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In Pursuit of a High-Temperature, High-Pressure, High-Viscosity Standard: The Case of Tris(2-ethylhexyl) Trimellitate William A. Wakeham,*,† Marc J. Assael,‡ Helena M. N. T. Avelino,§,∥ Scott Bair,⊥ Hseen O. Baled,# Babatunde A. Bamgbade,# Jean-Patrick Bazile,∇ Fernando J. P. Caetano,§,◆ María J. P. Comuñas,○ Jean-Luc Daridon,∇ Joaõ C. F. Diogo,§ Robert M. Enick,¶ Joaõ M. N. A. Fareleira,*,§ Josefa Fernández,○ M. Conceiçaõ Oliveira,§ Tânia V. M. Santos,§ and Chrysi M. Tsolakidou‡ †

Imperial College London, Chemical Engineering Department, Prince Consort Road, London SW7 2BY, United Kingdom Chemical Engineering Department, Aristotle University, Thessaloniki 54636, Greece § Centro de Química Estrutural, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, Lisbon 1049-001, Portugal ∥ Instituto Superior de Engenharia de Lisboa, Á rea Departamental de Engenharia Química, Instituto Politécnico de Lisboa, Rua Conselheiro Emídio Navarro, 1, 1959-007 Lisbon, Portugal ⊥ Center for High-Pressure Rheology, George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0405, United States # U.S. Department of Energy, National Energy Technology Laboratory, Research & Innovation Center, Pittsburgh, Pennsylvania 15236, United States ∇ Laboratoire des Fluides Complexes et leurs Réservoirs-IPRA, UMR5150, CNRS/TOTAL/Université de Pau & Pays Adour, 64000 Pau, France ◆ Universidade Aberta, Rua da Escola Politécnica, 147, 1269-001 Lisbon, Portugal ○ Thermophysical Properties Laboratory, Nafomat Group, Applied Physics Department, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain ¶ ORISE Faculty Fellow at National Energy Technology Center, Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States ‡

S Supporting Information *

ABSTRACT: This paper presents a reference correlation for the viscosity of tris(2-ethylhexyl) trimellitate designed to serve in industrial applications for the calibration of viscometers at elevated temperatures and pressures such as those encountered in the exploration of oil reservoirs and in lubrication. Tris(2-ethylhexyl) trimellitate has been examined with respect to the criteria necessary for an industrial standard reference material such as toxicity, thermal stability, and variability among manufactured lots. The viscosity correlation has been based upon all of the data collected in a multinational project and is supported by careful measurements and analysis of all the supporting thermophysical property data that are needed to apply the standard for calibration to a wide variety of viscometers. The standard reference viscosity data cover temperatures from 303 to 473 K, pressures from 0.1 to 200 MPa, and viscosities from approximately 1.6 to 755 mPa s. The uncertainty in the data provided is of the order of 3.2% at 95% confidence level, which is thought to be adequate for most industrial applications.

1. INTRODUCTION Professor Ken Marsh believed profoundly in three aspects of the overall scientific endeavor that we attempt to bring together in this paper dedicated to his memory. First, he was a lifelong believer in the performance of high-quality measurements of the thermophysical properties of materials.1 Second, he recognized and championed the importance of the compilation of critically evaluated experimental data for the properties of a selected set © 2017 American Chemical Society

of standard reference materials that could be used in the calibration and validation of experimental methods of measurement.2,3 Special Issue: Memorial Issue in Honor of Ken Marsh Received: February 14, 2017 Accepted: April 12, 2017 Published: April 24, 2017 2884

DOI: 10.1021/acs.jced.7b00170 J. Chem. Eng. Data 2017, 62, 2884−2895

Journal of Chemical & Engineering Data

Article

Table 1. Characterization of the TOTM Used in this Work TOTM

CAS number

supplier

purity

sample

lot number

1,2,4-benzenetricarboxylic acid tris(2-ethylhexyl) ester or Tris(2-ethylhexyl)trimellitate

3319-31-1

Sigma-Aldrich

99%

A B C D

MKBH8084V MKBQ0304V MKBT5164V MKBX3929V

Finally, and importantly, he strove to have these standards adopted in industrial practice.4 In the context of this work, it is also important to appreciate the efforts Professor Marsh devoted to the work of the International Union of Pure and Applied Chemistry (IUPAC), where he was the Chairman of several commissions and committees over many years. At a meeting in Boulder, Colorado, USA of the International Association for Transport Properties (IATP) in 2009, Professor Marsh spoke strongly for a project devoted to the establishment of an industrial reference standard for the viscosity of fluids at combined high pressure and high temperature. In this paper we describe progress on a piece of this project concerning one particular reference material. This is an internal project conceived and implemented by IATP (the former subcommittee on Transport Properties of the Thermodynamics Commission of IUPAC) at its 2010 meeting in Santiago de Compostela, Spain (http://transp.cheng.auth.gr/index.php/iatp/2010). Professor Marsh continued to take an active interest in the project by attendance at its meetings and through his work with the late Dr. Tony Goodwin. We feel this report on our progress with this aspect of the project is a fitting tribute to Professor Ken Marsh. The interest in a standard reference fluid for liquid viscosity at high temperatures and high pressure was prompted by the increasing tendency within the oil extraction business toward operations in wells of greater depth either on- or offshore that are characterized by temperatures of around 473 K and pressures in excess of 200 MPa. As a consequence, IUPAC launched a project (No. 2012-051-1-100; May 15, 2013) in which several IATP members are participating. The additional desirable feature of such a reference fluid is that it should have a moderately high viscosity (∼20 mPa s) under these conditions. To be specific, the objective of the project was to determine a suitable standard reference material with a viscosity of 20 mPa s at 473 K and 200 MPa. At the time the project was conceived, there were no available fluids satisfying these conditions as well as all those features normally expected of a standard reference material such as low toxicity, ready availability, and uniformity from lot-to-lot from a manufacturer. During the overall IATP project to date, a number of reference fluids have been proposed and examined including DIDP,5−7 Squalane,8−10 and Krytox.11−14 In turn, each of these proposals has moved the project nearer to fulfillment of its objective. In this work, we report on the latest development with regard to the examination of the liquid 1,2,4-benzenetricarboxylic acid tris(2-ethylhexyl) ester (CAS-No. 3319-31-1 and EC-No. 222-020-0) or tris(2-ethylhexyl) trimellitate (TOTM). It was first proposed as a standard reference material some years ago,15,16 and the present paper summarizes the work on this material, which has been conducted most recently to establish this material as a suitable standard. We examine not only its viscosity directly but also the other physicochemical properties of the fluid that are relevant to either the suitability of the fluid as a reference material (the effect of impurities on properties or its Newtonian character) or using the fluid as a calibrant of viscometers such as its density and surface tension. Our particular

purpose here is to summarize the work that has been performed; the details of individual studies, which support the quality of the data set out here, will be published elsewhere by individual groups of authors.

