid proposed by IATP is Krytox GPL102 oil, a mixture of polyperfluoroethers, with the general formula F-(CF(CF3) CF2O)n-CF2CF3, n = 9.528, that approximates the industrial requirement for a reference liquid with a nominal viscosity of about 20 mPa·s at a temperature of 473 K and a pressure of 200 MPa; conditions encountered deep-water crude-oil deposits of light oils.5 Although it satisfies many of the conditions for a standard reference fluid,1 Krytox GPL102 oil does have the disadvantage that samples produced in different lots may have slightly different distribution of polymer chain length in samples notwithstanding their freedom from other contaminants. This means that the viscosity of different lots may show a variation in the absolute viscosity. Hence, a round-robin comparison of high-pressure viscosity measurements on a specific sample drawn from a particular lot was initiated by a group of laboratories worldwide, employing a variety of viscometric techniques. Special Issue: Memorial Issue in Honor of Anthony R. H. Goodwin Received: May 16, 2015 Accepted: July 3, 2015

A

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oethers (Karl Fischer titration indicated undetectable levels of water, quantitative IR measurements revealed no detectable hydrocarbons, and ICP indicated the presence of metals only in ppm concentrations). The sample was used as received (see Table 1).

For the results of such a series of measurements to have validity as a standard reference value for viscosity, the manufacturers of the material need to maintain stocks of this particular lot, which has not yet been agreed. Nevertheless, the material may be useful for calibration of viscometers over a range of pressure because the effect of the precise polydispersity matters less for the pressure dependence than for the absolute value. The viscosity measurements performed in this work are part of the aforementioned study and carried out on round-robin Krytox GPL102 oil sample. The measurements were performed in a vibrating-wire viscometer operating in the transient decay mode, in the temperature range (282 to 363) K and up to 20 MPa. Furthermore, to confirm the Newtonian behavior of the liquid, a coaxial cylinder Haake Rotovisco viscometer was employed for additional measurements over the same temperature range and at atmospheric pressure.

Table 1. Sample Information Table chemical name Krytox GPL102 Oil

source lot number

initial mole fraction purity

purification method

1.000

none

DuPont lot K2391

The density values employed for the analysis of the measurements, and shown in the following tables, were calculated using a Tait equation of state based on Comuñas et al.7 measurements, made to 120 MPa between (278.15 to 398.15) K for the same lot of the sample. The correlation presents an AAD of 0.01 % and a maximum deviation of 0.05 %. It should however be noticed that, although the density measurements of Comuñas et al.7 were performed up to 120 MPa, there were only few measurements between (0.1 and 20) MPa. Hence the quoted uncertainty might be larger in the lower pressure range. For the density at atmospheric pressure, an equation proposed by Harris,8 derived from his own measurements performed with an AAD of 0.02 % (at the 95 % confidence level), was employed. These measurements agree excellently with the measurements of Comuñas et al.7 Table 2 contains the viscosity measurements performed at 0.1 MPa. The measurements were fitted for interpolation purposes to the equation

2. EXPERIMENTAL SECTION 2.1. Vibrating-Wire Viscometer. The vibrating-wire instrument employed for the present measurements has been described elsewhere.4,6 Thus, it will only be very briefly described here. The vibrating wire is made of a 300 μm diameter tungsten drawn wire with a length of 50 mm and a transverse fundamental resonant frequency in vacuo of about 1 kHz. Constant tensioning of the wire is achieved by keeping the wire-end supports separated by two 3 mm-diameter tungsten rods. The oscillations of the wire are induced electromagnetically and detected in a similar fashion. The magnets, goldplated to avoid chemical attack, are made from samarium− cobalt and produce a magnetic field of about 1 T at the wire. The oscillations are initiated by applying two pulses of current of opposite sign through the wire. Following initiation of the motion, the signal induced in the vibrating wire is observed as it decays with a bridge in which the wire forms one arm. The outof-balance signal, amplified by 30 000 times, is then observed with an A/D converter coupled to a microcomputer. This configuration enables sampling of the oscillating signal at a rate of 50 kHz with a resolution of 12 bits. Since the frequency of the oscillation is about 1 kHz, one obtains roughly 50 points per cycle of the wire’s motion. The viscometer is suspended from the upper closure inside the pressure vessel, which is itself contained in a temperature controlled bath. The temperature of the pressure vessel is recorded by two platinum resistance thermometers W85K3 (Degussa, Germany), one placed at its top and the other at its bottom. Both thermometers have been calibrated against a Class I platinum resistance thermometer (Tinsley, UK) according to ITS 90. The error in the reported temperature is less than ± 20 mK. The vibrating-wire viscometer was employed as an absolute instrument. Tests were carried out to ensure that the instrument operated in accordance with the theory of the instrument in all respects. An analysis of the uncertainties involved is described elsewhere,4,6 indicating that the instrument operates with an uncertainty of ± 1.5 % in the reported viscosity (at the 95 % confidence level). The round-robin sample of Krytox GPL102 oil (lot K2391) (CAS No.: 812693-47-3 number-average molar mass 1.72 kg· mol−1), was manufactured by DuPont and was purchased by the NETL (National Energy Technology Laboratory, US Department of Energy) from a distribution company ChemPoint. Its composition is quoted as ∼100 % polyfluor-

