Compressed-Liquid Density Measurements of Four Polyol Ester

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Cite This: Energy Fuels 2018, 32, 3775−3782

Compressed-Liquid Density Measurements of Four Polyol Ester-Based Lubricants Stephanie L. Outcalt* National Institute of Standards and Technology, Material Measurement Laboratory Applied Chemicals and Materials Division, 325 Broadway, Boulder, Colorado 80305-3337, United States S Supporting Information *

ABSTRACT: A vibrating-tube densimeter has been used to measure compressed-liquid densities of the fluids pentaerythritol tetrapentanoate (POE5), pentaerythritol tetraheptanoate (POE7), pentaerythritol tetranonanoate (POE9), and a fully qualified lubricant within a temperature range of 270 to 470 K at pressures within 0.5 to 50 MPa. The compressed-liquid densities of the lubricants studied cover a density range from 829 kg/m3 to 1063 kg/m3. The data have been extrapolated to atmospheric pressure and correlated with a Racket equation and the compressed-liquid density data have been correlated to Tait equations for comparison to existing literature data.

1. INTRODUCTION Lubricants serve to protect, clean, and seal the surfaces of moving components as they contact one another. Historically, mineral oil based lubricants have been used successfully; however, those compounds are typically not biodegradable and are toxic and thus can potentially pose long-term environmental hazards.1 The lubricants studied in this work pose less hazards and offer many advantages over mineral oil-based lubricants; they have better thermal and oxidative stability and their lower volatilities increase their lifetimes at higher temperatures.2 The ability of the polyol ester-based lubricants to function favorably at higher temperatures makes them particularly interesting to the aviation industry where turbine engines are being designed to operate at more extreme conditions to increase efficiency. Knowledge of the thermophysical properties of the lubricants that will be used in those engines is necessary for the development of equations of state (EOS) that will provide accurate property predictions during the engine design process. The measurements presented here are part of a broader scope of work performed at the National Institute of Standards and Technology (NIST) in Boulder, CO. The work includes measurements and modeling of density, heat capacity, speed of sound, thermal conductivity, and viscosity in addition to thermal decomposition and compositional analysis of the four lubricant samples; pentaerythritol tetrapentanoate (POE5), pentaerythritol tetraheptanoate (POE7), pentaerythritol tetranonanoate (POE9), and a fully qualified lubricant. While some density data exist in the literature for POE5, POE7, and POE9,1,3−8 there are no data for the fully qualified lubricant. This study expands the temperature range of available data by over 70 K for POE5 and over 116 K for POE7 and POE9. The fully qualified lubricant data are provided as that sample represents a fluid that meets the criteria set forth in the military specification for lubricating oil for aircraft turbine engines, MIL-PRF-23699F.9

Figure 1. Base structure of polyol esters where n = 3 for POE5, n = 5 for POE7 and n = 7 for POE9. n = 5 for POE7 and n = 7 for POE9. The samples measured in this work were obtained from the Naval Air Systems Command (NAVAIR). Compositional analyses of the samples were performed in our laboratories with gas chromatography (GC) with mass spectrometry (MS) detection, gas chromatography (GC) with a flame ionization detector (GC-FID) and 13C nuclear magnetic resonance (NMR) spectroscopy. The analysis is presented in detail in Urness et al.2 The POE5, POE7, and POE9 samples were found to have 96.7, 97.3, and 93.0 mol percent purities respectively based on the GC-FID analysis. The fully qualified lubricant sample was determined to be a mixture of polyol esters with additives to improve thermal stability, corrosion resistance, and hydrolytic degradation.2 Prior to measurements, samples were degassed following our standard procedure.10,11 First samples were transferred to 300 mL stainless steel cylinders. Closed cylinders were connected to a vacuum system and then submerged in liquid nitrogen to freeze the contained sample. Once the sample was frozen, the vapor space was evacuated. Once evacuated, the container was sealed and the sample was heated to facilitate driving remaining air into the vapor space. This “freeze-pump-thaw” cycle was repeated a minimum of three times to ensure the complete removal of dissolved air. 2.2. Experimental Section. Densities in the compressed-liquid state were measured with the vibrating-tube densimeter described in Outcalt and McLinden.12 In previous works, toluene (SRM 211D) and 99.999% propane have been used as calibration fluids. Due to the higher

2. MATERIAL AND METHODS

Received: January 4, 2018 Revised: February 16, 2018 Published: March 6, 2018

2.1. Sample Liquid. Figure 1 shows the base structure for polyol esters. In the case of the samples studied here, n is equal to 3 for POE5, This article not subject to U.S. Copyright. Published 2018 by the American Chemical Society