2. CHARACTERIZATION OF THE TOTM SAMPLES USED IN THE PRESENT WORK Trimellitate esters generally have a low vapor pressure, are liquid over a large temperature range, and have high viscosities; these characteristics make them suitable for specialty lubricants and grease base stocks.15,17 TOTM is increasingly used in the polymer industry as a plasticizer and for that reason is now widely available throughout the world. According to its material safety data sheet (MSDS), which refers to the European Directive 67/548/EEC, TOTM is classified as a nonhazardous substance, although it is noted that special care should be taken if it is swallowed, inhaled, or when in contact with the skin or eyes.18 These features mean that TOTM is suitable from a safety point of view as a standard reference material. The normal freezing and boiling temperatures are 230 and 687 K, respectively.18 Four different lots of TOTM were used, all supplied by Sigma-Aldrich, with designated lot numbers MKBH8084V, MKBQ0304V, MKBT5164V, and MKBX3929V and product number 538140. These four lots were used in various components of the work summarized here and for each a certificate of analysis stated a purity higher than 99.0% (mass).19 Table 1 summarizes the main characteristics of the TOTM samples. 2.1. Thermal Stability Tests. As the conditions under which the reference material must perform are far from ambient, thermal stability tests of this material were made. Four samples of TOTM were used in the test on its thermal stability. The first, sample 0, was used as a reference and maintained throughout the tests at the temperature of the air in the laboratory (∼293 K). The three other samples were held in closed glass containers immersed in an oil bath at ∼473 K exposed to atmospheric air: samples 1−3 were held for approximately 17, 41, and 74 h, respectively, in an oil bath. Subsequently, the samples were analyzed by mass spectrometry using an LCQ Fleet ion trap mass spectrometer equipped with an electrospray (ESI) ion source (Thermo Scientific). Aliquots of the control sample (S0) and of three heated samples collected at different heating times (S1−3) were diluted in methanol and analyzed by direct infusion in the ESI positive ion mode. The optimized experimental conditions were as follows: ion spray voltage, +4.5 kV; capillary voltage, +5 V; tube lens offset, −75 V; sheath gas (N2), 20 arbitrary units; auxiliary gas (N2), 5 arbitrary units; capillary temperature, 250 °C. Collision ion dissociation (CID) experiments were performed to fully characterize the protonated species. Tandem mass spectra (MS2) were obtained with an isolation window of 2 u, 17% relative collision energy, and with an activation energy of 30 ms. The spectra typically correspond to an average of 20−30 scans and are recorded in the range between 100 and 700 u. Data acquisition and processing were performed using the commercial Xcalibur software. The ESI mass spectra for the four samples are shown in 2885



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Figure 1. (a) Mass spectra of four samples of TOTM; (b) tandem mass spectrum of the precursor ion m/z 547 of sample S3.

Figure 1a, and the results of the CID experiments are shown in Figure 1b. An analysis of the spectra shows that the four samples display similar ESI profiles, yielding an intense peak (R.I. 100%) at m/z 547 attributed to the protonated molecule of TOTM (MW 546.78 g/mol). The MS2 spectra of precursor ions m/z 547 are identical, and the MS2 spectrum for m/z 547 of S3 is shown in Figure 1b. The spectrum displayed three main peaks attributed to product ions with m/z 435, 323, and 305 formed by losses of C8H16 (−112 u), 2xC8H16 (−224 u), and C8H18O plus C8H16 (−242 u), respectively. The protonated molecule of TOTM when fragmented by CID in the ion trap mass analyzer displays similar fragmentation behavior to that observed in the EI

mass spectrum of TOTM available in the NIST database (http:// webbook.nist.gov/chemistry). These results indicate that TOTM maintains its structural integrity when exposed to temperatures on the order of 473 K for approximately 3 days at atmospheric pressure. Eastman Chemical Company states in its safety data sheet for TOTM having the same CAS number (3319-31-1) that the decomposition temperature is 673 K.20 It is also worth noting that minor changes in the color of aged samples were observed when the samples were heated in the presence of air. However, Baled et al.21 have made viscosity measurements up to 523 K (points up to 477 K contribute to the present reference viscosity correlation) and did not report any alterations in the TOTM samples. In addition, Bamgbade et al.22 2886



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The measurements of lot B spanned the same temperature interval and pressures from 5 to 68 MPa. The results have shown mutual agreement for lots A and B within a maximum deviation within ±0.015%. The data for lot C,24 obtained using a U-tube Anton Paar DMA HPM densitometer with a claimed uncertainty of 0.1% at a 95% confidence level at temperatures from 293 to 373 K and pressures up to 140 MPa, agree with the results for lots A and B within the uncertainty of the latter, the maximum deviation being 0.12%. Bazile et al.24 have also independently calculated the density of TOTM from their speed-of-sound measurements performed at temperatures from 293 to 373 K and at pressures up to 200 MPa on lot C. Speed of sound measurements can be used directly in the formulations of equations of state, can also be used to derive precise density data, and have been especially useful here in obtaining the density of the liquid at high pressures.24,26,27 The expanded uncertainty for speed of sound measurements within the 95% confidence level is 0.06% between 0.1 and 100 MPa and 0.2% between 100 and 200 MPa. The estimated uncertainty in the density at 95% confidence level is 0.2%. These independent measurements agree well with all the U-tube measurements mentioned earlier within their uncertainty.24 Again, it would seem that the effect of the variability of composition of samples among lots has an effect upon the density comparable with the uncertainty in the density measurements themselves. 3.1.1. Effect of Water Impurities on Viscosity. The effect of water impurities on the viscosity of TOTM was studied by Diogo et al.23 The study was performed directly on TOTM (lot A) samples containing various amounts of water; the water content was determined using a Karl Fischer 831 KF Coulometer from Metrohm. The viscosity of a similar water-bearing sample was measured using micro-Ubbelohde capillaries using an automatic Schott ViscoSystem AVS 440 measuring unit along two isotherms at 303 and 328 K. The authors estimated that the effect of water on the viscosity of TOTM was an approximately 0.4% decrease in viscosity for an increase of approximately 10−4 in mass fraction of water contamination of a sample of TOTM.23 These results confirm that the effect of water contamination on the viscosity of TOTM samples is small and readily characterized. Thus, correction of data that may be obtained using a contaminated TOTM sample is simply effected. It is, in fact, a rather smaller effect than that reported for another liquid previously proposed to be an industrial reference fluid with moderately high viscosity, namely, DIDP.6 3.2. Density Data. As we have pointed out, many experimental methods for the determination of viscosity require knowledge of the liquid density. Furthermore, and importantly, the correlation of the viscosity of TOTM proposed here makes use of the density as well as the temperature as the independent variables because it leads to a much simpler representational equation. As a consequence, the density data is required over the same temperature and pressure ranges for which we have the viscosity of liquid TOTM. In Table 2, we list the source, temperature, and pressure range as well as the nominal uncertainties of the sets of density data at atmospheric pressure as well as highpressure density data for TOTM that can be found in the literature. Most of the results have been obtained using vibrating U-tube densitometers from Anton Paar with one set of data obtained by Bair12 with a bellows volumometer and another by Bamgbade et al.22 using another variable volume cell. Bazile et al.24 have measured the density of TOTM using two different methods. They have carried out measurements by a vibrating

measured the density up to 523.5 K using a different view cell, and they also did not notice any changes in color or odor of the TOTM sample. Most recently, we have made viscosity measurements on samples before and after heating to 473 K for 3 days, and the results were identical within the experimental error. All these observations suggest that TOTM is sufficiently thermally stable to serve as a reference material for the conditions described.

3. THERMOPHYSICAL PROPERTIES OF TOTM Many instruments for the measurement of the viscosity of fluids require auxiliary information on other thermophysical properties of the material for an evaluation of the property from direct observables. For that reason, we have conducted studies of a variety of properties of TOTM, the results of which are set out in the following paragraphs. 3.1. Effect of Impurities on Viscosity and Density. Each lot produced by a manufacturer of a chemical entity has the potential to contain very slightly different and low levels of impurities. Furthermore, it is almost inevitable in industrial applications that a standard reference material used as a calibrant will come into contact with moisture, perhaps from the air, during some component of the process of preparing practical viscometers and densitometers for operation in the field. It is preferable if the effect on the properties caused by contamination by water vapor is not unduly large and that it can be wellcharacterized. The study of the effect of small differences in composition of samples with the same general purity level has been carried out by comparing the thermophysical properties of TOTM samples drawn from different lots of nominally the same material. The properties have been measured with identical methods or with methods characterized by identical measurement uncertainties. Diogo et al. have measured the viscosity of one lot of TOTM (designated here as lot A)15 up to 65 MPa and from 303 to 373 K using the vibrating wire technique in the forced mode of operation. The viscosity of a second lot (lot B) was measured using the same experimental method and the same equipment23 at pressures from 5 to 100 MPa and in the same range of temperatures. The expanded uncertainty of the former results,15 at a 95% confidence level, was estimated differently for three levels of viscosity, namely, as less than ±2% for viscosities up to 68 MPa s, less than ±2.6% for viscosities between 69 and 268 mPa s, and less than ±3% for higher viscosities. A comparison with the measurements performed on lot B23 has shown agreement within the mutual uncertainty claimed for the measurements of lots A and B, which may be seen in Figure 1 in section 3.1 of ref 23. The maximum deviation encountered was only 1.9% for the lowest temperatures.23 The typical differences recorded, which are systematic, are probably attributable to different levels of purity among the lots but are at a level below that which it is possible to describe the uncertainty in the reference data. Three different lots of TOTM have been subject to density measurements using Anton Paar U-tube instruments; they are lots A−C. Lot C was used by Bazile et al.24 for their density and speed of sound measurements and by Liñeira del Rió et al.25 for viscosity measurements. The measurements performed on lots A16 and B23 were performed using the same Anton Paar DMA HP densitometer and have an estimated uncertainty of ±0.2% at a 95% confidence level. The density measurements carried out on lot A covered a temperature interval of 293−373 K and at pressures up to 68 MPa. 2887



