Viscosity Measurements of Two Potential ... - ACS Publications

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Viscosity Measurements of Two Potential Deepwater Viscosity Standard Reference Fluids at High Temperature and High Pressure Hseen O. Baled,*,† Deepak Tapriyal,†,§ Isaac K. Gamwo,† Babatunde A. Bamgbade,†,∥ Mark A. McHugh,†,∥ and Robert M. Enick†,‡ †

U.S. Department of Energy, National Energy Technology Laboratory, Research & Innovation Center, Pittsburgh, Pennsylvania 15236, United States ‡ Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States § AECOM, NETL Site Support Contractor, Pittsburgh, Pennsylvania 15236, United States ∥ Department of Chemical and Life Science Engineering, Virginia Commonwealth University, Richmond, Virginia 23284, United States S Supporting Information *

ABSTRACT: This paper reports high-pressure viscosity measurements for Krytox GPL 102 lot K2391 and tris(2-ethylhexyl) trimellitate (TOTM). These two viscous liquids have recently been suggested as potential deepwater viscosity standard (DVS) reference fluids for high temperature, high pressure viscosity studies associated with oil production from ultradeep formations beneath the deepwaters of the Gulf of Mexico. The measurements are performed using a windowed, variable-volume, rolling-ball viscometer at pressures between 7 and 242 MPa and temperatures between 314 and 527 K with an expanded uncertainty of 3% at a 95% confidence level. The viscosity results are correlated using an empirical temperature/pressure-dependent function and a modified Vogel−Fulcher−Tammann (VFT) Equation. The present viscosity data for TOTM and Krytox GPL 102 lot K2391 are in good agreement with the available reported data in the literature at lower temperatures and pressures. The viscosity values of TOTM and Krytox GPL 102 lot K2391 are 9.5 mPa·s and 25 mPa·s, respectively, at 473 K and 200 MPa, whereas the desired DVS viscosity value at this condition is 20 mPa·s. Although the viscosity of Krytox GPL 102 lot K2391 is closer to the targeted value, a comparison of the present viscosity results with data obtained for lot K1537 indicates a very large lot-to-lot variation of the viscosity for this polydisperse perfluoropolyether oil, which represents a significant deficiency for a DVS.

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INTRODUCTION The global increase in oil consumption and the depletion of reserves has led to exploration of new oil resources and recovery from reservoirs exhibiting increasingly high-temperature, high-pressure conditions. Such harsh conditions are typically found in ultradeep formations of the Gulf of Mexico and remote arctic regions. In 2009, the International Association for Transport Properties (IATP) has initiated a project aimed at determining a high-pressure deepwater viscosity standard (DVS) with a nominal value of about 20 mPa·s at a temperature of 473 K and pressure of 200 MPa.1 (The DVS target was originally established at 20 mPa·s at a temperature of 533 K and pressure of 241 MPa, but the difficulty in attaining these conditions experimentally resulted in a reduction of temperature and pressure.) A suitable DVS reference fluid could be used for calibration and validation of viscometers and rheometers at high temperatures and high pressures. The desirable attributes of the high-pressure viscosity standard candidate include thermal stability, inertness, insensitivity to UV radiation, hydrophobicity, monodispersity, © 2016 American Chemical Society

lot-to-lot consistency, occurrence as a liquid at ambient conditions and commercial availability. Further, the candidate should be safe to use in the laboratory and it should be environmentally benign. DuPont’s perfluoropolyether oil Krytox GPL 102 was proposed by our team and several members of the high pressure transport property community as a viable DVS that met most of the aforementioned requirements. Polyfluoroether oils are liquids at ambient conditions that exhibit very high thermal stability and hydrophobicity. Recently, we reported the viscosity of the perfluoropolyether oil Krytox GPL 102 lot K1537 at pressures to 245 MPa and temperatures to 533 K using a windowed rolling-ball viscometer and a Couette rheometer.2 The National Energy Technology Laboratory (NETL) in Pittsburgh provided nine research groups in Special Issue: In Honor of Kenneth R. Hall Received: February 14, 2016 Accepted: June 17, 2016 Published: June 29, 2016 2712

DOI: 10.1021/acs.jced.6b00128 J. Chem. Eng. Data 2016, 61, 2712−2719

Journal of Chemical & Engineering Data

Article

Table 1. Specifications of Chemical Samples

a

chemical

source

lot no.