⎛ ⎞ 1030 ⎟ η(T )/(mPa· s) = 0.05089exp⎜ ⎝ T /K − 148.5 ⎠

(1)

Table 2. Measurements of the Viscosity of Krytox GPL102 Oil Lot K2391 as a Function of Temperature at 0.1 MPaa T/K

ρ/kg·m−3

η/mPa·s

282.961 293.160 298.010 302.944 313.896 323.459 323.576 333.477 343.214 353.177 353.069 363.637

1883.9 1865.0 1855.9 1846.7 1826.1 1808.0 1807.8 1788.9 1770.3 1751.2 1751.4 1731.0

107 62.8 50.5 39.4 26.1 18.4 18.2 13.1 10.0 7.74 7.79 6.13

a

Standard uncertainties u are u(T) = 0.02 K and u(ρ) = 0.02 %,8 and the combined expanded uncertainty Uc is Uc(η) = 2 % (level of confidence = 0.95).

The standard deviation (at the 95 % confidence level) of the measurements from the above equation is 2 %, slightly higher than the instrument’s uncertainty due to the difficulties associated with the high viscosity of this liquid. In Figure 1 the percentage deviations of the present viscosity measurements from the values obtained by eq 1 are shown. In the same figure the deviations of the measurements of Harris8 who also B

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Table 3. Measurements of the Viscosity of Krytox GPL102 Oil Lot K2391a

Figure 1. Percentage deviations of the viscosity measurements of Krytox GPL102 oil lot K2391 as a function of temperature at atmospheric pressure from the values calculated by eq 1: ●, this work (vibrating wire); ▲, this work (coaxial cylinder); ○, Harris.8

performed measurements on the same round-robin sample with a falling-body viscometer and a quoted uncertainty of 2 % (at the 95 % confidence level) are also shown. There is some weak evidence of systematic differences between the results obtained by the different techniques but overall the agreement is within the mutual uncertainties. Finally, our viscosity measurements with the coaxial-cylinder instrument that will be discussed in the next section, are included. Table 3 shows the viscosity measurements performed along the nominal isotherms (298.15, 323.15, and 353.15) K at pressures up to 20 MPa. To convert the experimental viscosity values, η(T,p) to values at a nominal temperature, η(Tnom,p), eq 2 was employed. Since this correction is smaller than 1 %, this process does not introduce any significant additional error. The measurements were fitted for interpolation purposes to the equation η(T , p)/mPa·s = C exp(E + F(p /MPa))