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Table 2. Measurements of the Density of Liquid TOTM

a

year

first author

ref. no.

temperature range/K

pressure range/ MPa

number of data

method

lot number

purity/%

nominal uncertaintya

1998 2014 2015 2015 2015 2015 2016 2016 2016

Lorenzi Diogo Diogo Avelino Bair Avelino Bamgbade Bazile Bazile

30 16 23 29 12 29 22 24 24

288−358 293−373 293−373 388−403 313−410 328−423 314−523 293−373 293−373

0.1 0.1−68 0.1−68 0.1−68 0.1−350 0.1−68 3.5−270 0.1−200 0.1−140

10 66 16 22 18 50 79 182 135

U-tube U-tube U-tube U-tube Bellows piezometer U-tube Variable-Volume Speed of Sound U-Tube

n/a A B B B A C C C

99 99 99 99 99 99 99 99 99

0.04 kg m−3 0.2% 0.2% 0.2% 0.2% 0.2% 0.7% (0.1−0.2)% 0.1%

At 95% confidence level; n/a, not available.

The fitting parameters and statistical information on the quality of the fit are shown in Table 3. The values of the root-mean-square (rms) deviation, σ, and bias, Δ, of the experimental data from the correlation are defined as

U-tube densitometer and also by integration of their speed-ofsound measurements (see section 3.6). These data are all viewed as primary data because they have been conducted in equipment for which a full theory for the method is available and the measurements have been conducted with high precision. The data span the temperature range from 293 to 523 K and pressures from 0.1 to 250 MPa. The results obtained at atmospheric pressure were first correlated by the equation

⎡ 1 σ=⎢ ⎢N ⎣

2

ρ0 (T ) =

∑ biT i

Δ=

(1)

i=0

where ρ0 stands for the density at the pressure P0 = 0.1 MPa. The fitting parameters bi were obtained by fitting eq 1 to all the data at atmospheric pressure that were equally weighted. The rms deviation, σ, of all the data is 0.032%, and the bias, Δ, is essentially zero (0.002%); the values of the parameters are presented in Table 3.

1 N

1/2 ⎛ Xexp, i ⎞2 ⎤ ⎥ − 1⎟⎟ ∑ ⎜⎜ X ⎠ ⎥⎦ i ⎝ calc, i N

N

⎛ Xexp, i

∑ ⎜⎜ i

⎝ Xcalc, i

⎞ − 1⎟⎟ ⎠

(4)

(5)

where N is the total number of experimental data points, the subscripts (exp,i and calc,i) stand for the ith experimental and calculated data points, respectively, for property X, which stands for either the viscosity, η, or density, ρ. The deviations of the density data for liquid TOTM at atmospheric pressure are shown in Figure 2. The deviations at

Table 3. Fitting Parameters of Eqs 1 to 3 and Statistical Information on the Quality of the Fitting for All of the Density Data ρ b0/kg m−3 b1/kg m−3 K−1 b2/kg m−3 K−2 d0/MPa d1/MPa K−1 d2/MPa K−2 d3/MPa K−3 C rms deviation, σ/% bias, Δ/%

1207.540 −0.758786 4.14842 × 10−5 370.982 −0.60030 −1.090579 × 10−3 1.9977 × 10−6 0.087455 0.051 0.00

The whole set of density data, ρ, was then represented by a modified Tait-type equation28 −1 ⎧ ⎡ D + P ⎤⎫ ρ = ρ0 ⎨1 − C ln⎢ ⎥⎬ ⎣ D + P0 ⎦⎭ ⎩ ⎪

⎪

⎪

⎪

Figure 2. Deviations of the density data at atmospheric pressure in Table 2 from the correlation equation: ○, Diogo et al.;16 □, Diogo et al.;23 ●, Avelino et al. (lot B);29 △, Avelino et al. (lot A);29 , Bazile et al. (Speed of Sound);24 ◊, Bazile et al. (U-tube);24 ×, Lorenzi et al.30

(2)

where D and C are empirical fitting parameters. It is assumed that C is temperature independent and that the temperature dependence of D is described by the equation

high pressures are shown in Figures 3 and 4 as a function of temperature and pressure, respectively. The maximum absolute deviation is on the order of 0.15%, which is within the nominal uncertainty of the measurements. 3.3. Viscosity Data. Besides the data sets used explicitly to study the effect of impurities on the viscosity,15,23 other experimental determinations of the viscosity of liquid TOTM have been performed. All of these are summarized in Table 4, and

2

D=

∑ diT i i=0

(3)

The fitting parameters C and di were obtained by fitting eqs 2 and 3 to all the data indicated in Table 2, again equally weighted. 2888



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it can be seen that samples from the four different lots of the material have been used, which enlarges the information available on the effect that small variations of the chemical composition of TOTM might have on the viscosity. In addition, the table lists the reference source for the data, temperature, and pressure ranges as well as the nominal uncertainties of the sets of atmospheric pressure and high-pressure viscosity measurements for TOTM. All of the measurements are viewed as primary data in the sense adopted by IATP9,31 for the purposes of developing representational reference correlations. The uncertainties of the data are different in different regimes, and this is ultimately recognized in the overall uncertainty claimed for the correlated data. Four viscosity measurement sets have been found for TOTM at atmospheric pressure, namely, those published by Lorenzi et al.,30 Diogo et al.,15 Assael and Tsolakidou,32 and Liñeira del Rió et al.25 The former two sets of data were both obtained using capillary viscometers. Assael and Tsolakidou32 used a rotating disk viscometer, and Liñeira del Rió et al.25 used a Stabinger rotational viscometer. Five viscosity measurement sets on compressed liquid TOTM have been reported by Diogo et al.,15,23 Bair,12 Baled et al.,21 and Liñeira del Rió et al.25 Diogo et al. measured the viscosity of two lots, A15 and B,23 using a vibrating-wire viscometer. Baled et al.21 measured the viscosity of lot C of TOTM using a windowed, variable-volume, rolling ball viscometer. Two more viscosity data sets of TOTM lot C were reported, one by Liñeira del Rió et al.25 using a falling body viscometer and another by Bair12 using a falling body viscometer. 3.3.1. Reference Correlation for Viscosity. The data of Table 4 were correlated using a semiempirical method proposed by Li et al.,33 which is a heuristic development of the kinetic theory for dense hard-sphere fluids applied to the van der Waals model of a liquid.34 The same type of correlation scheme has been applied to TOTM data and several other systems15,35−40 and to develop a reference correlation of the viscosity of toluene over wide ranges of temperature and pressure.31 The correlation uses density and temperature rather than pressure and temperature as independent variables because a much simpler and precise correlation results. As in previous works, the use of this particular tailor-made correlation scheme instead of the

Figure 3. Deviations of the density data at high pressure in Table 2 as a function of the temperature: *, Bair;12 ○, Diogo et al.;16 □, Diogo et al.;23 ●, Avelino et al. (lot B);29 △, Avelino et al. (lot A);29 −, Bazile et al. (Speed of Sound);24 ◊, Bazile et al. (U-tube);24 +, Bamgbade et al.22

Figure 4. Deviations of the density data at high pressure in Table 2 as a function of the pressure: *, Bair;12 ○, Diogo et al.;16 □, Diogo et al.;23 ●, Avelino et al. (lot B);29 △, Avelino et al. (lot A);29 −, Bazile et al. (Speed of Sound);24 ◊, Bazile et al. (U-tube);24 +, Bamgbade et al.22