CAS no.

purity/wt %

Mw/g·mol−1

Krytox GPL 102 TOTM squalane

DuPont Sigma-Aldrich Sigma-Aldrich

K2391 MKBT5164 V BCBL8628 V

812693-47-3 3319-31-1 111-01-3

100 99 99

1720a 546.78 422.81

Approximate number-average molar mass provided by DuPont.

by an empirical temperature/pressure-dependent function and a modified Vogel−Fulcher−Tammann (VFT) equation.

Europe, Australia, South America, and North America with Krytox GPL 102 samples from lot K2391 for their studies of this fluid with their viscometers. Bair3 measured the viscosity of this Krytox lot at temperatures of 313, 343, 383, and 433 K and pressures to 850 MPa with falling cylinder viscometers and reported a deviation of greater than 10% between the viscosity measured for lots K1537 and K2391. The difference in the viscosity between the two lots can be attributed to the lot-to-lot variations in molecular weight distribution of this polydisperse polymer. Harris4 also measured the viscosity of the Krytox GPL 102 lot K2391 at temperatures between 273 and 368 K and pressures to 226 MPa using a falling body viscometer and reported an average deviation of 20% from the results obtained with the lot K15372 supporting the findings from Bair regarding the effect of compositional differences between the Krytox lots. Very recently Mylona et al.5 carried out viscosity measurements on the same Krytox GPL 102 lot K2391 in the temperature range 282 to 364 K and up to 20 MPa with a vibrating-wire viscometer, and the results obtained agree well with the measurements of Harris.4 Even though Krytox GPL 102 satisfies many of the requirements for a standard reference fluid,6 the results of the conducted series of viscosity measurements indicate that lot-to-lot variation of this polydisperse perfluoropolyether could be a major obstacle preventing its long-term acceptance as the DVS. NETL has acquired a large number of samples of Krytox GPL 102 lot K2391 in order to eliminate any lot-to-lot variations in chemical composition, and samples of this liquid are still available at no cost from the corresponding author. The rheology community is considering other DVS candidates, especially high purity liquids with a single molecular structure. Several monodisperse liquids that have garnered attention as DVS candidates include squalane,7−10 bis(2ethylhexyl)phthalate (DEHP),7 and di(2-ethylhexyl)sebacate (DEHS).11 These candidate fluids were primarily suggested to replace diisodecyl phthalate (DIDP) as a reference material because the commercial supplier reportedly ceased production of high purity DIDP. Unfortunately, these fluids exhibit low viscosity values relative to the DVS target.12 Recently, however, Diogo et al.13 proposed tris(2-ethylhexyl) trimellitate (TOTM) as a promising alternative to Krytox GPL 102. The authors performed vibrating-wire viscosity measurements on two different samples of TOTM at pressures to 100 MPa and temperatures between 303 and 373 K and obtained consistent results with the two different samples.14 The aim of the present paper is to present viscosity measurements with a windowed, variable-volume, Inconel rolling-ball viscometer for TOTM and Krytox GPL 102 lot K2391 at pressures to 242 MPa and temperatures between 314 and 527 K. The data thus obtained extend the pressure and temperature ranges of the available literature high-pressure data3−5,13,14 for these two fluids enabling a better judgment and evaluation of their potential as high viscosity reference fluids at high temperatures and high pressures. The results are described