p/MPa

T/K

0.10 4.45 6.45 8.32 9.18 10.78 12.62 14.23 16.53 19.56

298.010 298.010 298.010 298.010 298.010 298.010 298.010 298.010 298.035 298.035

0.10 4.35 5.82 8.42 10.39 12.40 14.33 16.25 17.72 19.65

323.459 323.459 323.459 323.459 323.459 323.459 323.459 323.459 323.459 323.445

0.10 1.35 3.40 5.52 7.49 9.40 11.39 13.41 15.34 17.98

353.069 353.069 353.069 353.069 353.069 353.083 353.083 353.083 353.083 353.083

ρ/kg·m−3

η(T,p)/mPa·s

Tnom = 298.15 K 1855.4 50.5 1865.7 60.7 1870.2 66.0 1874.4 71.5 1876.2 72.8 1879.7 77.9 1883.5 84.0 1886.8 89.2 1891.4 97.8 1897.3 110 Tnom = 323.15 K 1807.4 18.4 1819.3 21.4 1823.2 22.9 1830.0 25.3 1834.9 26.8 1839.7 29.0 1844.3 30.2 1848.7 32.7 1852.0 34.9 1856.3 36.6 Tnom = 353.15 K 1751.0 7.79 1755.4 8.28 1762.4 8.74 1769.4 9.39 1775.5 10.1 1781.3 10.8 1787.1 11.5 1792.8 12.1 1798.1 12.9 1805.0 13.9

η(Tnom,p)/mPa·s 50.2 60.3 65.6 71.0 72.3 77.4 83.5 88.6 97.3 109 18.6 21.6 23.1 25.5 27.1 29.3 30.5 33.1 35.3 37.0 7.78 8.27 8.72 9.37 10.1 10.7 11.4 12.1 12.9 13.9

a

Standard uncertainties u are u(T) = 0.02 K and u(ρ) = 0.05 %,7 and the combined expanded uncertainty Uc is Uc(η) = 2 % (level of confidence = 0.95).

(2)

where C = 1 mPa·s, and the values of the constants E (−) and F (MPa−1), for each isotherm, are shown in Table 4. In the same table, the uncertainties u (at the 95 % confidence level) of the measurements from the above equation are also shown. In Figure 2 the percentage deviations of the present viscosity measurements for the three isotherms, from the values obtained by eq 2, are shown. In the same figure the deviations of the measurements of Harris8 who also performed measurements (at 323.15 K and (9.7 and 11) MPa) on the same round-robin sample with a quoted uncertainty of 2 % (at the 95 % confidence level) are also shown. All values agree with eq 2 within 2 %. 2.2. Coaxial-Cylinder Viscometer. For the aforementioned measurements to be valid, it is imperative that Krytox GPL102 oil behaves as a Newtonian liquid. Only in a Newtonian liquid is the viscosity constant, independent of the shear rate, and thus a plot of the shear stress against the shear rate is a straight line. To confirm this, a coaxial cylinder (Haake Rotovisco Rheometer, Model RV2) was employed for the measurements. The device is equipped with a stationary outer cylinder and a rotating inner cylinder and the sample fills the annular space. To calibrate the instrument the viscosity of squalane,2 and the viscosity of DIDP,6 both known with an uncertainty of 1.5 % (at the 95 % confidence level), were used at (288 and 303) K.

Table 4. Coefficients of eq 2 T/K

E

F/MPa−1

u/%

298.15 323.15 353.15

3.92104 2.92804 2.06131

0.0397 0.0353 0.0323

1.0 2.0 1.5

According to the equipment manufacturer the viscosity η is obtained from the relation

GS (3) n −1 −1 −1 where, G (mPa·s·scale ·grad ·min ) is the instrument factor characteristic of the type of measuring drive unit and sensor system, while n (min−1), is the actual number of revolutions per minute and S (scale·grad), is torque of every run. In addition to the viscosity, the shear stress, τ (Pa), and the shear rate, D (s−1), can readily be obtained. As already mentioned for a Newtonian fluid a plot of the shear stress against the shear rate is a straight line through the origin, and from the slope of this line, the viscosity of the fluid is obtained at the given temperature and pressure.9 η /(mPa·s) =

C

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Table 5. Coaxial-Cylinder Measurements of the Viscosity of Krytox® GPL102 Oil Lot K2391 as a Function of Temperature at 0.1 MPaa

Figure 2. Percentage deviations of the viscosity measurements of Krytox GPL102 oil lot K2391 as a function of pressure from the values calculated by eq 2: (○, 298.15 K; △, 323.15 K; □, 353.15 K), this work; ●, 323.15 K, Harris.8

In Figure 3 the experimental shear stress is plotted as a function of the shear rate at different temperatures. In the same