Table 4. Measurements of the Viscosity of Liquid TOTM year

first author

ref.

temperature range/K

1998

Lorenzi

30

298−368

0.1

8

2014

Diogo

15

303−328

0.1

4

2014

Diogo

15

303−373

0.1−68

328

capillary Ubbelohde capillary Ubbelohde vibrating wire

2015

Diogo

23

303−373

0.1−100

93

vibrating wire

2015 2015 2016 2016

Bair Bair Baled Assael

12 12 21 32

313−373 313−423 314−523 298−358

100−1000 0.1−350 3.5−270 0.1

20 25 58 10

MHP falling body rolling ball rotating disk

2016

Liñeira del Rió Liñeira del Rió

25

303−353

0.1−150

29

25

278−373

0.1

20

falling body VisLPT1 Stabinger

2016

pressure range/ MPa

number of data points

lot number

purity/%

a

n/a

99

b

c

A

99

1%

std oil NVS 20 AW std oil NVS 20 AW

A

99

2.0−3.0

B

99

2.0−3.0

B B C D

99 99 99 99

3.0 3.0 3.0 5.0

C

99

3.5

C

99

1

method

calibrant

Cannon N100 squalaned water and squalane e e

nominal uncertainty/%

Calibration performed according to ref.42 b1 × 10−4 mm2 s−1 cCalibration by the manufacturer (Schott). dSource of calibration data in ref 43. Calibration by the manufacturer and verified with standard fluids N75, S600, and N100 from Cannon Instrument Co. as well as with squalane (Sigma-Aldrich, 99%); data in ref 8. N/a, not available. a e

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“universal” equation proposed by Assael et al.41 is because we can gain an improved representation for just one substance. Nevertheless, for quickly determining the viscosity at any values of temperature and pressure in the appropriate ranges, an automatic calculation scheme is provided in the Supporting Information. In the present method, a dimensionless viscosity, η*, is defined using SI units as34,41 ⎛ 1 ⎞1/2 ⎟ η* = 6.035 × 108⎜ η(Vm)2/3 ⎝ MRT ⎠

Table 5. Fitting Coefficients, ai, of Eq 8, m and n of Eq 9, and the Statistical Parameters RMS Deviation, σ, and Bias, Δ, for the Reference Correlation m (m3 mol−1 K−1) n (m3 mol−1 K−2) a0 a1 a2 a3 a4 a5 σ/% Δ/%

(6)

where M is the molar mass, R is the gas constant, T is the temperature, and Vm is the molar volume. It is assumed that the dimensionless viscosity, η*, depends only on Vm/V0, where V0 is a characteristic molar volume

⎛V ⎞ η* = fη ⎜ m ⎟ ⎝ V0 ⎠

of temperature and pressure set out by the oil industry. Furthermore, for the quality of the correlation to be improved, only viscosity data up to 1000 mPa s was considered. As a consequence, the data in Table 4 outside these intervals were not included in developing the present correlation. The fitting therefore made use of 545 data points covering viscosity values up to 800 mPa s and has resulted in a fit with a root-mean-square (rms) deviation, σ, of 2.4%. Assuming a 95% confidence level, we have withdrawn 18 possible outlying data points with corresponding deviations larger than twice the rms deviation. In particular, the following experimental points were withdrawn: two values from the highest pressures measured by Bair12 and six points from the highest viscosity data obtained by Baled et al.21 In addition, we have eliminated seven points from the data of Liñeira del Rió et al.,25 which include their results for the highest viscosities; finally, three points from the set reported by Assael and Tsolakidou32 were excluded because they deviate more from the correlation than the uncertainty of their measurements. A second fitting procedure was carried out, incorporating 527 experimental viscosity points. The fitting parameters are given in Table 5. The data have an rms deviation equal to 1.57%. The expanded uncertainty of the present viscosity results is estimated as ±3.2% at a 95% confidence level. The deviations of all the measurements from the proposed correlation are shown in Figures 5 and 6, and listed in Table 6 are the maximum deviations of each data set from the present correlation shown as percentages. The largest deviations are less than 2.5%. 3.3.3. Comparisons. Most of the results obtained at atmospheric pressure show very small deviations from the correlation scheme. In particular, the measurements reported by Diogo et al.15 obtained with a capillary differ from the present correlation by less than ±0.3%, which is within the uncertainty of ±1% claimed by those authors. Good agreement has also been found with the results reported by Liñeira del Rió et al.25 using the Stabinger viscometer with a nominal uncertainty of ±1.0% because their deviations from eq 8 do not exceed 1.1%. The data set presented by Assael and Tsolakidou32 obtained using a rolling ball viscometer shows a maximum relative deviation of 4.0%, which is within the uncertainty of the measurement method. The results published by Lorenzi et al.30 obtained with a capillary viscometer show a maximum relative deviation of −4.4%. The values reported by Diogo et al.,15,23 with a nominal uncertainty of ±2.0−3.0%, deviate from eq 8 by less than −4.9% with rms deviation equal to 1.6%; the majority of their results have deviations from the correlation of approximately ±2.0%; only nine points have deviations of approximately 5% for the

(7)

It is thus possible to superimpose the curves of η* for each isotherm as a function of log(Vm/V0) by performing horizontal shifts along the log(Vm/V0) axis. The amount by which log(Vm/V0) has to be shifted to achieve superposition on the reference isotherm leads to the value V0(T)/V0(Tref) and hence gives a measure of the temperature effect on the characteristic volume. In this way, the value of V0 for each temperature is obtained. The existence of a slight temperature variation of V0 is interpreted as providing the ability to correct for the finite gradient of the repulsive potential of real molecules.34 The dimensionless viscosity, η*, for TOTM was correlated with the molar volume by the equation i ⎡ ⎛ Vm ⎞⎤ ⎢ ⎥ log10(η*) = ∑ a i log10⎜ ⎟ ⎢ ⎝ V0 ⎠⎥⎦ i=0 ⎣

−0.429149 6.1968 × 10−4 8.723136 −5.4986 × 10 −4.6294 × 102 8.9429 × 103 −4.7993 × 104 8.8238 × 104 1.6 0.02

5

(8)

The temperature dependence of V0 is described by the empirical polynomial relation V0(T ) × 106 (m 3 mol−1) = V0,ref + m(T − Tref ) + n(T − Tref )2

(9)

The fitting coefficients ai and m and n of eqs 8 and 9 were obtained by simultaneous fitting of those equations to all the equally weighted experimental data found in the sources listed in Table 4. The correlation of the viscosity with the molar volume was accomplished using Excel and MatLab software. The optimum parameters were obtained by the function FMINSEARCH (multidimensional nonlinear minimization with a Nelder−Mead algorithm). The values for the various parameters thus determined are quoted in Table 5. For the parameters of eq 9 to be obtained, a reference value for V0 at an arbitrary temperature, Tref, was calculated. In the present work, we adopt the same reference temperature, Tref = 303.16 K, and characteristic molar volume V0,ref = 462.4376 × 10−6 m3 mol−1, obtained previously for TOTM,15 using a procedure whereby it is assumed that the value of V0,ref is equivalent to the volume of close-packing of hard spheres.34 3.3.2. The Correlation Procedure. Taking into consideration the aim set out by oil exploration requirements, the temperature and pressure ranges of the present correlation scheme were adopted as 303−477 K and 0.1−200 MPa, respectively. These limits are narrower than the range of available viscosity data for TOTM, and we apply them to reduce the uncertainty of the reference data while still maintaining the very demanding range 2890



