A Literature Review on Viscometers that Measure the Viscosity at Extreme Conditions
By Krista Melish
Introduction
A literature review was completed for recent publications regarding improvements and modifications to different types of viscometers. The focus was placed on the papers published within the last fifteen years that describe the viscometers designed to measure the viscosity of fluids at high temperatures and pressures. The purpose of this report is to identify reliable references to be used for future studies.
The knowledge gained from this study will apply to the design of a viscometer that accurately measures the viscosity of oil and natural gas at reservoir conditions. This viscosity measurement can be used to predict the density of the fluid.
Below is a condensed description of the various types of viscometers and a brief summary of the progression of the instruments over time. The types of viscometers have been categorized into the following six major groups for the purpose of this report: vibrating wire, capillary, falling body, torsional quartz-crystal, oscillating body, and rolling ball.
Vibrating Wire Viscometer
J. T. Tough, W. D. McCormick, and J. G. Dash first used the vibrating wire viscometer to study the viscosity of liquid helium.1 The basic apparatus consists of a metal wire clamped at either end and placed in a permanent magnetic field. The wire is surrounded by the sample fluid. A voltage is applied to the wire, causing the wire to oscillate. The viscosity is calculated based on the damping of the translational vibrations. Several different working equations have been used to calculate the viscosity from the velocity, frequency, or damping of the oscillation as long as the wire properties are known.
The theory of the vibrating wire viscometer was improved by Mostert et. al in 1988.2 Their publication includes the equations necessary to calculate the viscosity based on the mechanical motion of the wire and on the motion of the surrounding fluid. In 2005, a student at the University of Canterbury wrote a dissertation that expands the method. 3 Modifications to the method by varying the material, radius and length, and clamping methods of the wire have made this instrument able to measure the viscosity of liquids and gases with an accuracy of 0.1%.x [3]According to the references studied, the vibrating wire viscometer can measure the viscosity of fluids at temperatures up to 473.15 Kx [4]and at pressures up to 1 GPa.4 Other high pressure viscosity measurements were performed at 300 MPa5 and 200 MPa. 6,7
Alternatively, Retsina et. al published a paper in 1986 in which a rod with a much larger diameter was used instead of a wire.8 The theory was tested on water and produced an accuracy of 0.1%.
The vibrating wire viscometer requires a smaller sample fluid volume than the falling body and oscillating viscometers. The construction is also very simple relative to the other methods, securing the reproducibility of results..x[8]
Capillary Viscometer
The capillary viscometer is the most used viscometer, because it is easily operated and simply constructed. G. Sagaidakova performed an early study of the capillary viscometer in 1943.9 A capillary viscometer allows the sample liquid to flow through a tube with a very small diameter, referred to as a capillary. The viscosity is calculated by measuring the volumetric flow rate of the liquid and the pressure drop as long as the diameter and length of the tube and the volume of the fluid is predetermined.
The capillary viscometer has successfully measured the viscosity at temperatures up to 100 MPa with an accuracy of 0.1%. Another study measured the viscosity to 0.5%. The capillary viscometer has also measured viscosity at high temperatures of 500 K,10 575 K,11 and 573.15 K.12
Falling Body Viscometer
Falling body viscometers rely on the force of gravity to drive a sinker through a vertical tube containing the sample fluid. The sinkers are typically magnetic or consist of a metallic core and are of various geometries that may affect the frictional effects between the tube and sinker, drag forces, velocity of the sinker, and reproducibility of the results.x The most commonly used sinker geometry is the cylinder. Sphere, needle13, tube14, and cup shaped sinkers have also been explored.
The viscosity is commonly calculated by measuring the time taken for the sinker to be displaced a known distance. When the sinker passes by the magnetic coils marking the distance travelled by the sinker, a current is induced. The time between two voltage readings is used to calculate the viscosity as long as the sinker dimensions and displacement is predetermined. Alternatively, the viscosity has also been calculated by measuring the terminal velocity of the sinker. When the sinker is dropped in the fluid, it accelerates until reaching terminal velocity. The sinker density and dimensions, tube dimensions, and fluid densities must be known to use this method.
This falling body viscometer has been modified by varying the methods to hold, raise, and release the sinker and by varying the sinker detection methods. This apparatus has measured the viscosity of fluids at high pressures of 1.4 Gpa,15 1 GPa,16 500 MPa,17 and 400 MPa18 and at temperatures up to 438.15 K.18 The falling body viscometer can measure the viscosity with an accuracy of 1%.