3775

DOI: 10.1021/acs.energyfuels.8b00050 Energy Fuels 2018, 32, 3775−3782

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Table 1. Measured Compressed-Liquid Densities of POE5 with Extrapolated Ambient Pressure Densities Shown in Italicsa 270 K p/MPa 50.01 45.02 40.01 35.00 30.01 25.02 20.02 15.02 10.05 5.01 4.04 3.01 2.01 1.01 0.53 0.083

290 K

ρ/ kg·m−3 1063.3 1061.0 1058.6 1056.2 1053.7 1051.2 1048.6 1046.0 1043.3 1040.4 1039.9 1039.3 1038.7 1038.1 1037.8 1037.6 390 K

p/MPa

ρ/ kg·m

49.99 45.02 40.03 35.02 30.04 25.01 20.01 15.03 10.05 5.02 4.02 3.02 2.03 1.03 0.54 0.083

980.8 977.4 973.9 970.2 966.4 962.5 958.4 954.2 949.7 945.0 944.0 943.0 942.1 941.1 940.6 940.1

−3

310 K

330 K

350 K

370 K

p/MPa

ρ/ kg·m−3

p/MPa

ρ/ kg·m−3

p/MPa

ρ/ kg·m−3

p/MPa

ρ/ kg·m−3

49.99 45.04 40.04 35.02 30.01 25.02 20.03 15.05 10.04 5.03 4.00 3.04 2.03 1.02 0.51 0.083

1049.2 1046.7 1044.2 1041.5 1038.8 1036.1 1033.3 1030.4 1027.4 1024.4 1023.8 1023.1 1022.5 1021.9 1021.6 1021.3 410 K

50.02 45.04 40.01 35.01 30.01 25.01 20.01 15.02 10.00 5.05 4.01 3.02 2.05 1.02 0.53 0.083

1035.0 1032.3 1029.6 1026.7 1023.8 1020.9 1017.8 1014.7 1011.4 1008.1 1007.4 1006.7 1006.0 1005.3 1005.0 1004.6

50.02 45.03 40.02 35.01 30.01 25.01 20.01 15.02 10.03 5.04 4.02 3.03 2.01 1.01 0.50 0.083

1020.9 1018.0 1015.1 1012.1 1009.0 1005.8 1002.5 999.2 995.7 992.1 991.3 990.6 989.8 989.1 988.7 988.4

50.01 45.03 40.00 35.03 30.02 25.02 20.04 15.02 10.04 5.04 4.01 3.02 2.00 1.02 0.52 0.083 450 K

1007.5 1004.3 1001.1 998.0 994.6 991.2 987.7 984.1 980.3 976.4 975.6 974.7 973.9 973.1 972.6 972.3

430 K

p/MPa

ρ/ kg·m

50.01 45.02 40.04 35.01 30.03 25.05 20.01 15.01 10.01 5.03 4.01 3.01 2.03 1.04 0.51 0.083

968.1 964.4 960.7 956.7 952.7 948.5 944.1 939.4 934.6 929.5 928.3 927.3 926.2 925.1 924.5 924.0

−3

ρ/ kg·m−3

p/MPa 50.00 45.02 40.03 35.01 30.05 25.02 19.99 15.01 10.02 5.02 4.01 3.05 2.02 1.01 0.51 0.083 470 K

994.0 990.7 987.4 984.0 980.5 976.8 973.0 969.0 965.0 960.7 959.8 958.9 958.0 957.0 956.6 956.2

p/MPa

ρ/ kg·m−3

p/MPa

ρ/ kg·m−3

p/MPa

ρ/ kg·m−3

50.00 45.01 40.04 35.03 30.01 25.02 20.03 15.03 10.01 5.04 4.03 3.01 2.01 1.03 0.52 0.083

955.5 951.6 947.6 943.5 939.1 934.6 929.8 924.8 919.5 913.9 912.8 911.5 910.3 909.1 908.5 908.0

50.05 45.01 40.01 35.01 30.03 25.02 20.00 15.01 10.02 5.04 4.01 3.01 2.01 1.03 0.53 0.083

943.2 939.1 934.8 930.3 925.7 920.8 915.6 910.2 904.5 898.3 897.0 895.7 894.4 893.0 892.4 891.7

50.03 45.01 40.04 35.02 30.01 25.01 20.01 15.02 10.01 5.02 4.01 3.01 2.02 1.03 0.54 0.083

931.0 926.6 922.1 917.4 912.4 907.2 901.6 895.8 889.5 882.7 881.3 879.8 878.3 876.8 876.1 875.4