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the deviations are within the uncertainties of the measurement method. Baled et al.21 have reported viscosity data for TOTM at pressures between 7 and 242 MPa and temperatures between 314 and 527 K with an expanded uncertainty of 3%. The deviations encountered from eq 9 for their entire data set used in the present correlation vary from −4.88 to +3.3%, which is within the overall uncertainty of the experimental method. Viscosities at high pressures were also measured by Liñeira del Rió et al.25 All their data show negative deviations from the present correlation from −4.8 to −1.5%. 3.4. Shear Dependence of the Viscosity. When viscosity is the standard reference property of interest, it is important to verify under what conditions it is legitimate to consider the fluid as Newtonian for its later applications as a calibrant. For that reason, two independent studies have been carried out to investigate the limits of the Newtonian behavior of TOTM. Assael and Tsolakidou32 have measured the viscosity of TOTM in the temperature range 298−358 K at 0.1 MPa. A rotating disk viscometer (TA Instruments model AR550) was employed, and the authors investigated the rheological behavior at 298 and 352 K employing shear stresses from 25 to 107 Pa for the lowest temperature and shear rates from 100 to 500.8 s−1. Under these conditions, TOTM was found to behave as a perfect Newtonian fluid.32 Bair carried out an experimental study aiming to investigate the rheological behavior of TOTM at sufficiently large shear stresses to characterize the Newtonian limit. The shear dependence of the viscosity of low-molecular-mass organic liquids, like TOTM, is of extreme importance to tribology, especially to elastohydrodynamics, where it is not possible to predict film thickness and friction from the assumption of Newtonian behavior.44 Liquids, like TOTM, evidence Newtonian behavior for the low values of shear stress that are useful for the majority of the applications of an industrial reference liquid as reported by Assael and Tsolakidou.32 However, at high pressure it is possible to observe shear-dependent viscosity, which has been the objective of Bair. The architecture and operation of the original equipment used by Bair was previously described.45 Bair has measured the viscosity of TOTM (Sigma-Aldrich, lot MKBQ0304V) at almost a single temperature and three different pressures, namely (296.4 K, 600 MPa), (296.6 K, 650 MPa), and (296.8 K, 700 MPa), using maximum shear stresses up to 11.5, 11.8, and 15.2 MPa, respectively.

Figure 5. Deviations of the viscosity data at high pressures in Table 6 from the correlation eqs 8 and 9 as a function of the temperature. *, Bair;12 ○, Diogo et al. (HP);15 □, Diogo et al.;23 ●, Diogo et al. (atm);15 △, Liñeira del Rió et al. (HP);25 −, Assael and Tsolakidou;32 ◊, Liñeira del Rió et al. (atm);25 +, Baled et al.;21 ×, Lorenzi et al.30

Figure 6. Deviations of the viscosity data at high pressures in Table 6 from the correlation eqs 8 and 9 as a function of the pressure. *, Bair;12 ○, Diogo et al. (HP);15 □, Diogo et al.;23 ●, Diogo et al. (atm);15 △, Liñeira del Rió et al. (HP);25 −, Assael and Tsolakidou;32 ◊, Liñeira del Rió et al. (atm);25 +, Baled et al.;21 ×, Lorenzi et al.30

highest temperature and highest pressure. Deviations of the data obtained by Bair12 range from −4.2 to +4.2% with the average relative deviation being less than 2.0%. The majority of

Table 6. Statistical Characteristics of Individual Data Sets for the Fits in Table 4 Including Temperature and Pressure Ranges Taken into the Correlations, Number of Data Points, Np, Used in the Correlations, Number of Points Eliminated (Deviations Greater than Twice the RMS Deviation, σ) and Minimum and Maximum Deviations first author

ref

temperature range/K

pressure range/MPa

number of data points used in correlation

number the data points eliminated (>2σ)

relative deviation range/%

σ/%

nominal uncertainty/%

Lorenzi Diogo Diogo Diogo Bair Baled Assael Liñeira del Rió Liñeira del Rió

30 15 15 23 12 21 32 25

298−368 303−328 303−373 303−373 313−423 314−477 298−352 303−353

0.1 0.1 0.1−68 0.1−100 0.1−150 3.5−200 0.1 0.1−150

8 4 328 93 19 45 7 25

0 0 0 0 2 6 3 7

−4.44 to 1.49 −0.30 to −0.11 −1.91 to 3.82 −1.65 to 4.86 −4.20 to 4.23 −4.81 to 3.26 1.71 to 4.01 −4.76 to −1.54

1.11 0.12 0.07 0.16 0.56 0.38 1.01 0.84

a 1% 2.0−3.0 2.0−3.0 3.0 3.0 5.0 3.5

25

298−373

0.1

16

0

−1.13 to 0.23

0.21

a

1.0

1 × 10−4 mm2 s−1 2891



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Table 7. Shear-Dependent Viscosity of TOTM at High Pressures from Bair 296.4 K, 600 MPa

296.6 K, 650 MPa

296.8 K, 700 MPa

γ̇/s−1

τ/kPa

η̂/Pa s

γ̇/s−1

τ/kPa

η̂/Pa s

γ̇/s−1

τ/kPa

η̂/Pa s

359 508 762 1023 1530 2560

2490 3755 5590 7012 8842 11535

6934 7392 7335 6855 5762 4510

149 359 508 762 1023

2531 6199 8029 10417 11789

16995 17263 15804 13670 11524

70.1 96.4 149 359 508 762

3145 4294 6504 11331 12906 15193

44889 44566 43682 31555 25407 19938

disk facing two reflectors fixed at different positions. This acoustic sensor is located within a high pressure vessel connected to a volumetric pump that allows generating pressure up to 200 MPa. The cell is thermoregulated in a liquid bath controlled by a thermostat with stability of 0.02 K, and the temperature is measured by means of a platinum probe (Pt100). Pressure was measured by two pressure gauges fixed between the cell and the pump. One was calibrated in the full scale (0.1 to 200 MPa) with an uncertainty of 0.1 MPa. The other was only calibrated between 0.1 and 100 MPa with an uncertainty of 0.01 MPa in this pressure range. Consequently, the expanded uncertainty for speed of sound measurements with the conventional coverage factor kP = 2 (P = 95%) is 0.06% between 0.1 and 100 MPa and 0.2% between 100 and 200 MPa. Measurements were carried out along isotherms at 10 K intervals from 293.15 to 373.15 K in the pressure range 0.1 to 200 MPa. The pressure step adopted during the experiments was fixed at 10 MPa up to 100 and 20 MPa above to have a sufficient number of data points to allow a good fit by correlation functions on each isotherm. The full set of data was fitted to a twodimensional rational function which correlates with 1/c2 instead of the speed of sound c

Shear dependence of the viscosity occurs when the product of the applied shear rate and a relaxation time characteristic of the fluid approaches unity. This is the rotational relaxation time, λ,46,47 of the molecule, and it can be estimated from the Einstein−Debye48 equation.

λ=

ηM ρRT

(10)

where M is the molar mass, ρ is the density, T is the temperature, and R is the gas constant. The shear stress at the Newtonian limit should therefore be

τ = ηγ ̇ =

η ρRT = λ M

(11)

and substitution of typical values for TOTM yields, for the Newtonian limit, a shear stress of approximately 5 MPa. The viscosities measured by Bair are listed in Table 7. It can be seen that, for shear stress greater than 5 MPa, the viscosity is strongly shear thinning. It follows that the viscosity correlated by eqs 8 and 9 with the parameters of Table 5 are to be applied not only within the temperature and pressure ranges of the data used to generate the correlation 303 K < T < 477 K and 0.1 MPa < P < 200 MPa but also to shear stresses below 5 MPa if the fluid is to be assumed Newtonian. 3.5. Surface Tension. For viscometers in which a free liquid surface is present, such as suspended-level capillary viscometers in particular, it is important to be able to make corrections for the small effect of surface tension on the measurements. Thus, if TOTM is to be a useful calibrant, values of its surface tension under relevant conditions are important. Surface tension measurements were performed on TOTM lots A and B23 by the pendant drop method using a technique previously described by Morgado et al.49 Analysis of the drop profiles was performed using the axisymmetric drop shape analysis (ADSA) method developed by Rió et al.50 The repeatability of the surface tension measurements is better than ±0.3%, and the overall uncertainty of the results is estimated to be ±0.5% based on previous studies by Morgado et al.49 Table 5 in ref 23 lists values for the ratio of the surface tension to density. It is actually this ratio and not the surface tension alone that is necessary to evaluate the correction of the surface tension effect on the capillary viscosity measurements according to the treatment described in section 5 of ref 5. 3.6. Speed of Sound. Speed of sound measurements can be used directly in the formulations of equations of state, can be used to derive precise density data, and have been especially useful here in obtaining the density of the liquid at high pressures as was reported earlier in the paper. Speed of sound measurements on TOTM were carried out at the University of Pau using a pulse-echo technique operating at 3 MHz. The apparatus, which has been described previously,24,26,27 is essentially made up of an acoustic sensor composed of one piezoelectric

