(74x) Prediction of High-Temperature and High-Pressure Dynamic Viscosity of Hydrocarbons By Van Der Waals Transport Equation of State

According to the review of liquid viscosity by Brush (1962), ¹ “there is no general agreement on whether viscosity is essentially due to the attractive and repulsive forces,” but on macroscopic scale both viscosity and density are function of the thermodynamic equilibrium state of the fluid² (therefore, they both surrender to the Law of Corresponding States ^3,4) while on microscopic scale both properties reflect the effects of molecular motion and interaction. So, in accordance with the hypothesis enunciated by Phillips (1927)⁵ and later improvements by Little-Kennedy (1966)⁶ and Lawal (1986), ⁷ a method is established for predicting Newtonian viscosity or dynamic viscosity (η) over the entire PVT states of single-phase fluids such as polar and nonpolar substances, hydrocarbon, non-hydrocarbon, petroleum fractions and high-molecular-weight-fluids of the type currently being measured for high-temperature and high-pressure (HTHP) deep-water formations ^8-17 and carbon dioxide sequestration.

By using the1986 formalism of the Viscosity Equation of State (VEOS) development, the VEOS technique is designed on the basis of the phenomenological similarity between PVT and TηP spinodal graphs and is solely depended on accurate critical viscosity of pure substances.  There is no resorting to the judicious choice of liquid density correlation or any volumetric properties because the coexistence gas-liquid viscosities, the dilute-gas viscosity, the dense and supercritical fluid viscosities are based on the four-parameter cubic equation of state⁷ which is valid over the entire PVT states, include the vapor-liquid critical point.

The VEOS is validated by the prediction of accurate coexistence gas-liquid viscosities over the entire PVT states of pure substances, including polar and nonpolar substances, inert gases (Argon, Helium, Xenon), hydrocarbons of high-molecular-weights and non-hydrocarbons (nitrogen, carbon dioxide, hydrogen sulfide) and liquid viscosity of very viscous fluids.

References:

1. Brush, S. G., “Theories of Liquid Viscosity,” Chem. Rev. 62, 513, 1962

2. Brule, M. R., Starling, K. E., Ind. Eng. Chem. Process Des. Dev., 23, 833, 1984

3. Ely, J. F., Hanley, H. J. M., “Prediction of Transport Properties: 1. Viscosity of Fluids and Mixtures,” Ind. Eng. Chem. Fund. 20, 323-332, 1981

4. Ely, J. F., Hanley, H. J. M., “Prediction of Transport Properties: 2. Thermal Conductivity of Pure Fluids and Mixtures,” Ind. Eng. Chem. Fund. 22, 90-97, 1983

5. Phillips, P., “The Viscosity of Carbon Dioxide,” Proc. Roy. Soc. 87A, 48, 1927

6. Little, J. E., Kennedy, H. T., “A Correlation of the Viscosity of Hydrocarbon Systems with Pressure, Temperature and Composition,” Soc. Pet. Eng. J., 157 (June1968)

7. Lawal, A. S., “Prediction of Vapor and Liquid Viscosities From the Lawal-Lake-Silberberg Equation of State,” In SPE/DOE Paper No.14926 in the Proceeding of  SPE/DOE Fifth Symposium on Enhanced Oil Recovery of the Society of Petroleum Engineers and the Department of Energy held in Tulsa, OK, April 20-23, 1986

8. Caudwell, D. R.; Vesovic, V.; Trusler, J. P. M.; Wakeham, W. A., “The viscosity and Density of n-Dodecane and n-Octadecane at Pressures up to 200 MPa and Temperatures up to 473K,” Int. J. Thermophysics, 25, 1340-52, 2004

9. Caudwell, D. R.; Trusler, J. P. M.; Vesovic, V.; 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

10. Y.L. Sen, Kiran, E., “High-pressure viscosity and density of n-alkanes,”  Int. J. of Thermophysics, 13, 411-442, 1992

11. Burgess, W. A., Tapriyal, D., Gamwo, I. K., Morreale, B. D., McHugh, M. A., Enick, R. M., “Viscosity Models Based on the Free Volume and Frictional Theories for Systems at Pressures to 276 MPa and Temperatures to 533 K,” Ind. Eng. Chem. Res., 51, 16721-33, 2012

12. Liu, K.; Wu, Y.; McHugh, M. A.; Baled, H.; Enick, R. M.; Morreale, B. D., “Equation of State Modeling of High-Pressure, High-Temperature Hydrocarbon Density Data,” J. Supercrit. Fluids, 55, 701, 2010

13. Baled, H. O.,  Xing, D., Katz, H., Tapriyal, D., Gamwoa, I. K., Soong, Y., Bamgbade, B. A., Wu, Y.,  Liu, K., McHugh, M. A., Enick, R. M., “Viscosity of n-Hexadecane, n-Octadecane and n-Eicosane at pressures up to 243 MPa and temperatures up to 534 K,” J. Chem. Thermodynamics, 72, 108-116, 2014

14. Ducoulombier, D.; Zhou, H.; Boned, C.; Peyrelasse, J.; Saint-Guirons, H.; Xans, P., “Pressure (1−1000 bar) and Temperature (20−100 °C) Dependence of the Viscosity of Liquid Hydrocarbons,” J. Phys. Chem., 90, 1692-1700, 1986

15. Hogenboom, D. L.; Webb, W.; Dixon, J. A., “Viscosity of Several Liquid Hydrocarbons as a Function of Temperature, Pressure, and Free Volume,” J. Chem. Phys., 46, 2586-98, 1967  

16. Tanaka, Y.; Hosokawa, H.; Kubota, H.; Makita, T., “Viscosity and Density of Binary Mixtures of Cyclohexane with n-Octane, n-Dodecane, and n-Hexadecane Under High Pressures,” Int. J. Thermophysics, 12, 245-264, 1991

17. Assael, M. J.; Papadaki, M., “Measurements of the Viscosity of n-Heptane, n-Nonane, and n-Undecane at Pressures up to 70 MPa,” Int. J. Thermophysics, 12, 801−810, 1991