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EXPERIMENTAL SECTION Materials. The polydisperse Krytox GPL 102 lot K2391 oil was purchased from DuPont through the distribution company ChemPoint. The tris(2-ethylhexyl) trimellitate (TOTM) and squalane, both of which are well-defined monodisperse compounds, were obtained from Sigma-Aldrich. All chemicals were used as received without further purification. The provenance and mass fraction purity of the chemical samples used in this study are given in Table 1. Mylona et al.5 measured the water content for the same sample of Krytox GPL 102 using Karl Fischer titration and reported undetectable levels of water. Rolling-Ball Viscometer. The windowed, variable-volume, rolling-ball viscometer used for the present viscosity measurements is described in detail elsewhere2,15,16 and only the main features are described here. The viscometer, constructed from Inconel 718, has an inside diameter (ID) of 1.5875 cm and a maximum working volume of 50 cm3. A ball made of Inconel 718 (to minimize the effects of temperature on the calibration constant) is used in this study. It has a diameter of 1.5796 cm (99.502% of the viscometer ID). A borescope is positioned against the window at the front end of the viscometer to confirm that only a single fluid phase exists and to verify that the ball is continuously rolling rather than sliding or becoming momentarily immobile during a measurement. The rolling speed of the ball is determined using a light detection system that consists of a fiber optic light source (Model LSX 24B, InterTest) and fiber optic cables (Model IF23SM900, Banner Engineering Corporation) attached to small sapphire windows secured in ports located radially on the viscometer. The light is detected by optic sensors (Model R55FVWQ, Banner Engineering Corporation) interfaced with a computer through a LabVIEW program to measure the roll time of a ball through one set of opposing ports. The desired operating pressure is obtained using a high-pressure generator (Model 37-5.75-60, High Pressure Equipment Company) to compress water that moves a floating piston sealed with an O-ring. The system pressure is measured using a pressure transducer (Model 345BWS, Viatran Corporation, accurate to within ±0.1% of full scale reading of 413.68 MPa). A type-K thermocouple (Omega Corporation) was used to measure the temperature of the fluid in the view cell. The thermocouple was calibrated (293 to 533 K) against a high precision thermometer (Medicus Health, 0.01 °C resolution, accurate to ±0.05 °C). The temperature of the viscometer was controlled with a precision temperature controller (Oakton Digi-Sense, 0.1 °C resolution, calibrated by InnoCal using methods traceable to NIST standards). The observed temperature variation for each reported isotherm is within ±0.3 K. The working equation16 for the calibration constant, k, of a rolling-ball viscometer is 2713


Journal of Chemical & Engineering Data k=

μ·v (ρb − ρfl )sin θ

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Article

RESULTS AND DISCUSSION The density data of Krytox GPL 102 lot K2391 and TOTM required to solve for viscosity values using eq 1 are obtained with eq 3, a modified Tait equation18 ρ − ρ0 p+B = C log10 ρ p0 + B (3)

(1)

where k has units of (m3/s2), μ is the viscosity (Pa·s), v is the terminal velocity (m/s) of the rolling ball, ρb and ρfl are the ball density and fluid density (kg/m3), respectively, and θ is the angle of inclination measured with a digital protractor (Model Pro 3600, Applied Geomechanics, accurate to within ±0.1°). The viscometer is calibrated with squalane. The calibration data cover temperatures between (313 and 473) K, pressures between (7 and 200) MPa, and viscosity values between (1 and 374) mPa·s. Viscosity data for squalane are obtained from Harris7 and Schmidt et al.9 Density data of squalane required for the calibration are obtained from Harris7 and Bamgbade et al.17 The calibration results are shown in Figure 1, which

where ρ is density, p is pressure, ρ0 is density at p0 = 0.1 MPa, and B and C are parameters for an isotherm determined by fitting eq 3 to high pressure densities measured by Bamgbade et al.19 The employed density data cover pressures to 270 MPa and temperatures between (315 and 521) K for Krytox GPL 102 and between (293 and 524) K for TOTM. The following equations are used to determine the values of ρ0 and B at a given temperature T 2

ρ0 =

∑ aiT i

(4)

i=0 2

B=

∑ biT i

(5)

i=0

The coefficients ai and bi are listed in Table 3. The average absolute percent deviation (AAPD) shown in Table 3 refers to Table 3. Parameters for the Best Fit of the Modified Tait equation

Figure 1. Rolling-ball viscometer calibration constant, k, at different pressures, p, measured with squalane at: ●, 313 K; ■, 343 K; ◆, 383 K; ▲, 423 K; ▼, 473 K.

presents the calibration constant values, k, as a function of pressure for each isotherm (the calibration data are listed in Table S1 of the Supporting Information). The pressure dependence reflects the decrease in the ball diameter and the simultaneous increase in the cell internal diameter with increasing pressure. Increasing temperature increases both the ball diameter and the tube inner diameter, and the resultant effect on the calibration constant is minimized by manufacturing the ball and cell from the same Inconel alloy. The calibration constant, k, is linearly correlated with the pressure for all isotherms, eq 2 k = a·p + b

313 343 383 423 473

4.64689 4.76913 4.93010 4.78033 4.86440

× × × × ×

10 10−4 10−4 10−4 10−4

1.1782 −0.6091 −1.3162 321.84 −0.6986 3.5394 0.223 0.17 0.10

1 n

n

∑ i=1

|ρi ,exp − ρi ,calc | ρi ,exp

·100 (6)

