Viscosity Correlations
In the following sections, a detailed description of three viscosity models are given. Viscosity models are used in equation of state modeling and blackoil PVT.
Lee Correlation
The viscosity model proposed by Lee in 1966^{1} is a relatively simple model for describing reservoir gas and oil viscosities. This correlation is not used much in the industry any more, but is a simple correlation to give first order estimates.
The correlation is given by
Note
The units for the temperature: (R) and density: (lb/ft3).
where
Corresponding States Principle Correlation
whitson comment
Note from Markus Hays Nielsen: Be cautious if you are moving your EOS model from PVTp to Eclipse, as PVTp has an option for tuning the CSP model that Eclipse does not have. This might give inconsistent results between your PVT model in the two softwares.
The procedure of the corresponding states principle (CSP) for viscosity modeling as described bt Pedersen in 1982^{2} is given below and is adapted from "Phase Behavior of Petroleum Reservoir Fluids"^{3}.
 Calculate \(T_c\) and \(p_c\) from equation \eqref{eq:Tc} and \eqref{eq:pc}
 Estimate Methane density from equation \eqref{eq:dens} which is the McCarty modified BWR EOS and the reduced densities from equation \eqref{eq:red_dens} where \(a_n\) are empirical constants.
 Calculate mixture molecular weight (\(MW\)) from equation \eqref{eq:MW_mix} and equations \eqref{eq:MW_w} and \eqref{eq:MW_n}.
 Calculate \(\alpha_{mix}\) factor from equations \eqref{eq:alpha}.
 Calculate corresponding state methane \(T_{methane}\) and \(p_{methane}\) from equations \eqref{eq:To} and \eqref{eq:po} respectively also using equation \eqref{eq:Tcij} where \(\alpha_{methane}\) is defined by using equation \eqref{eq:alpha} but with the molecular weight instead of the mixture molecular weight (\(MW_{mix}\)).
 Calculate mixture viscosity from equation \eqref{eq:mix_visc} where \(\mu_{methane}\) is calculated using equation \eqref{eq:mix_methane} and \(c_1\) to \(c_6\) are constants.
Note
The units for this model are given in pressure:(atm), temperature: (K), density: (mol/L) and gas constant: (L.atm/mol.K) and viscosity: (1 E4 cP)
LohrenzBrayClark Correlation
The LohrenzBrayClark viscosity correlation (LBC) is an adaptation of the original work by Jossi, Stiel and Thodos^{4}. The details for the correlation are given below.
where \(\rho_r=\rho/\rho_c\), \(\mu^*\) is the lowpressure gas mixture viscosity and \(\xi\) is the viscosityreducing parameter. The constants \(a_n\) we originally treated as universal constants by LBC, but are typically used as tuning parameters for a given set of viscosity data.
The viscosityreducing parameter (\(\xi\)) is defined by
and the critical density is defined by
The critical volumes for heptane plus components (\(C_{7+}\)) are either defined by correlation or tuning. One example of a critical volume correlation is given by ^{3}
Note
The units for the critical volume is ft3/lb and the density is in g/cm3.
Finally, the dilute gas mixture viscosity (\(\mu^*\)) is given by Herning and Zippener ^{5} as
where \(\mu_i^*\) is given by Stiel and Thodos^{6} as
for \(T_{ri}<1.5\) and
for \(T_{ri} \geq 1.5\)
For equations \eqref{eq:visc_comp_dilute_1} and \eqref{eq:visc_comp_dilute_2} the component viscosityreducing parameter is given by

A. L. Lee, M. H. Gonzalez, and B. E. Eakin. The viscosity of natural gases. Journal of Petroleum Technology, 18:paper SPE–1340–PA, 1966. doi:https://doi.org/10.2118/1340PA. ↩

K. S. Pedersen and Aa. Fredenslund. An improved corresponding states model for the prediction of oil and gas viscosities and thermal conductivities. Chemical Engineering Science, 42:182–186, 1987. doi:https://doi.org/10.1016/00092509802257. ↩

K. S. Pedersen, P. L. Christensen, and J. A. Shaikh. Phase behavior of petroleum reservoir fluids. CRC press, 2014. ↩↩

J. A. Jossi, L. I. Stiel, and G. Thodos. The viscosity of pure substances in the dense gaseous and liquid phases. AIChE Journal, 8:59–63, 1962. doi:https://doi.org/10.1002/aic.690080116. ↩

F. Herning and L. Zipperer. Calculation of the viscosity of technical gas mixtures from the viscosity of the individual gases. Gas u. Wasserfach, 79:69, 1936. ↩

L. I. Stiel and G. Thodos. The viscosity of nonpolar gases at normal pressures. AIChE Journal, 7:611–615, 1961. doi:https://doi.org/10.1002/aic.690070416. ↩