The combined expanded uncertainties Uc are Uc(T) = 30 mK, Uc(p) = 0.01 MPa, Uc(ρ) = 0.7 kg·m−3 to 0.8 kg·m−3 at T < 423 K and 1.1 kg·m−3 to 1.2 kg·m−3 at T ≥ 423 K (level of confidence = 0.95). a

density ranges of the fluids studied in this work, toluene (SRM 211D) and HPLC grade water were used as calibration fluids. These fluids cover most of the density range of the samples studied in this work. The toluene and water samples underwent the same degassing procedure described above. Toluene was measured at 142 state points from 270 to 470 K at pressures from 0.5 to 50 MPa and water was measured at 104 points from 290 to 470 K at pressures from 2 to 45 MPa. Additionally, the period of oscillation of the U-tube was measured under vacuum from 270 to 470 K in 20 K increments. The NIST database REFPROP13 was used to predict the densities of the water and toluene. The calibration data were combined and correlated with the equation of May et al.14 Parameters for the equation were determined using nonlinear leastsquares fitting. The correlation represents the toluene and water data to average absolute deviations (AAD) of 0.13 kg·m−3 and 0.18 kg·m−3 respectively. The uncertainty in densities predicted by the equation of state for water increases from less than 0.003% at temperatures below 423 K, to 0.05% at temperatures above that, in the temperature and pressure range of this work. The overall combined uncertainty (k = 2, 95% confidence level) in densities presented here was calculated with the root sum of squares method (as described in the ISO Guide to the Expression of Uncertainty in Measurement15) to be 0.7 kg·m−3 to 0.8 kg·m−3 at temperatures below 423 K and 1.1 kg·m−3 to 1.2 kg·m−3 at temperatures of 423 K and above. The uncertainty encompasses the uncertainties in

the temperature measurement (±30 mK), pressure measurement (±10 kPa), equations of state for water and toluene, and the repeatability of the measurements of the lubricant samples. In general, each of the samples was measured from 270 to 470 K in 20 K increments and from 0.5 to 50 MPa along each isotherm and at least two isotherms were repeated to check for thermal degradation of the samples. The relatively high melting points of all but the POE5 sample resulted in the pressure range of the measurements at lower isotherms (270 and 290 K) being reduced to avoid solidifying the sample and measurements at 270 K not being performed on the POE9 sample.

3. RESULTS AND CORRELATION Measured compressed-liquid densities of POE5, POE7, POE9, and fully qualified lubricant are presented in Tables 1, 2, 3, and 4, respectively. The lubricants studied herein exhibit viscosities far greater than water particularly at lower temperatures and higher pressures. As such, calculations to determine the viscosity effect for the POE5, POE7, and POE9 samples were carried out following the method communicated in Fandino et al.1 and Fedele et al.5 The greatest correction was 0.7 kg·m−3 for the POE5 sample at 270 K and 50 MPa. At temperatures of 370 K and 3776


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Table 2. Compressed-Liquid Densities of POE7 with Extrapolated Ambient Pressure Densities Shown in Italicsa 270 K

290 K

ρ/ kg·m−3

p/ MPa

29.99 25.01 20.01 15.01 10.04 5.01 4.00 3.01 2.02 1.02 0.54 0.083

1011.9 1009.5 1007.0 1004.4 1001.8 999.0 998.5 997.9 997.4 996.8 996.6 996.3 390 K

p/ MPa

ρ/ kg·m

50.00 45.03 40.03 35.03 30.02 25.01 20.01 15.03 10.03 5.02 4.04 3.03 2.03 1.01 0.52 0.083

944.0 940.7 937.4 933.9 930.3 926.5 922.6 918.6 914.4 909.9 909.0 908.1 907.1 906.1 905.7 905.2

310 K

330 K

350 K

370 K

p/ MPa

ρ/ kg·m−3

p/ MPa

ρ/ kg·m−3

p/ MPa

ρ/ kg·m−3

p/ MPa

ρ/ kg·m−3

50.01 45.01 40.01 35.03 30.02 25.03 20.01 15.01 10.01 5.02 4.01 3.06 2.02 1.02 0.55 0.083

1007.5 1005.1 1002.6 1000.1 997.5 994.9 992.2 989.4 986.6 983.7 983.1 982.5 981.9 981.2 980.9 980.7 410 K

50.03 45.02 40.03 35.02 30.02 25.01 20.01 15.01 10.01 5.01 4.02 3.01 2.03 1.01 0.51 0.083

994.4 991.8 989.2 986.5 983.7 980.9 978.0 975.0 971.9 968.7 968.1 967.4 966.8 966.1 965.8 965.5

50.03 45.01 39.99 35.01 29.99 25.06 20.04 15.02 9.99 5.02 4.00 3.02 2.03 1.04 0.53 0.083

981.5 978.8 976.0 973.1 970.1 967.2 964.0 960.8 957.4 954.0 953.3 952.6 951.9 951.1 950.8 950.4

50.02 45.02 40.02 35.02 30.03 25.01 20.03 15.02 10.02 5.03 4.06 3.03 2.01 1.02 0.52 0.083 450 K

968.8 965.9 962.9 959.9 956.7 953.4 950.1 946.6 943.0 939.2 938.5 937.7 936.9 936.1 935.7 935.3