The AAPD values of the fit of the modified Tait equation to the experimental density data are 0.11% for Krytox GPL 102 lot K2391 and 0.17% for TOTM. The standard deviation of the absolute deviations is also given in Table 3. Tables 4 and 5 list viscosity data for Krytox GPL 102 lot K2391 and TOTM, respectively. The data are also illustrated in Figures 2 and 3. The standard uncertainties, u, are u(T) = 0.30 K, u(P) = 0.4 MPa, u(t) = 0.001 s, u(θ) = 0.1°. The estimated relative expanded uncertainty, Ur, in the reported viscosity data calculated by applying the law of error propagation20 to eq 1, is Ur(μ) = 0.03 at a confidence level of approximately 95% (coverage factor, k = 2). The viscosity data listed in Tables 4 and 5 are correlated by a nonlinear surface fit as a simultaneous function of temperature and pressure given by eq 7. This empirical correlation provides an excellent fit of the data collected in this study and allows a

Table 2. Parameters, a and b, Used in Equation 2 to Correlate the Calibration Results −4

TOTM

2.4748 −2.3029 7.0534 251.52 −0.8282 7.2162 0.200 0.11 0.13

AAPD =

(2)

a × 108/m3·s−2·MPa−1

Krytox GPL 102

the deviation of the experimental densities measured by Bamgbade et al.,19 ρi,exp, from values calculated with the modified Tait equation, ρi,calc,

where p is the pressure. The slope, a, and intercept, b, values are listed in Table 2.

T/K

coefficient a0·10−3/kg·m−3 a1/kg·m−3·K−1 a2·104/kg·m−3·K−2 b0·/MPa b1/MPa·K−1 b2·104/MPa·K−2 C AAPD/% δ/%

b × 108/m3·s−2 0.167256 0.165841 0.162417 0.161698 0.160889 2714



Article

Table 4. Viscosity Data for Krytox GPL 102 Lot K2391a T/K

p/MPa

μ/mPa·s

T/K

p/MPa

μ/mPa·s

T/K

p/MPa

μ/mPa·s

314.1 314.1 314.1 314.1 314.1 314.1 314.1 314.1 343.8 343.8 343.8 343.8 343.8 343.8 343.8 376.9 376.9 376.9 376.9 376.9

7.88 8.02 34.79 34.87 69.81 103.7 138.6 172.4 21.80 36.19 70.93 104.6 105.5 138.3 173.5 6.76 6.81 22.80 37.22 72.08

33.45 33.45 85.12 86.33 243.3 597.8 1444 3288 20.19 30.53 75.79 161.2 164.5 324.1 657.1 5.566 5.675 9.077 13.25 29.19

376.9 376.9 376.9 376.9 376.9 376.9 423.2 423.2 423.2 423.2 423.2 423.2 423.2 423.2 423.2 423.2 423.2 473.8 473.8 473.8

105.3 140.7 173.4 190.0 210.1 242.0 9.68 22.17 36.81 70.73 105.0 105.1 139.5 173.7 198.8 220.1 241.4 7.76 23.72 36.07

55.42 102.5 174.5 227.1 311.6 510.2 2.896 3.971 5.550 10.81 19.00 18.90 31.21 48.79 66.48 85.79 110.2 1.599 2.271 2.903

473.8 473.8 473.8 473.8 473.8 473.8 473.8 473.8 524.2 524.2 524.2 524.2 524.2 524.2 524.2 524.2 524.2 524.2 524.2

70.60 105.2 105.4 139.5 173.7 201.5 219.0 241.9 12.46 23.55 37.81 70.99 105.0 105.0 139.9 174.1 199.0 224.8 242.4

5.248 8.590 8.564 13.08 18.99 25.09 29.69 36.68 1.225 1.513 1.941 3.200 4.897 4.917 7.145 9.861 12.22 15.05 17.23

a

Standard uncertainties u are u(T) = 0.3 K, u(p) = 0.4 MPa, and the relative expanded uncertainty is Ur(μ) = 0.03 at a confidence level of approximately 95%.