T/K

η/mPa·s

283.75 288.35 293.45 298.35 302.65 307.35 312.95 317.95 322.85 328.05 333.05 337.25 342.85 347.95 352.55 357.85 361.85

103 81.4 60.5 48.6 39.7 33.2 26.8 21.8 18.9 15.4 13.4 11.9 9.92 8.93 7.94 6.95 6.45

a

Standard uncertainty u is u(T) = 0.02 K, and the combined expanded uncertainty Uc is Uc(η) = 3 % (level of confidence = 0.95).

self-diffusion, and thermal-conductivity coefficient data over a wide range of temperatures and pressures. Using a consistent set of values for the close-packed volume V0, it was initially shown that, in the case of n-alkanes, the scheme provides a satisfactory correlation of dense fluid transport coefficient data,10,12 and it can thus be used with confidence to predict transport coefficients for these compounds under other conditions of temperature and pressure. The method was subsequently applied to simple organic molecular liquids11 and extended to n-alkane mixtures,17 aromatic hydrocarbons,13 nalkanols,14 and refrigerants,15 while recently its application to mixtures of alkyl benzenes with other hydrocarbons18 was investigated. It has been demonstrated that this scheme can lead to predictions of transport coefficients for these systems at pressures up to 600 MPa, with an uncertainty of ± 6 %. The scheme is based on the assumption that transport coefficients of real dense fluids, expressed in terms of the reduced volume V/V0 (where V is the molar volume), is directly proportional to values given by the exact hard-sphere theory.19 The proportionality factor, described as the roughness factor Rλ for the thermal conductivity and Rη for the viscosity, accounts for molecular roughness and departure from molecular sphericity. The original scheme was tested in the range 1.5 ≤ (V/V0) ≤ 5. Very recently Ciotta et al.20 proposed a modification of the original expression for the viscosity, allowing an extension of the scheme’s range to high viscosity fluids. This modification was successfully employed to correlate the viscosity and the thermal conductivity of ionic liquids.21 In this work we will employ the scheme as modified by Ciotta et al.,20 to correlate the viscosity of Krytox GPL102 oil. According to this scheme, it was found that the reduced coefficients for viscosity, η*, defined as

Figure 3. Shear stress and percentage deviations of experimental shearstress values from the fitted ones, as a function of shear rate at different temperatures.

figure, percentage deviations of experimental shear-stress values from the fitted ones, as a function of shear rate at different temperatures and 0.1 MPa, are also shown. The straight-line dependence indicates that Krytox GPL102 behaves as a Newtonian fluid. In Table 5 the viscosity measurements obtained by the coaxial-cylinder viscometer are shown. The uncertainty of these measurements is estimated to be 3 % (at the 95 % confidence level). The deviations of these measurements from the values calculated by eq 1 are shown in Figure 1. The agreement is within 2 %, which is considered excellent.

3. THEORETICAL SECTION During the 1990s, in a series of papers,10−15 a scheme based on the Enskog hard-sphere theory, as corrected by Alder et al.,16 was developed for the simultaneous correlation of viscosity, D

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η* = 6.035·108 1 (M /kg·mol−1)(R /J·mol−1·K−1)(T /K)

× ×

(η /μPa·s)(V /m 3·mol−1)2/3 Rη

(4)

is a function of the reduced molar volume Vr = V/V0, where V (m3·mol−1) is the molar volume, and V0 (m3·mol−1), is a characteristic molar volume of the liquid, weakly dependent on temperature (originally conceived as the close-packed volume). In the above equations, M (kg·mol−1), represents the molar mass and R the universal gas constant (= 8.3141 J·mol−1·K−1). Finally, parameter Rη, introduced for polyatomic molecules, accounts for deviations from the behavior of smooth hard spheres.10 According to this scheme,10−15 the aforementioned function was proposed to be universal for all liquids and given by

Figure 4. Percentage deviations of the viscosity measurements of Krytox GPL102 oil as a function of reduced volume, Vr, from the values calculated by the scheme of eqs 4 to 6: (●, 0.101 MPa; ◆, 298.15 K; ▲, 323.15 K; ■, 353.15 K), this work (vibrating wire); ○, this work (coaxial cylinders); ∗, Harris.8

7

log10(η*) =

∑ aηiV r‐i

(5)

i=0

excellent. In the same figure all the measurements of Harris8 are also shown. The agreement is again very good. It should be stressed that while eqs 4 to 6 are reliable for use within the range of temperature and pressure studied here their use outside of the range specified should be undertaken with care and not extended to very high pressures and temperatures where the model has not been tested.