−3

430 K

p/ MPa

ρ/ kg·m

50.03 45.02 40.01 35.02 30.03 25.01 20.03 15.02 10.02 5.04 4.01 3.03 2.02 1.01 0.53 0.083

932.2 928.7 925.1 921.4 917.6 913.5 909.4 905.0 900.4 895.5 894.5 893.5 892.4 891.4 890.9 890.4

−3

ρ/ kg·m−3

p/ MPa 50.00 45.01 40.01 35.01 30.02 25.02 20.01 15.03 10.04 5.03 4.02 3.04 2.03 1.03 0.53 0.083 470 K

956.2 953.1 949.9 946.7 943.3 939.8 936.2 932.5 928.5 924.4 923.6 922.7 921.9 921.0 920.6 920.2

p/ MPa

ρ/ kg·m−3

p/ MPa

ρ/ kg·m−3

p/ MPa

ρ/ kg·m−3

50.00 45.03 40.03 35.01 30.03 25.01 20.01 15.02 10.02 5.03 4.02 3.01 2.02 1.01 0.52 0.083

920.5 916.8 913.0 909.1 905.0 900.7 896.2 891.4 886.4 881.1 880.0 878.9 877.8 876.6 876.0 875.5

50.04 45.03 40.03 35.03 30.04 25.02 20.01 14.99 10.04 5.05 4.01 3.02 2.01 1.03 0.53 0.083

909.1 905.2 901.1 896.9 892.5 887.9 883.1 877.9 872.5 866.7 865.5 864.3 863.0 861.7 861.1 860.5

50.02 45.02 40.02 35.04 30.04 25.01 20.03 15.05 10.03 5.02 4.02 3.05 2.04 1.05 0.52 0.083

897.7 893.6 889.3 884.8 880.1 875.2 870.0 864.5 858.6 852.2 850.9 849.5 848.1 846.7 846.0 845.3


Table 3. Compressed-Liquid Densities of POE9 with Extrapolated Ambient Pressure Densities Shown in Italicsa 290 K p/ MPa

310 K

ρ/ kg·m

−3

p/ MPa

330 K

ρ/ kg·m

−3

p/ MPa

350 K

ρ/ kg·m

−3

p/ MPa

370 K

ρ/ kg·m

−3

p/ MPa

390 K −3

ρ/ kg·m

p/ MPa

ρ/ kg·m−3

50.02

970.2

49.99

957.7

50.08

945.8

50.01

933.7

49.99

922.0

45.01

967.7

45.01

955.1

45.00

943.0

45.02

930.8

45.01

918.8

40.01

965.1

40.00

952.4

40.00

940.1

40.01

927.7

40.02

915.6

35.01

962.6

35.02

949.6

35.01

937.2

35.03

924.6

35.03

912.3

30.02

959.9

30.04

946.8

30.03

934.1

30.02

921.3

30.03

908.8

25.01

970.7

25.00

957.2

25.02

943.9

25.01

931.0

25.01

918.0

24.99

905.2

20.00

968.1

20.00

954.4

20.05

940.9

20.04

927.8

20.02

914.5

20.03

901.5

15.00

965.4

15.02

951.5

15.02

937.8

15.01

924.4

15.03

910.9

15.02

897.6

10.01

962.7

10.02

948.5

10.01

934.6

10.01

921.0

10.03

907.2

10.05

893.6

5.01

959.9

5.03

945.5

5.03

931.3

5.01

917.4

5.03

903.2

5.03

889.3

4.04

959.3

4.01

944.8

4.03

930.6

4.02

916.6

4.00

902.4

4.01

888.4

3.05

958.7

3.01

944.2

3.04

929.9

3.02

915.9

3.03

901.6

3.03

887.5

2.04

958.2

2.02

943.6

2.04

929.2

2.02

915.1

2.02

900.8

2.04

886.6

1.02

957.6

1.03

942.9

1.02

928.5

1.02

914.4

1.04

899.9

1.03

885.7

0.51

957.3

0.51

942.6

0.52

928.1

0.53

914.0

0.53

899.5

0.53

885.3

0.083

957.0

0.083

942.3

0.083

927.8

0.083

913.6

0.083

899.1

0.083

884.8

3777


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Table 3. continued 410 K

430 K

p/ MPa

ρ/ kg·m

50.03 45.02 40.01 35.02 30.00 25.01 20.02 15.01 10.00 5.02 4.02 3.03 2.01 1.02 0.52 0.083

910.6 907.3 903.8 900.3 896.6 892.8 888.8 884.6 880.2 875.5 874.5 873.6 872.6 871.6 871.1 870.6