A 0 + A1T + A 2 T 2 + A3T 3 + BP + CP2 + DP3 1 = 1 + ET + FP c2 (12)

The fitting parameters were determined by fitting eq 12 to all speed of sound data reported by Bazile et al.24 with the same weight for each data. The fitting parameters and statistical information on the fit are also summarized in Table 8. Table 8. Fitting Parameters of Eq 12 for Correlating Speed of Sound from 293 to 373 K and 0.1 to 200 MPa A0/s2 m−2 A1/s2 m−2 K−1 A2/s2 m−2 K−2 A3/s2 m−2 K−3 Δ/% σ/%

−1.58470 × 10−07 2.58524 × 10−10 −4.75770 × 10−12 3.55128 × 10−15

B/s2 m−2 MPa−1 C/s2 m−2 MPa−2 D/s2 m−2 MPa−3 E/K−1 F/MPa−1

1.12056 × 10−09 −2.33730 × 10−12 2.81851 × 10−15 −1.48117 × 10−03 5.92484 × 10−03

4.2 × 10−03 0.071

High-pressure density data were obtained from speed of sound measurements by integration of the Newton Laplace equation P

ρ(P , T ) − ρ(0.1MPa, T ) =

P

∫0.1MPa 1/c 2 dP + T ∫0.1MPa (αP 2/CP) dP (13)

where αP is the isobaric expansion coefficient and CP the heat capacity at constant pressure. The integration was performed numerically using a predictor corrector27 that requires density and heat capacity at atmospheric pressure to initiate the iterative procedure. The density data at atmospheric pressure (0.1 MPa) 2892



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Table 9. Recommended Values for the Viscosity and Density of Liquid TOTM at Several Nominal Temperatures and Pressures T/K

p/MPa

ρ/kg m−3

η/mPa s

T/K

p/MPa

ρ/kg m−3

η/mPa s

303 303 303 303 303 303 323 323 323 323 323 323 323 323 343 343 343 343 343 343 343 343 363 363 363 363 363 363 363 363 373 373 373 373 373 373 373 373 393 393 393 393 393 393 393 393 393 393 393

0.1 1.0 5.0 10.0 25.0 50.0 0.1 1.0 5.0 10.0 25.0 50.0 75.0 100.0 0.1 1.0 5.0 10.0 25.0 50.0 75.0 100.0 0.1 1.0 5.0 10.0 25.0 50.0 75.0 100.0 0.1 1.0 5.0 10.0 25.0 50.0 75.0 100.0 0.1 1.0 5.0 10.0 25.0 50.0 75.0 100.0 125.0 150.0 175.0

981.4 982.0 984.3 987.2 995.3 1007.7 966.8 967.4 969.9 973.0 981.8 995.1 1006.9 1017.5 952.2 952.8 955.6 959.0 968.5 982.8 995.3 1006.6 937.6 938.3 941.3 945.1 955.5 970.8 984.2 996.1 930.3 931.0 934.3 938.2 949.0 964.9 978.8 991.1 915.7 916.6 920.1 924.4 936.3 953.5 968.3 981.3 992.9 1003.5 1013.3

155.0 158.3 173.4 194.1 270.3 459.3 52.7 53.7 58.2 64.3 86.1 137.5 215.5 332.1 22.9 23.3 25.0 27.3 35.3 53.3 79.2 116.0 11.9 12.0 12.8 13.9 17.6 25.4 36.1 50.6 8.9 9.1 9.7 10.5 13.1 18.7 26.1 35.8 5.4 5.5 5.9 6.4 7.9 11.1 15.0 20.1 26.4 34.6 44.9

393 413 413 413 413 413 413 413 413 413 413 413 413 433 433 433 433 433 433 433 433 433 433 433 433 453 453 453 453 453 453 453 453 453 453 453 453 473 473 473 473 473 473 473 473 473 473 473 473

200.0 0.1 1.0 5.0 10.0 25.0 50.0 75.0 100.0 125.0 150.0 175.0 200.0 0.1 1.0 5.0 10.0 25.0 50.0 75.0 100.0 125.0 150.0 175.0 200.0 0.1 1.0 5.0 10.0 25.0 50.0 75.0 100.0 125.0 150.0 175.0 200.0 0.1 1.0 5.0 10.0 25.0 50.0 75.0 100.0 125.0 150.0 175.0 200.0

1022.3 901.2 902.2 906.1 910.9 923.9 942.4 958.1 971.9 984.2 995.2 1005.4 1014.8 886.8 887.8 892.2 897.4 911.6 931.6 948.3 962.8 975.7 987.3 997.8 1007.5 872.3 873.5 878.3 884.1 899.5 920.9 938.6 953.9 967.3 979.3 990.2 1000.3 857.9 859.2 864.5 870.8 887.5 910.2 928.8 944.7 958.6 971.0 982.3 992.6

57.9 3.5 3.6 3.8 4.1 5.2 7.1 9.6 12.6 16.2 20.7 26.2 32.9 2.4 2.5 2.6 2.8 3.5 4.9 6.6 8.5 10.8 13.6 16.9 20.8 1.8 1.9 2.0 2.1 2.6 3.5 4.7 6.1 7.7 9.5 11.7 14.2 1.6 1.6 1.7 1.7 2.0 2.7 3.5 4.5 5.6 7.0 8.5 10.2

aimed to “calibrate instruments” and to “check the performance of instruments”. In particular, we classified DIDP as an “industrial reference fluid”. We have also focused our attention on general issues raised by practical calibration procedures, in particular when capillary viscometers are employed. In the same article, the need to determine reference fluids for viscosity being more viscous than water by several orders of magnitude was discussed. 4.1. Reference Values. We propose that the reference correlation derived from the various sources of data set out in this paper allows us to designate TOTM as a similar “industrial reference fluid”. To that end, reference values for the viscosity of

were obtained from U-tube densimeter measurements. The expanded uncertainty of the density results was estimated by performing numerical perturbation tests to be 0.1% between 0.1 and 100 MPa and 0.2% between 100 and 200 MPa within a 95% confidence limit.

4. INDUSTRIAL REFERENCE STANDARD FOR VISCOSITY In a previous article,5 we have discussed the subject of reference materials for viscosity. We followed Marsh’s nomenclature6 and classified DIDP as a “working reference material” as its proposal 2893



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International Union of Pure and Applied Chemistry (IUPAC) within the framework of the Project 2012-051-1-100. This work was supported by the strategic project PEst-OE/QUI/UI0100/ 2013 funded by Fundaçaõ para a Ciência e a Tecnologia (FCT), Portugal. The authors are grateful to Ana Dias research technician fellowship at the Node IST at CQE of the Portuguese Mass Spectrometry Network, project REM2013 funded by Fundaçaõ para a Ciência e a Tecnologia (FCT), Portugal. M.J.P.C. and J.F. acknowledge the support of the Spanish Ministry of Economy and Competitiveness and the FEDER program through the ENE2014-55489-C2-1-R project as well as of Xunta de Galicia through the EM2013/031 and GRC ED431C 2016/001 Projects. J.F. and M.J.P.C. acknowledge the assistance of J. M. Liñeira del Rió and M. J. G. Guimarey for the viscosity measurements.

TOTM for several nominal temperatures and pressures are listed in Table 9. They were generated with the aid of the correlations derived here. The uncertainty ascribed to the data is under 3.2% within a 95% confidence level. In the Supporting Information, an Excel executable file is available to be used as a tool to interpolate the viscosity and density values for TOTM for any pairs of temperature and pressure within the ranges shown in Table 9. 4.2. Sample Preparation. It is helpful for users of TOTM as a reference material to note that the study of the effect of using different lots from a manufacturer upon the viscosity reported (section 3.1) shows that the variations are well within the expanded uncertainty of the reference data as obtained from the present correlation scheme. Therefore, the use of samples with a purity greater than 99% seems to be sufficient precaution without any further treatment. The evidence summarized here shows that it would be advisible in practical applications to determine the water content of samples to decide whether a drying procedure would be necessary.