10

In the original scheme, in order to derive the universal eq 5, data for monatomic gases were employed, and the equation referred to a range of η* < 50. As already mentioned, in 2014 Ciotta et al.20 proposed an extension to eq 5, based on highviscosity hydrocarbons, for η* < 2000; its coefficients are shown in Table 6. The equation was successfully tested in

3. CONCLUSIONS New measurements of the viscosity of a specific round-robin sample of Krytox GPL102 oil have been presented in the temperature range (282 to 364) K and up to 20 MPa. The measurements were performed in a vibrating-wire instrument with an uncertainty of 2 % (at the 95 % confidence level). The Newtonian behavior of Krytox GPL102 oil was confirmed by examining its shear stress vs shear strain behavior at shear rates up to 1200 s−1. Finally, a scheme based on considerations of the hard-scheme theory was employed to successfully correlate all present measurements within 2.5 % (at the 95 % confidence level).

Table 6. Coefficients of eq 5 i

aηi

0 1 2 3 4 5 6 7

0 5.14262 −35.5878 192.05015 −573.37246 957.41955 −833.36825 299.40932

■

correlating the viscosity of ionic liquids,21 in which case η* was up to 2000000. It should be noted that the original Ciotta et al.20 equation included a dilute-gas term; this was not included here as this term is negligible in the case of high-viscosity liquids. Employing the present experimental data, for Krytox GPL102 Oil lot K2391, the characteristic molar volume, V0 (m3·mol−1), and parameter Rη were optimized to best fit the data treating the liquids as if it consisted of a single molecular species. The parameter Rη was found equal to 3.3 ± 0.005, while

*Tel.: +30 2310 996163. Fax: +30 2310 996170. E-mail: [email protected]. Funding

The work described in this paper was carried out under the auspices of the International Association for Transport Properties. Partial financial support from the International Union of Pure and Applied Chemistry (IUPAC) under the framework of the Project No. 2012-051-1-100 is gratefully acknowledged.

Vo/m 3·mol−1 = 9.608376· 10−4 − 7.461234·10−7(T /K) + 6.016604·10−10(T /K)2

AUTHOR INFORMATION

Corresponding Author

Notes

(6)

The authors declare no competing financial interest.

■

Eqs 4 to 6 form a self-consistent set from which the viscosity at any temperature and density can be obtained. In Figure 4 the percentage deviations of the experimental data obtained in this work, from the values calculated by the scheme of eqs 4 to 6, are shown. As it can be seen in the figure, the scheme correlates all measurements performed in this work with an uncertainty of 2.4 % (at the 95 % confidence level), which is considered

ACKNOWLEDGMENTS The authors will also like to express their gratitude to Dr Isaac K. Gamwo (National Energy Technology Laboratory, US Department of Energy) and Professor Robert M. Enick (National Energy Technology Laboratory, US Department of Energy, and Swanson School of Engineering, University of E

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(19) Chandler, D. J. Chem. Phys. 1975, 62, 1358; Rough hard sphere theory of the self-diffusion constant for molecular liquids. J. Chem. Phys. 1975, 62, 1358−1363. (20) Ciotta, F.; Trusler, J. P. M.; Vesovic, V. Extended hard-sphere model for the viscosity of dense fluids. Fluid Phase Equilib. 2014, 363, 239−247. (21) Gaciño, F.; Comuñas, M. J. P.; Fernández, J.; Mylona, S. K.; Assael, M. J. Correlation and Prediction of Dense Fluid Transport Coefficients. IX. Ionic Liquids. Int. J. Thermophys. 2014, 35, 812−829.

Pittsburgh), for arranging the supply of the round-robin sample of Krytox GPL102 oil lot K2391.

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DOI: 10.1021/acs.jced.5b00421 J. Chem. Eng. Data XXXX, XXX, XXX−XXX