−3

450 K −3

470 K

p/ MPa

ρ/ kg·m

p/ MPa

ρ/ kg·m

50.02 45.02 40.02 35.02 30.01 25.02 20.02 15.00 10.03 5.01 4.01 3.04 2.02 1.04 0.51 0.083

899.4 895.9 892.3 888.5 884.6 880.5 876.2 871.6 866.9 861.8 860.8 859.7 858.6 857.6 857.0 856.5

50.02 45.02 40.04 35.01 30.02 25.04 20.00 15.02 10.02 5.04 4.04 3.01 2.02 1.02 0.54 0.083

888.5 884.8 880.9 876.9 872.7 868.3 863.7 858.8 853.6 848.2 847.0 845.8 844.6 843.4 842.9 842.3

−3

p/ MPa

ρ/ kg·m−3

50.01 45.02 40.04 35.02 30.01 25.02 20.03 15.02 10.01 5.00 4.03 3.01 2.01 1.01 0.53 0.083

877.7 873.8 869.7 865.4 860.9 856.2 851.3 846.0 840.4 834.4 833.2 831.9 830.6 829.2 828.6 828.0


Table 4. Compressed-Liquid Densities of the Fully Qualified Lubricanta 270 K p/ MPa

290 K

ρ/ kg·m

−3

p/ MPa

310 K

ρ/ kg·m

−3

p/ MPa

330 K

ρ/ kg·m

−3

350 K

ρ/ kg·m

p/ MPa

−3

p/ MPa

370 K

ρ/ kg·m

−3

p/ MPa

ρ/ kg·m−3

50.01

1008.6

50.00

995.5

49.99

982.7

50.04

970.1

45.03

1006.0

45.04

992.8

45.01

979.7

45.01

967.0

40.02

1030.3

39.94

1016.6

40.04

1003.3

40.01

989.9

40.04

976.7

40.03

963.8

35.01

1028.0

35.02

1014.1

35.02

1000.6

35.02

987.0

35.02

973.6

35.03

960.5

30.03

1025.6

30.04

1011.5

30.04

997.8

30.01

984.1

30.00

970.5

30.01

957.1

25.01

1023.2

25.01

1008.9

25.01

995.0

25.01

981.0

25.01

967.2

25.01

953.6

20.01

1020.7

20.01

1006.2

20.01

992.0

20.02

977.9

20.01

963.8

20.02

950.0

15.01

1018.2

15.03

1003.4

15.02

989.0

15.01

974.7

15.03

960.4

15.01

946.2

10.03

1015.6

10.01

1000.6

10.02

985.9

10.04

971.4

10.03

956.7

10.02

942.3

5.01

1012.9

5.00

997.6

5.03

982.7

5.01

967.9

5.03

952.9

5.02

938.2

4.04

1012.3

4.01

997.0

4.02

982.0

4.02

967.2

4.01

952.1

4.00

937.3

3.01

1011.8

3.02

996.4

3.01

981.4

3.01

966.4

3.03

951.4

3.02

936.5

2.01

1011.2

2.03

995.8

2.01

980.7

2.02

965.7

2.02

950.6

2.01

935.6

1.03

1010.7

1.03

995.2

1.04

980.1

1.03

965.0

1.03

949.8

1.02

934.7

0.52

1010.4

0.52

994.9

0.53

979.7

0.53

964.6

0.55

949.4

0.52

934.3

0.083

1010.1

0.083

994.6

0.083

979.4

0.083

964.3

0.083

949.0

0.083

933.9

390 K p/ MPa

410 K

ρ/ kg·m

−3

p/ MPa

430 K

ρ/ kg·m

−3

450 K

ρ/ kg·m

p/ MPa

−3

p/ MPa

470 K −3

ρ/ kg·m

p/ MPa

ρ/ kg·m−3

50.02

957.7

50.01

945.7

50.00

933.9

50.02

922.4

49.99

910.9

45.01

954.5

45.02

942.2

45.01

930.3

44.99

918.4

44.99

906.8

40.01

951.1

40.03

938.6

40.02

926.4

40.06

914.4

40.03

902.5

35.03

947.5

35.02

934.9

35.03

922.5

35.01

910.2

35.02

898.0

30.03

943.9

30.01

931.0

30.03

918.3

30.01

905.7

30.01

893.3

25.03

940.1

25.02

927.0

25.00

914.0

25.00

901.1

25.00

888.3

20.03

936.2

20.02

922.8

20.00

909.5

20.03

896.3

20.04

883.1

15.01

932.1

15.01

918.3

15.02

904.7

15.02

891.1

15.01

877.5

10.03

927.9

10.01

913.7

10.02

899.7

10.03

885.7

10.01

871.6

5.02

923.4

5.03

908.9

5.02

894.4

5.00

879.8

5.01

865.2

4.01

922.5

4.00

907.8

4.04

893.3

4.03

878.6

4.01

863.8

3.01

921.5

3.04

906.8

3.03

892.1

3.01

877.3

3.03

862.5

2.04

920.6

2.01

905.8

2.02

891.0

2.01

876.1

2.04

861.1

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Table 4. continued 390 K

410 K

p/ MPa

ρ/ kg·m

1.03 0.53 0.083

919.6 919.2 918.7

−3

430 K

p/ MPa

ρ/ kg·m

1.01 0.53 0.083

904.7 904.2 903.7

−3

450 K

p/ MPa

ρ/ kg·m

1.02 0.53 0.083

889.8 889.3 888.7

−3

470 K −3

p/ MPa

ρ/ kg·m

p/ MPa

ρ/ kg·m−3

1.02 0.53 0.083

874.8 874.2 873.6

1.03 0.54 0.083

859.7 859.0 858.3