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(1) Goodwin, A. R. H., Marsh, K. N., Wakeham, W. A., Eds.; Measurement of the Thermodynamic Properties of Single Phases; Experimental Thermodynamics; Elsevier Science: Amsterdam, Netherlands, 2003, Vol. VI. (2) Marsh, K. N. Role of Reference Materials for the Realization of Physicochemical Properties. Past, Present, and Future. Pure Appl. Chem. 2000, 72, 1809−1818. (3) Marsh, K. N. Recommended Reference Materials for the Realization of Physicochemical Properties; IUPAC, Ed.; Blackwell Scientific Publications: U.K., 1987. (4) Wakeham, W. A. The Life and Career of Kenneth Neil Marsh. J. Chem. Thermodyn. 2017, 104, 288−289. (5) Caetano, F. J. P.; Fareleira, M. N. A.; Fernandes, A. C.; Oliveira, C. M. B. P.; Serro, A. P.; Sim, M.; Almeida, D.; Wakeham, W. A. Diisodecylphthalate (DIDP) a Potential Standard of Moderate Viscosity: Surface Tension Measurements and Water Content Effect on Viscosity. Fluid Phase Equilib. 2006, 245, 1−5. (6) Caetano, F. J. P.; Fareleira, J. M. N. A.; Fröba, A. P.; Harris, K. R.; Leipertz, A.; Oliveira, C. M. B. P.; Trusler, J. P. M.; Wakeham, W. A. An Industrial Reference Fluid for Moderately High Viscosity. J. Chem. Eng. Data 2008, 53, 2003−2011. (7) Al Motari, M. M.; Kandil, M. E.; Marsh, K. N.; Goodwin, A. R. H. Density and Viscosity of Diisodecyl Phthalate C 6 H 4 (COOC 10 H 21) 2, with Nominal Viscosity at T) 298 K and P) 0. 1 MPa of 87 mPa, S, at Temperatures from (298. 15 to 423. 15) K and Pressures up to 70 MPa. J. Chem. Eng. Data 2007, 52, 1233−1239. (8) Comuñas, M. J. P.; Paredes, X.; Gaciño, F. M.; Fernández, J.; Bazile, J. P.; Boned, C.; Daridon, J. L.; Galliero, G.; Pauly, J.; Harris, K. R.; Assael, M. J.; Mylona, S. K. Reference Correlation of the Viscosity of Squalane from 273 to 373 K at 0.1 MPa. J. Phys. Chem. Ref. Data 2013, 42, 0−6. (9) Mylona, S. K.; Assael, M. J.; Comuñas, M. J. P.; Paredes, X.; Gaciño, F. M.; Fernández, J.; Bazile, J. P.; Boned, C.; Daridon, J. L.; Galliero, G.; Pauly, J.; Harris, K. R. Reference Correlations for the Density and Viscosity of Squalane from 273 to 473 K at Pressures to 200 MPa. J. Phys. Chem. Ref. Data 2014, 43 (1), 013104−1−013104−11. (10) Schmidt, K. A. G.; Pagnutti, D.; Curran, M. D.; Singh, A.; Trusler, J. P. M.; Maitland, G. C.; McBride-Wright, M. New Experimental Data and Reference Models for the Viscosity and Density of Squalane. J. Chem. Eng. Data 2015, 60, 137−150. (11) Harris, K. R. Temperature and Pressure Dependence of the Viscosities of Krytox GPL102 Oil and Di(pentaerythritol) Hexa(isononanoate). J. Chem. Eng. Data 2015, 60, 1510−1519. (12) Bair, S. The Temperature and Pressure Dependence of the Viscosity and Volume for Two Reference Liquids. Lubr. Sci. 2016, 28, 81−95. (13) Mylona, S. K.; Assael, M. J.; Karagiannidis, L.; Jannakoudakis, P. D.; Wakeham, W. A. Measurements of the Viscosity of Krytox GPL102 Oil in the Temperature Range (282 to 364) K and up to 20 MPa. J. Chem. Eng. Data 2015, 60, 3539−3544.

5. CONCLUSIONS We have set out in this paper all the material necessary to qualify TOTM as a moderately high viscosity industrial reference material in the sense defined by Professor Ken Marsh2,3 some years ago. The viscosity data tabulated as standard reference data cover the range from 303 to 473 K, the pressure range from 0.1 to 200 MPa, and viscosities from 1.6 to 755 mPa s. In particular, at a pressure of 200 MPa and temperature of 473 K, the viscosity for the liquid is 10.2 × 10−3 Pa s. The uncertainty in the data provided is on the order of 3.2% at 95% confidence level and is thought to be adequate for most industrial applications. We hope that the efforts of the many individuals who have contributed to the work summarized in this paper and of Professor Ken Marsh will be rewarded by the use of these new data in industrial practice.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00170. Executable Excel file to interpolate the viscosity and density values for TOTM for any pairs of temperature and pressure within the ranges shown in Table 9 (ZIP)

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

William A. Wakeham: 0000-0002-0838-370X Marc J. Assael: 0000-0003-1221-6899 Jean-Luc Daridon: 0000-0002-0522-0075 Josefa Fernández: 0000-0002-9528-6173 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been conducted under the guidance of the International Association for Transport Properties (IATP; http://transp.cheng.auth.gr/index.php/iatp/terms). The work described in this paper was carried out under the auspices of the 2894