Table 5. Viscosity Data for Tris(2-ethylhexyl) Trimellitate (TOTM) Lot MKBT5164 Va T/K

p/MPa

μ/mPa·s

T/K

p/MPa

μ/mPa·s

T/K

p/MPa

μ/mPa·s

315.1 315.1 315.1 315.1 315.1 315.1 315.1 347.1 347.1 347.1 347.1 347.1 347.1 347.1 347.1 347.1 387.5 387.5 387.5 387.5

8.71 23.09 36.55 69.62 71.42 104.2 138.8 9.18 22.49 36.42 70.16 70.37 104.1 138.5 173.5 219.9 11.78 22.08 36.11 70.65

92.64 125.0 163.5 301.3 310.8 540.6 934.0 22.72 28.88 36.54 62.43 62.32 101.1 159.1 244.9 420.8 7.262 8.542 10.48 16.60

387.5 387.5 387.5 387.5 387.5 428.6 428.6 428.6 428.6 428.6 428.6 428.6 428.6 428.6 477.8 477.8 477.8 477.8 477.8 477.8

72.75 104.7 140.1 173.4 215.4 9.40 21.67 36.94 70.47 105.4 139.5 172.3 203.2 237.6 11.62 23.68 37.69 37.76 70.98 105.5

17.21 25.32 37.04 51.68 77.27 3.143 3.632 4.460 6.643 9.700 13.20 17.63 22.51 29.74 1.649 1.916 2.232 2.235 3.227 4.336

477.8 477.8 477.8 477.8 477.8 477.8 527.4 527.4 527.4 527.4 527.4 527.4 527.4 527.4 527.4 527.4 527.4 527.4

106.0 139.3 174.2 196.8 219.3 240.8 10.41 23.11 36.43 69.91 105.2 105.7 139.0 172.9 200.7 201.6 223.7 241.6

4.336 5.743 7.352 8.536 10.02 11.62 1.015 1.161 1.333 1.790 2.466 2.469 3.097 3.835 4.578 4.601 5.224 5.761

a Standard uncertainties u are u(T) = 0.3 K, u(p) = 0.4 MPa, and the relative expanded uncertainty is Ur(μ) = 0.03 at a confidence level of approximately 95%.

calculated values with the surface fitting correlation, eq 7, μi,calc, for n data points

comparison of our data with literature data collected at different temperature and pressure conditions ⎛ ⎞ a0 + a1T + b1p + b2p2 + c1Tp ⎟ μ = exp⎜ 2 2 ⎝ 1 + a 2T + b3p + a3T + b4p + c 2Tp ⎠

AAPD =

(7)

The coefficients in eq 7 are given in Table 6 for both Krytox GPL 102 and TOTM. All digits should be used to get an accurate reproduction of the viscosity data. In Table 6, AAPD now refers to the average absolute percent deviation, eq 8, between experimental data obtained in this study, μi,exp, and

1 n

n

∑ i=1

|μi ,exp − μi ,calc | μi ,exp

·100 (8)

Figures 4 and 5 show the residuals for the eq 7 fit of the experimental viscosities presented in this work. The experimental viscosity data are also fitted to a modified Vogel−Fulcher−Tammann (MVFT) equation4,7 2715



Article

Figure 2. Viscosity measurements of Krytox GPL102 lot K2391: ●, 314.1 K; ■, 343.8 K; ◆, 376.9 K; ▲, 423.2 K; ▼, 473.8 K; ▶, 524.2 K. Lines represent viscosity results obtained with eq 7.

Figure 4. Residuals for the eq 7 fit of the measured viscosities for Krytox GPL102 lot K2391: ●, 314.1 K; ■, 343.8 K; ◆, 376.9 K; ▲, 423.2 K; ▼, 473.8 K; ▶, 524.2 K.

Figure 3. Viscosity measurements of tris(2-ethylhexyl) trimellitate (TOTM): ●, 315.1 K; ■, 347.1 K; ◆, 387.5 K; ▲, 428.6 K; ▼, 477.8 K; ▶, 527.4 K. Lines represent viscosity results obtained with eq 7.

Figure 5. Residuals for the eq 7 fit of the measured viscosities for TOTM: ●, 315.1 K; ■, 347.1 K; ◆, 387.5 K; ▲, 428.6 K; ▼, 477.8 K; ▶, 527.4 K.