above, the correction for all three samples is 0.1 kg·m−3 or less. As the viscosity corrections rely on viscosity correlations (from other researchers in this case) that include their own uncertainties and because the maximum correction for the fluids studied in this work is well below the maximum uncertainty stated for the measurements herein, the densities shown in the tables have not been corrected for viscosity effects. The compressed-liquid densities of each of the lubricants were extrapolated to ambient pressure (0.083 MPa, atmospheric pressure at NIST in Boulder, CO) as detailed previously.16 Those densities are shown in italics in Tables 1−4. Extrapolated densities were correlated with a modification of the Rackett equation17 (originally developed to relate the reduced volume of saturated liquids to the reduced temperature and critical compressibility factor). The modified equation is written as

ρ = β1·β2−(1 + (1 − T / β3)

β4 )

(1)

where the correlated parameters β1 and β3 should loosely represent the critical density and critical temperature of the fluid being fitted. The resulting correlation parameters are listed in Table 5. The correlations represent the extrapolated densities with average absolute deviations of 0.03%, 0.01%, 0.02%, and 0.01% for POE5, POE7, POE9, and fully qualified lubricant, respectively. Figures 2−4 illustrate deviations of ambient pressure density data found in the literature and extrapolated densities presented

Table 5. Parameters of the Rackett Correlations for the Extrapolated Densities of the Four Lubricants at an Ambient Pressure of 83 kPa and Temperatures from 270 to 470 K POE5

POE7

parameter

value

std. dev.

β1 (kg·m−3) β2 β3 (K) β4

209.9 0.406 882.0 0.705

1.4 1 × 10−3 2.0 1 × 10−3 POE9

value

std. dev.

209.9 0.9 0.4160 9 × 10−4 882.0 1.2 0.6966 8 × 10−4 fully qualified lubricant

parameter

value

std. dev.

value

std. dev.

β1 (kg·m−3) β2 β3 (K) β4

209.9 0.421 915.0 0.737

1.7 2 × 10−3 2.8 1 × 10−3

209.9 0. 4136 882.0 0.6809

0.8 8 × 10−4 1.1 7 × 10−4

Figure 3. Percent density deviations of POE7 literature data and extrapolated densities of this work from Rackett equation correlated to extrapolated densities of this work. Dashed lines represent the maximum uncertainty bounds of this work (0.09% at T < 423 K and 0.14% at T ≥ 423 K) from the Rackett correlation.

Figure 2. Percent density deviations of POE5 literature data and extrapolated densities of this work from Rackett equation correlated to extrapolated densities of this work. Dashed lines represent the maximum uncertainty bounds of this work (0.09% at T < 423 K and 0.14% at T ≥ 423 K) from the Rackett correlation.

Figure 4. Percent density deviations of POE9 literature data and extrapolated densities of this work from Rackett equation correlated to extrapolated densities of this work. Dashed lines represent the maximum uncertainty bounds of this work (0.09% at T < 423 K and 0.14% at T ≥ 423 K) from the Rackett correlation. 3779


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where ρref is calculated from eq 1 (representing density at atmospheric pressure) and

here from the Rackett correlations for POE5, POE7, and POE9. To aid in interpretation of the figures, Table 6 lists the author

D(T ) = β5 + β6Tr + β7Tr2

Table 6. Author Stated Purities of the Samples of POE5, POE7, and POE9 Studied fluid

reference

where Tr = T/273.15 K. Parameters C, β5, β6, and β7 for each of the four lubricants studied in this work are given in Table 7. The lubricants POE7, POE9, and fully qualified lubricant are correlated to an AAD of 0.01% by the Tait equations presented here while the POE5 equation has an AAD of 0.03%. Additionally, isothermal compressibility has been calculated (as a derivative of eq 2) for each of the fluids and is included as Supporting Information. To compare literature values to compressed-liquid densities measured in this work Figures 5−7 illustrate deviations from a

author stated purity

POE5 Fandiño et al.4 Fedele et al.5 Segovia et al.6 Shobha and Kishore7 Wahlström and Vamling18 This work