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(14) Fortin, T. J.; Laesecke, A. Characterization of the Temperature Dependence of Viscosity and Density of Several Perfluoropolyether Oils. In ECTP2014 - 20th European Conference on Thermophysical Properties, 2014; http://ectp2014.fc.up.pt/Programme/Oral/OA1_11. pdf (accessed Mar 2, 2017). (15) Diogo, J. C. F.; Avelino, H. M. N. T.; Caetano, F. J. P.; Fareleira, J. M. N. A. Tris(2-Ethylhexyl) Trimellitate (TOTM) a Potential Reference Fluid for High Viscosity. Part I: Viscosity Measurements at Temperatures from (303 to 373) K and Pressures up to 65 MPa, Using a Novel Vibrating-Wire Instrument. Fluid Phase Equilib. 2014, 384, 50−59. (16) Diogo, J. C. F.; Avelino, H. M. N. T.; Caetano, F. J. P.; Fareleira, J. M. N. A. Tris(2-Ethylhexyl) Trimellitate (TOTM) a Potential Reference Fluid for High Viscosity. Part II: Density Measurements at Temperatures from (293 to 373) K and Pressures up to 68 MPa. Fluid Phase Equilib. 2014, 384, 36−42. (17) Diolube trimellitates esters; http://www.diolube.com/ DiolubeTrimellitateEsters.htm (accessed Feb 1, 2017). (18) Sigma-Aldrich Trioctyl trimellitate Safety Data Sheet; http:// www.sigmaaldrich.com/MSDS/MSDS/DisplayMSDSPage. do?country=PT&language=EN-gener ic&productNu mber= 538140&brand=ALDRICH&PageToGo-ToURL=%2Fsafety-center. html (accessed Jan 3, 2017). (19) Certificate of Analysis Advanced Search - Sigma-Aldrich; https:// www.sigmaaldrich.com/catalog/AdvancedSearchPage.do (accessed Jan 5, 2017). (20) Eastman Chemical Company. Safety Data Sheet - TOTM (CAS No.: 3319-31-1). 2014; http://ws.eastman.com/ProductCatalogApps/ PageControllers/MSDS_PC.aspx?Product=71001096 (accessed Jan 31, 2017). (21) Baled, H. O.; Tapriyal, D.; Gamwo, I. K.; Bamgbade, B. A.; McHugh, M. A.; Enick, R. M. Viscosity Measurements of Two Potential Deepwater Viscosity Standard Reference Fluids at High Temperature and High Pressure. J. Chem. Eng. Data 2016, 61, 2712−2719. (22) Bamgbade, B. A.; Gamwo, I. K.; Foley, A.; Tapriyal, D. Exploring the high-temperature, high-pressure volumetric properties of two viscosity reference standard fluids. Fluid Phase Equilib. In preparation, 2017. (23) Diogo, J. C. F.; Avelino, H. M. N. T.; Caetano, F. J. P.; Fareleira, J. M. N. A.; Wakeham, W. A. Tris(2-Ethylhexyl) Trimellitate (TOTM) as a Potential Industrial Reference Fluid for Viscosity at High Temperatures and High Pressures: New Viscosity, Density and Surface Tension Measurements. Fluid Phase Equilib. 2016, 418, 192−197. (24) Bazile, J. P.; Nasri, D.; Daridon, J. Speed of Sound, Density, and Derivative Properties of TOTM under High Pressure. J. Chem. Eng. Data 2017, ASAP DOI: 10.1021/acs.jced.7b00162. (25) Liñeira del Río, J. M.; Guimarey, M. J. G.; Comuñas, M. J. P.; Fernández, J. Characterizing the High Pressure Viscosity Behaviour of Trioctil Trimelitato up to 150 MPa. J. Chem. Thermodyn. To be submitted, 2017. (26) Comuñas, M. J. P.; Bazile, J. P.; Baylaucq, A.; Boned, C. Density of Diethyl Adipate Using a New Vibrating Tube Densimeter from (293.15 to 403.15) K and up to 140 MPa. Calibration and Measurements. J. Chem. Eng. Data 2008, 53, 986−994. (27) Daridon, J. L.; Lagourette, B.; Labes, P. Compressibilities of Ternary Mixtures C1-nC16-CO2 under Pressure from Ultrasonic Measurements of Sound Speed. Int. J. Thermophys. 1996, 17, 851−871. (28) Dymond, J. H.; Malhotra, R. The Tait Equation: 100 Years on. Int. J. Thermophys. 1988, 9, 941−951. (29) Avelino, H. M. T. N.; Caetano, F. J. P.; Fareleira, J. M. N. A.; Pereira, M. F. V.; Santos, F. J. V.; Santos, T. V. M.; Wakeham, W. A. J. Chem. Eng. Data To be submitted, 2017. (30) De Lorenzi, L. De; Fermeglia, M.; Torriano, G. Density, Kinematic Viscosity, and Refractive Index for Bis (2-Ethylhexyl) Adipate, Tris (2-Ethylhexyl) Trimellitate, and Diisononyl Phthalate. J. Chem. Eng. Data 1998, 43, 183−186. (31) Assael, M. J.; Avelino, H. M. T.; Dalaouti, N. K.; Fareleira, J. M. N. A.; Harris, K. R. Reference Correlation for the Viscosity of Liquid Toluene from 213 to 373 K at Pressures to 250 MPa. Int. J. Thermophys. 2001, 22, 789−799.

(32) Assael, M. J.; Tsolakidou, Ch. M. Rheological behavior of TOTM from 20 to 80 °C at 0.1 MPa″. Int. J. Thermophys. To be submitted, 2017. (33) Li, S. F. Y.; Trengove, R. D.; Wakeham, W. A.; Zalaf, M. The Transport Coefficients of Polyatomic Liquids. Int. J. Thermophys. 1986, 7, 273−284. (34) Dymond, J. H. Hard-Sphere Theories of Transport Properties. Chem. Soc. Rev. 1985, 14, 317−356. (35) Diogo, J. C. F.; Caetano, F. J. P.; Fareleira, J. M. N. A. Viscosity and Density Measurements of Compressed Liquid Dimethyl Adipate Using Oscillating Body Techniques. Fluid Phase Equilib. 2014, 367, 85−94. (36) Pádua, A. A. H.; Fareleira, J. M. N. A.; Calado, J. C. G.; Wakeham, W. A. Density and Viscosity Measurements of 1,1,1,2-Tetrafluoroethane (HFC-134a) from 199 to 298 K and up to 100 MPa A. J. Chem. Eng. Data 1996, 41, 731−735. (37) Pádua, A. A. H.; Fareleira, J. M. N. A.; Calado, J. C. G.; Wakeham, W. A. Density and Viscosity Measurements of 2,2,4-Trimethylpentane (Isooctane) from 198 to 348 K and up to 100 MPa. J. Chem. Eng. Data 1996, 41, 1488−1494. (38) Avelino, H. M. T.; Fareleira, J. M. N. A.; Wakeham, W. A. Simultaneous Measurement of the Density and Viscosity of Compressed Liquid Toluene. Int. J. Thermophys. 2003, 24, 323−336. (39) Avelino, H. M. N. T.; Fareleira, J. M. N. A.; Oliveira, C. M. B. P. Viscosity of Compressed Liquid 1,1,1-Trifluoroethane (HFC-143a) and Pentafluoroethane (HFC-125). J. Chem. Eng. Data 2006, 51, 1672− 1677. (40) Avelino, H. M. N. T.; Fareleira, J. M. N. A.; Oliveira, C. M. B. P. Viscosity Measurements of Compressed Liquid Refrigerant Blend R507A, Using a Vibrating-Wire Technique. J. Chem. Eng. Data 2008, 53, 53−56. (41) Assael, M. J.; Dymond, J. H.; Papadaki, M.; Patterson, P. M. Correlation and Prediction of Dense Fluid Transport Coefficients. I. NAlkanes. Int. J. Thermophys. 1992, 13, 269−281. (42) De Lorenzi, L.; Fermeglia, M.; Torriano, G. Density, Refractive Index, and Kinematic Viscosity of Diesters and Triesters. J. Chem. Eng. Data 1997, 42, 919−923. (43) Harris, K. R. Temperature and Pressure Dependence of the Viscosities of 2-Ethylhexyl Benzoate, bis(2-Ethylhexyl) Phthalate, 2,6,10,15,19,23-Hexamethyltetracosane (Squalane), and Diisodecyl Phthalate. J. Chem. Eng. Data 2009, 54, 2729−2738. (44) Liu, Y.; Wang, Q. J.; Bair, S.; Vergne, P. A Quantitative Solution for the Full Shear-Thinning EHL Point Contact Problem Including Traction. Tribol. Lett. 2007, 28, 171−181. (45) Bair, S. High-Pressure Rheology for Quantitative Elastohydrodynamics; Elsevier: Amsterdam, 2007. (46) Cui, S. T.; Gupta, S. a; Cummings, P. T.; Cochran, H. D. Molecular Dynamics Simulations of the Rheology of Normal Decane, Hexadecane, and Tetracosane. J. Chem. Phys. 1996, 105, 1214−1220. (47) McCabe, C.; Cui, S.; Cummings, P. T.; Gordon, P. A.; Saeger, R. B. Examining the Rheology of 9-Octylheptadecane to Giga-Pascal Pressures. J. Chem. Phys. 2001, 114, 1887−1891. (48) Paluch, M.; Sekula, M.; Pawlus, S.; Rzoska, S. J.; Ziolo, J.; Roland, C. M. Test of the Einstein-Debye Relation in Supercooled Dibutylphthalate at Pressures up to 1.4 GPa. Phys. Rev. Lett. 2003, 90, 175702−01−175702−04. (49) Morgado, P.; Lobanova, O.; Müller, E. A.; Jackson, G.; Almeida, M.; Filipe, E. J. M. SAFT-γ Force Field for the Simulation of Molecular Fluids: 8. Hetero-Segmented Coarse-Grained Models of Perfluoroalkylalkanes Assessed with New Vapour−liquid Interfacial Tension Data. Mol. Phys. 2016, 114, 2597−2614. (50) Río, O.; Neumann, A. Axisymmetric Drop Shape Analysis: Computational Methods for the Measurement of Interfacial Properties from the Shape and Dimensions of Pendant and Sessile Drops. J. Colloid Interface Sci. 1997, 196, 136−147.

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NOTE ADDED AFTER ASAP PUBLICATION This article published April 24, 2017 with a mistake in the Supporting Information. The corrected Supporting Information file published July 25, 2017. 2895


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