Table 6. Coefficients for Nonlinear Surface Fit, Equation 7 coefficient a0 a1/K−1 b1/MPa−1 b2/MPa−2 c1/K−1·MPa−1 a2/K−1 b3/MPa−1 a3/K−2 b4/MPa−2 c2/K−1·MPa−1 AAPD % δ/%

Krytox GPL 102 4.5643 −8.8841 2.6682 −1.3877 1.3855 −1.1190 −1.7189 6.0034 −5.0838 1.3290 0.81 0.71

× × × × × × × × × ×

3

10 100 101 10−2 10−2 10−1 10° 10−3 10−3 10−2

Table 7. Coefficients for Vogel−Fulcher−Tammann Correlation, Equation 9

TOTM −1.0293 2.0019 −4.3691 −9.0507 2.8721 −5.4095 3.0301 −2.1705 2.5189 −1.9692 0.54 0.49

× × × × × × × × × ×

1

10 10−2 10−2 10−6 10−5 10−3 10−3 10−6 10−6 10−5

coefficient a b/MPa−1 c/MPa−2 d/K e/(K·MPa−1) f/(K·MPa−2) g/(K·MPa−3) T0/K AAPD % δ/%

−2.3979 7.8397 −2.8990 8.4039 4.6243 −9.3370 2.7080 1.6424 1.35 1.24

× × × × × × × ×

100 10−3 10−5 102 100 10−3 10−5 102

TOTM −2.9659 4.5358 −1.0980 9.9439 2.4188 −3.7070 8.5433 1.7868 0.80 0.56

× × × × × × × ×

100 10−3 10−5 102 100 10−3 10−6 102

Figures 6 and 7 show the residuals for the eq 9 fit of the experimental viscosities presented in this work. The performance of the nonlinear surface fit model, eq 7, is slightly better than that of the modified Vogel−Fulcher−Tammann equation, eq 9, and we recommend using eq 7 when interpolating within the experimental conditions of this work. However, eq 7 is an

μ = exp[a + bp + cp2 + (d + ep + fp2 + gp3 ) /(T − T0)]

Krytox GPL 102

(9)

The coefficients are given in Table 7. 2716



Article

For comparison with literature data, the surface fit correlation eq 7 and the modified Vogel−Fulcher−Tammann (MVFT) equation, eq 9, are used to interpolate the viscosity for Krytox GPL 102 and TOTM. Table 8 summarizes the literature sources for high pressure viscosity data along with the AAPD and the maximum deviation MD relative to the viscosities calculated with both eq 7 and eq 9 over the range of temperature and pressure for which these correlations were derived. When eq 7 is used for comparison with literature data, 82% of Krytox GPL 102 data points and 89% of TOTM data points have deviations less than 3%. If MVFT equation (eq 9) is employed instead of the surface fit correlation (eq 7), 92% of Krytox GPL 102 literature data points and 95% of TOTM data points have deviations less than 3%. Figure 8 shows that when eq 9 is employed for comparison of Krytox GPL 102 viscosity data, the data of Bair3 show Figure 6. Residuals for the eq 9 fit of the measured viscosities for Krytox GPL102 lot K2391: ●, 314.1 K; ■, 343.8 K; ◆, 376.9 K; ▲, 423.2 K; ▼, 473.8 K; ▶, 524.2 K.

Figure 8. Residuals for the eq 9 fit of the viscosities for Krytox GPL102 lot K2391. Bair:3 ■, 313 ; □, 343 K; ▲, 383 K; ▶, 433 K. Harris:4 ▼, 323 K; ◀, 343 K; ◆, 363 K. Mylona et al.:5 ◇, 298 K; ●, 323 K; ○, 353 K.

Figure 7. Residuals for the eq 9 fit of the measured viscosities for TOTM: ●, 315.1 K; ■, 347.1 K; ◆, 387.5 K; ▲, 428.6 K; ▼, 477.8 K; ▶, 527.4 K.

deviations ranging from −0.95% to +8.9% with an absolute percent deviation of 3.6% and most deviations occur at 433 K. Deviations for the data of Harris4 range from −4.6% to +0.04% with an absolute percent deviation of 1.5% and most deviations occur at 323 K. The deviations of the data reported by Mylona et al.5 range from −0.11% to −3.5% with an absolute percent deviation of 2.5%. Figure 9 shows that TOTM viscosity data of Diogo et al.13 deviate from +0.06% to +3.7% with an absolute percent

empirical correlation that has been derived by fitting the experimental data without any theoretical foundation, whereas the Vogel−Fulcher−Tammann equation, eq 9, has a theoretical basis,21,22 and hence eq 9 may allow safer extrapolation beyond the range of experimental data.