Torsional Vibrating Quartz-Crystal Viscometer
Warren Perry Mason developed the torsional vibrating quartz-crystal viscometer in 1947. He used quartz as a resonator because of the material’s low dependency on temperature and the piezoelectric properties the quartz exhibits when cut properly.x The quartz-crystal is equipped with metallic electrodes to which an alternating voltage is applied, causing the crystal to vibrate with a torsional motion at a resonant frequency. When placed in a body of fluid, the shear waves are damped. Viscosity is determined by calculating the change in frequency or in resonant resistance from that in a vacuum. The fluid density and crystal dimensions and properties must be known.
The torsional vibrating quartz-crystal viscometer has been used to measure the viscosity of fluids up to temperatures of 600 K19 and pressures of 687 MPa.20 Other high pressure studies were performed at 200 MPa with an accuracy of 0.5%.21
This apparatus is small, simple, and lacks macroscopically moving parts and calculates viscosity fairly accurately without the need for pressure difference calculations.
Oscillating body viscometers
Miesowicz first used an oscillating disk viscometer in 1936. The basic apparatus consists of a body attached to a wire suspended vertically. The body oscillates back and forth due to an induced electric field. The oscillation is damped when placed in the fluid. The angular frequency of the oscillations in the fluid and in a vacuum must be measured, as well as the damping decrement to determine the viscosity of the fluid. The dimensions of the body must also be known. The body geometries that have been studied include the cup, sphere, disk, and cylinder.
Many successful oscillating cup viscometers have been designed to work at very high temperatures. For example, M. Kehr et. al tested the viscosity of pure metals at 1873 K.22
Rolling ball
Robert Hubbard was one of the first people to perform a theoretical study on the rolling ball viscometer in1943. The viscosity can be calculated for this method if the time it takes a ball to travel a known distance of an inclined tube filled with the sample fluid is measured. Magnetic sensors are used to detect the position of the ball. Improvements to the rolling ball viscometer have been made by modifying the tube angle, ball material, and ball diameter. The design of a rolling ball microviscometer improved this technique because it requires a very small sample volume.23
This method has been used to measure viscosity at pressures up to 800 MPa24 and 350 MPa25 and temperatures up to 398 K.26 An accuracy of 0.95% has been obtained using the rolling ball viscometer.24
Temperature and Pressure Ranges of Viscometers
Each type of viscometer can be modified to measure viscosity at different conditions. For aesthetic purposes, the chart below has been constructed to show the working pressure and temperature ranges for the viscometers studied in the literature review. The bottom-middle box has been omitted, because the low pressure and low temperature conditions are of no interest in this study. The numbers presented correlate to the bibliography included in Appendix A.
Table 1. Viscometer temperature and pressure ranges
Temperature273 K / 450 K
/ 100 MPa / 33, 75 / 1, 2, 4, 12, 14, 28, 32, 33, 45, 48, 51, 52, 61, 69, 71, 72, 75,77,78 / 30, 31, 34, 51, 69
10 MPa / 75 / 1, 2, 3, 4, 5, 6, 7, 10, 13, 14, 15, 16, 17, 18, 22, 23, 24, 25, 32, 33, 35, 36, 38, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68,69, 70, 71, 72, 75,77,78 / 10, 25, 34, 35, 51, 54, 56, 58, 66, 69
0.1 MPa / 75 / 34, 35
Table 1 above shows that a majority of the viscometers have been designed to measure viscosity at temperatures between 273 K and 450 K and pressures between 10 MPa and 100 MPa. However, there are several viscometers designed to work at even more extreme conditions.
References
1. Tough, J.T., McCormick, W.D., and Dash, J.G. ,Viscosity of Liquid He II, Phys. Rev. 132, 2373, 1963.
2. Mostert, R., Van Der Gulik, P.S., and Van Den Berg, H.R., The Working Equations of a Vibrating Wire Viscometer, Physica A: Statistical and Theoretical Physics. 156(3), 909-920,1989.
3. Kandil, M., The Development of a Vibrating Wire Viscometer and a Microwave Cavity Resonator,
4. Van der Gulik, P.S., Mostert, R., and Van den Berg, H.R., The Viscosity of Methane at 273 K up to 1 GPa, Fluid Phase Equilibria. 79, 301-311, 1992.
5. Assael, M.J., and Wakeham, W.A.,Vibrating-Wire Viscometry on Liquids at High Pressure, Fluid Phase Equilibria. 75, 269-285, 1992.
