Viscosity Models Based on the Free Volume and Frictional Theories for Systems at Pressures to 276 MPa and Temperatures to 533 K

This study presents methods for accurate viscosity modeling using the frictional theory (f-theory) and the free volume theory (FV theory) of viscosity at temperatures to 533 K and pressures to 276 MPa, which are high-temperature, high-pressure (HTHP) conditions associated with ultradeep porous sandstone or carbonate layers that retain crude oil or natural gas. The perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS), the HTHP-volume-translated (VT) Peng-Robinson EoS, and the HTHP-volume-translated-Soave-Redlich-Kwong EoS (HTHP-VT-PR and HTHP-VT-SRK, respectively) are used to provide input information for both the f-theory and the FV theory. Viscosity values returned by these models are compared to available experimental data for n-alkanes with carbon numbers 1-18, branched alkanes, single and double ring aromatics, and naphthenic compounds. As currently constituted, the f-theory model underpredicts viscosity by as much as 20% at pressures near 276 MPa, but this deficiency is reduced by incorporating an empirical correction term that is a function of temperature and normal melting point. Viscosity predictions from the modified f-theory are comparable with viscosity values returned by FV theory for n-alkanes, although FV theory provides better viscosity modeling than either the f-theory or the modified f-theory for branched and aromatic hydrocarbons. FV theory viscosity values are characterized by a mean absolute percent deviation (MAPD) of 3% or less from the experimental data, with the most accurate results (MAPD similar to 2%) obtained when the PC-SAFT is used to calculate the density input needed for the FV theory calculations. However, FV theory viscosity values actually become slightly less accurate when experimental density data are used, which indicates that FV theory itself has an inherent inaccuracy at extreme conditions unrelated to the accurate prediction of the density input.