(3)

greater than 95% greater than 98% 99% “pure within the sensitivity of these measurements” greater than 95% 96.7 mol percent

POE7 Fandiño et al.1 El-Magly et al.3 Fedele et al.5 Shobha and Kishore7 This work

greater than 95% greater than 97% greater than 98% “pure within the sensitivity of these measurements” 97.3 mol percent

POE9 Fandiño et al.1 El-Magly et al.3 Shobha and Kishore7 Wahlström and Vamling8 This work

greater than 95% greater than 97% “pure within the sensitivity of these measurements” greater than 95% 93.0 mol percent

Figure 5. Percent density deviations of POE5 literature data from the Tait equation correlated to compressed-liquid densities of this work. Dashed lines represent the maximum uncertainty bounds of this work (0.09% at T < 423 K and 0.14% at T ≥ 423 K) from the Tait correlation.

stated purity for each of the POEs. The fully qualified lubricant is not represented as there are no literature data for that fluid. Figure 2 illustrates that the data of Fedele et al.,5 and all but one point of Segovia et al.6 agree with the Rackett correlation of this work within the stated experimental uncertainty of this work, whereas most of the data of Whalstrom and Vamling18 and all of the data of Fandino et al.4 and Shoba and Kishore7 have higher deviations. Figure 3 shows the POE7 extrapolated densities of this work in good agreement with the data of Fedele et al.5 and relatively large positive deviations for other data sets. The data of El-Magly et al.3 and five points of Shoba and Kishore7 have deviations in excess of 1.2%. Finally, Figure 4 (POE9) shows good agreement between the ambient pressure densities of this work and those of Whalstrom and Vamling8 below 343 K with other authors again showing positive deviations. The compressed-liquid densities tabulated in Tables 1−4 have been correlated with a Tait equation of the form ρ (T , p) =

baseline of the Tait correlations. Again, there is no figure for the fully qualified lubricant as there are no literature data for this fluid. Like the ambient pressure densities, Figure 5 shows that the compressed-liquid densities measured in this work for POE5 agree (within the experimental uncertainty) with the data of Fedele et al.5 and most of the data of Segovia et al.,6 while the data of Fandino et al.4 are consistently higher. Comparisons of POE7 data shown in Figure 6 indicate good agreement between our data and Fedele et al.5 with the data of Fandino et al.1 significantly higher. Finally, the data of Fandino et al.1 are again higher than our measured densities of POE9 shown in Figure 7.

4. CONCLUSIONS Compressed-liquid densities have been measured for four lubricant samples from 270 to 470 K at pressures from 0.5 to 50 MPa. The compressed-liquid densities of the lubricants studied cover a density range from 829 kg/m3 to 1063 kg/m3. The density ranges of the four fluids overlap approximately 100 kg/m3, from

ρref (T , pref ) ⎛ p + D(T ) ⎞ 1 − C ln⎜ p + D(T ) ⎟ ⎝ ref ⎠

(2)

Table 7. Parameters for the Tait Correlations of the Compressed-Liquid Densities of POE5, POE7, POE9, and Fully Qualified Lubricant Measured in This Work POE5

POE7

POE9

fully qualified lubricant

parameter

value

std. dev.

value

std. dev.

value

std. dev.

value

std. dev.

C β5 (MPa) β6 (MPa) β7 (MPa)

0.0879 520.7 −481.2 121.6

1 × 10−4 0.9 0.9 0.3

0.0839 427.6 −368.0 86.5

1 × 10−4 0.9 0.9 0.3

0.0837 431.9 −372.6 88.3

1 × 10−4 0.7 0.7 0.2

0.0835 428.9 −368.6 86.5

1 × 10−4 0.9 0.9 0.3

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reflection of the quality of the data, but probably more a function of the differences in the compositions of the samples studied.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.energyfuels.8b00050. Additional information as noted in the text (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Stephanie L. Outcalt: 0000-0001-8143-7316


Notes

The author declares no competing financial interest.

■

ACKNOWLEDGMENTS The author thanks James McDonnell and Dawn Schmidt at the U.S. Naval Air Systems Command (NAVAIR) for funding this work and providing the lubricant samples. Contribution of the National Institute of Standards and Technology. Not subject to Copyright © in the U.S.A.