6. Caudwell, D.R., Trusler, J.P.M., Vesovic, V., and Wakeham, W.A., The Viscosity and Density of n-Dodecane and n-Octadecane at Pressures up to 200 MPa and Temperatures up to 473 K, International Journal of Thermophysics, 25(5), 2004.
7. Caudwell, D.R., Trusler, J.P.M., Vesovic, V., and Wakeham, W.A., Viscosity and Density of Five Hydrocarbon Liquids at Pressures up to 200 Mpa and Temperatures up to 473 K, J. Chem. Eng. Data, 54, 359–366, 2009.
8. Retsina, T., Richardson, S.M., and Wakeham, W.A., The Theory of a Vibrating-Rod Viscometer, Applied Scientific Research. 43, 325-346, 1987.
9. Sagaidakova, G., Theory of a Capillary Viscometer, Journal of Engineering Physics and Thermophysics. 36(4), 457-462, 1972.
10. Yusibani, E., Nagahama,Y., Kohno, M., Takata, Y., Woodfield, P.L., Shinzato, K., and Fujii, M., A Capillary Tube Viscometer Designed for Measurements of Hydrogen Gas Viscosity at High Pressure and High Temperature, Int J Thermophys, 32, 1111–1124, 2011.
11. Abdulagatova, I.M., and Azizov, N.D., Viscosity for Aqueous Li2SO4 Solutions at Temperatures from 298 to 575 K and at Pressures up to 30 MPa, J. Chem. Eng. Data. 48, 1549-1556, 2003.
12. Abdulagatova, I.M., Zeinalovab, A., and Azizov, N.D., Viscosity of aqueous Na2SO4 solutions at temperatures from 298 to 573 K and at pressures up to 40 MPa, Fluid Phase Equilibria. 227, 57–70, 2005.
13. Park, N.A., Cho, Y.I., and Irvine, T.F., Steady Shear Viscosity Measurements of Viscoelastic Fluids with the Falling Needle Viscometer, Journal of Non-Newtonian Fluid Mechanics, 34, 351-357, 1990.
14. Gui, F., and Irvine, T.F., An Absolute Falling Tube Viscometer, Experimental Thermal and Fluid Science. 12, 325-337, 1996.
15. Bair, S., and Qureshi, F., Accurate Measurements of Pressure-Viscosity Behavior in Lubricants, Tribology Transactions, 45(3), 390, 2002.
16. Bair, S., A Routine High-Pressure Viscometer for Accurate Measurements to 1 GPa, Tribology Transactions. 47(3), 356, 2004.
17. Schaschke, C.J., Abid, S., and Heslop, M.J., High-Pressure Viscosity Measurement of Fatty Acids and Oils, High Pressure Research. 27(1), 33–37, 2007.
18. Laesecke, A., and Bair, S., High-Pressure Viscosity Measurements of 1,1,1,2-Tetrafluoroethane, Int J Thermophys. 32, 925–941, 2011.
19. Diller, D.E., and Frederick, N.V., Torsional Piezoelectric Crystal Viscometer for Compressed Gases and Liquids, International Journal of Thermophysics, 10(1), 1989.
20. Collings, A.F., and McLaughlin, E., Torsional Crystal Technique for the Measurement of Viscosities of Liquids at High Pressure, Trans. Faraday Soc. 67, 340-352, 1971.
21. Vieira dos Santos, F.J., and Nieto de Castro, C.A., Viscosity of Toluene and Benzene Under High Pressure, International Journal of Thermophysics. 18(2), 1997.
22. Kehr, M., Hoyer, W., and Egry, I., A New High-Temperature Oscillating Cup Viscometer, Int J Thermophys. 28,1017–1025, 2007.
23. Dandekar, A.Y., Andersen, S.I., and Stenby, E.H., Measurement of Viscosity of Hydrocarbon Liquids Using a Microviscometer, J. Chem. Eng. Data, 43, 551-554, 1998.
24. Nishibata, K., and Izuchi, M., A Rolling Ball Viscometer for High Pressure Use. Physica B+C. 139-140, 903-906, 1986.
25. Sawamura, S., and Takashi Yamashita, T., Rolling-Ball Viscometer for Studying Water and Aqueous Solutions under High Pressure, 429.
26. Paredes, X., Fandiño, O., Comuñas, M. J. P., Pensado, A.S., Fernández, J., Study of the Effects of Pressure on the Viscosity and Density of Diisodecyl Phthalate, J. Chem. Thermodynamics. 41, 1007–1015, 2009.
Appendix A
INCLUDE THE EXCEL SPREADSHEET
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