Table 8. Summary of Average Absolute Percent Deviation, AAP, and Maximum Deviation, MD, of Literature Data for Krytox GPL 102 Lot K2391 and Tris(2-ethylhexyl) Trimellitate, TOTM eq 7 authors

T/K

p/MPa

Bair3 Harris4 Mylona et al.5

313−433 273−368 298−353

0−850 0.1−226 0.1−20

Bair3 Diogo et al.13

313−423 303−373

0.1−1000 1−65

method

uncertainty/%

Krytox GPL 102 falling ball ±3 falling body ±2 vibrating wire ±2 TOTM falling body ±3 vibrating wire ±2 to ±2.6 2717

eq 9

AAPD

MD

AAPD

MD

4.6 1.6 2.7

9.8 4.5 4.4

3.6 1.5 2.5

8.9 4.6 3.4

2.7 1.3

6.2 3.9

3.0 1.9

6.2 3.7



Article

could be a serious obstacle toward its acceptance as a DVS. TOTM has an inherent advantage as a DVS in this respect because its structure is monodisperse.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00128. The calibration data of the rolling-ball viscometer presented in Figure 1 are listed in Table S1. (PDF)

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AUTHOR INFORMATION

Corresponding Author

* Tel.: +1 412 258 0503. Fax: +1 412 624 9639. E-mail: [email protected]. Notes

Figure 9. Residuals for the eq 9 fit of the viscosities for TOTM. Bair:3 ■, 313 K; □, 343 K; ▲, 373 K; ▶, 423 K. Diogo et al.:13 ▼, 303 K; ◀, 313 K; ◆, 323 K; ◇, 343 K; ●, 358 K; ○, 373 K.

The authors declare no competing financial interest. Samples from Krytox GPL 102 lot K2391 are still available at no cost from the corresponding author.

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deviation of 1.9%. Deviations for the data of Bair3 range from +0.35% to +6.2% with an absolute percent deviation of 3% and most deviations occur at 313 and 423 K. The present viscosity data for Krytox GPL 102 lot K2391 are on average 21% lower than those reported in our previous work2 for a different lot. This supports the findings from other researchers3,4 about the effect of compositional differences in Krytox GPL 102 lots. Although the Krytox is a very high purity polyfluoroether oil, it is a polydisperse polymer. Because it is inherently more difficult to replicate a molecular weight distribution from lot-to-lot and because molecular weight has a significant impact on viscosity, it is likely that these types of compositional variations led to the lot-to-lot differences in Krytox GPL 102 viscosity. In an effort to enable researchers in different laboratories to more fairly compare Krytox GPL 102 viscosity values measured with various apparatuses, the National Energy Technology Laboratory (NETL) is still distributing samples of the Krytox GPL 102 lot K2391 at no cost via requests to the corresponding author. The viscosity values of TOTM and Krytox GPL 102 lot K2391 calculated with eq 7 or eq 9 are 9.5 mPa·s and 25 mPa·s, respectively, at 473 K and 200 MPa, whereas the desired DVS viscosity value at this condition is 20 mPa·s.

ACKNOWLEDGMENTS This research was supported in part by an appointment to the National Energy Technology Laboratory Research Participation Program, sponsored by the U.S. Department of Energy and administered by the Oak Ridge Institute for Science and Education.

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REFERENCES

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CONCLUSIONS The viscosity of two potential viscosity reference fluids, Krytox GPL 102 and tris(2-ethylhexyl) trimellitate (TOTM), has been measured at temperatures to 527 K and pressures to 242 MPa, using a windowed, variable-volume, rolling-ball viscometer calibrated with squalane. The viscosity data presented in this work were correlated with an empirical 10-parameter surface fitting function and a modified Vogel−Fulcher−Tammann (MVFT) equation. The present results for both Krytox GPL 102 and TOTM are in good agreement with data from the literature and most of the data points are within the experimental uncertainty of 3.0%. The viscosity of Krytox GPL 102 lot K2391 is about 25% higher than the desired DVS viscosity value of 20 mPa·s at 473 K and 200 MPa, whereas the viscosity of TOTM is about 50% lower than the nominal value of DVS. Despite the remarkable thermal stability and hydrophobicity of DuPont’s Krytox perfluoropolyether oil, the effect of lot-to-lot polydispersity variations on viscosity 2718



Article

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