■

REFERENCES

(1) Fandiño, O.; Pensado, A. S.; Lugo, L.; López, E. R.; Fernández, J. Volumetric behaiour of the environmentally compatible lubricants pentaerythritol tetraheptanoate and pentaerythritol tetranonanoate at high pressures. Green Chem. 2005, 7, 775−783. (2) Urness, K. N.; Gough, R. V.; Widegren, J. A.; Bruno, T. J. Thermal Decomposition Kinetics of Polyol Ester Lubricants. Energy Fuels 2016, 30 (12), 10161−10170. (3) El-Magly, I. A.; Nagib, H. K.; Mokhtar, W. M. Aspects of the behavior of some pentaerythritol ester base cynlubes for turbo-engines. Egypt. J. Pet. 2013, 22, 169−177. (4) Fandiño, O.; García, J.; Comuñas, M. J. P.; López, E. R.; Fernández, J. PρT Measurements and Equation of State (EoS) Predictions of Ester Lubricants up to 45 MPa. Ind. Eng. Chem. Res. 2006, 45 (3), 1172−1182. (5) Fedele, L.; Marinetti, S.; Bobbo, S.; Scattolini, M. PρT Experimental Measurements and Data Correlation of Pentaerythritol Esters. J. Chem. Eng. Data 2007, 52 (1), 108−115. (6) Segovia, J. J.; Fandiño, O.; López, E. R.; Lugo, L.; Carmen Martín, M.; Fernández, J. Automated densimetric system: Measurements and uncertainties for compressed fluids. J. Chem. Thermodyn. 2009, 41 (5), 632−638. (7) Shobha, H. K.; Kishore, K. Structural dependence of density in high molecular weight esters. J. Chem. Eng. Data 1992, 37 (4), 371−376. (8) Wahlström, Å.; Vamling, L. Solubility of HFCs in Pentaerythritol Tetraalkyl Esters. J. Chem. Eng. Data 2000, 45 (1), 97−103. (9) Lubricating Oil, Aircraft Turbine Engine, Synthetic Base, NATO Code No. O-156. 1997. (10) Outcalt, S. L.; Lemmon, E. W. Bubble-Point Measurements of Eight Binary Mixtures for Organic Rankine Cycle Applications. J. Chem. Eng. Data 2013, 58, 1853−1860. (11) Outcalt, S. L.; Fortin, T. J. Density and Speed of Sound Measurements of Four Bioderived Aviation Fuels. J. Chem. Eng. Data 2012, 57 (10), 2869−2877. (12) Outcalt, S. L.; McLinden, M. O. Automated Densimeter for the Rapid Characterization of Industrial Fluids. Ind. Eng. Chem. Res. 2007, 46, 8264−8269. (13) Lemmon, E. W.; Huber, M. L.; McLinden, M. O. NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.11; National Institute of Standards and Technology, Standard Reference Data Program: Gaithersburg, 2014.


876 kg/m3 to 971 kg/m3, with the densities of POE5 > fully qualified lubricant > POE7 > POE9 for similar state points. The order of the densities of the POEs may have to do with the length of the hydrocarbon chain attached to the base ester (See Figure 1). The smaller the side chain of the POE, may allow for a more tightly packed molecular structure and hence the greater the density from smallest side chain (POE5) to largest (POE9). Measured data have been tabulated and densities at 10 MPa and below (along each isotherm measured) have been extrapolated to predict an ambient pressure density. Those predicted ambient pressure densities and the compressed-liquid densities of POE5 and POE7 agree with some of the literature data5,6,8 while they are consistently lower than other data sets for all three of the pentaerythritol esters (POEs).1,3,4,7 The pentaerythritol esters are the product of synthesis; depending on the purity of the starting materials and the synthesis process followed in each laboratory, the end-products can be very different in their percent purity as well as the impurities they contain. Each author cited in this work, studied their specific samples. No two authors studied samples of the same purity (or composition of impurities) for a given POE. As such, agreement between the data sets of various authors is not necessarily a 3781


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(14) May, E. F.; Tay, W. J.; Nania, M.; Aleji, A.; Al-Ghafri, S.; Trusler, J. P. M. Physical apparatus parameters and model for vibrating tube densimeters at pressures to 140 MPa and temperatures to 473 K. Rev. Sci. Instrum. 2014, 85 (9), 095111. (15) International Organization of Standardization (ISO). Guide to the Expression of Uncertainty in Measurement; ISO: Geneva, Switzerland. 1995. (16) Outcalt, S. L.; Fortin, T. J. Density and Speed of Sound Measurements of Four Bioderived Aviation Fuels. J. Chem. Eng. Data 2012, 57 (10), 2869−2877. (17) Rackett, H. G. Equation of state for saturated liquids. J. Chem. Eng. Data 1970, 15 (4), 514−517. (18) Wahlström, Å.; Vamling, L. Solubility of HFC32, HFC125, HFC134a, HFC143a, and HFC152a in a Pentaerythritol Tetrapentanoate Ester. J. Chem. Eng. Data 1999, 44 (4), 823−828.

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Compressed-Liquid Density Measurements of Four Polyol Ester

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