Compositional Viscosity Models

Overview

Equations of state predict thermodynamic properties (pressure, volume, fugacity) but not transport properties such as viscosity. Separate viscosity models are required to estimate phase viscosities from composition, temperature, and pressure (or density).

In compositional modeling, viscosity is needed for:

• Mobility calculations — $\lambda = k_{r}/\mu$ controls flow rates
• Displacement efficiency — viscosity ratio affects sweep
• Well performance — pressure drop depends on viscosity
• Pipeline design — friction factor correlations require viscosity

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Gas Viscosity: Lee-Gonzalez-Eakin (1966)

Method

The Lee-Gonzalez-Eakin (LGE) correlation estimates gas viscosity from temperature, density, and molecular weight:

$$\mu_g = 10^{-4} K \exp(X \rho_g^Y)$$

Where:

$$K = \frac{(9.4 + 0.02 M_w)T^{1.5}}{209 + 19 M_w + T}$$

$$X = 3.5 + \frac{986}{T} + 0.01 M_w$$

$$Y = 2.4 - 0.2X$$

Applicability

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Liquid Viscosity: Lorentz-Bray-Clark (LBC, 1964)

Method

The LBC method uses a corresponding states approach based on reduced density:

$$[(\mu - \mu^*)^{1/4}\xi + 10^{-4}] = f(\rho_r)$$

Where:

• $\mu$ = mixture viscosity at conditions
• $\mu^*$ = low-pressure gas viscosity (from Herning-Zipperer mixing rule)
• $\xi$ = viscosity-reducing parameter
• $\rho_r = \rho/\rho_c$ = reduced density

The function $f(\rho_r)$ is a fourth-degree polynomial:

$$f(\rho_r) = a_1 + a_2\rho_r + a_3\rho_r^2 + a_4\rho_r^3 + a_5\rho_r^4$$

With coefficients: $a_1 = 0.1023$, $a_2 = 0.023364$, $a_3 = 0.058533$, $a_4 = -0.040758$, $a_5 = 0.0093324$.

Critical Properties for Mixtures

$$T_{c,mix} = \frac{\sum_i z_i V_{c,i} T_{c,i}}{\sum_i z_i V_{c,i}}$$

$$P_{c,mix} = \frac{R T_{c,mix}}{\sum_i z_i V_{c,i}}$$

Strengths and Limitations

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Liquid Viscosity: Pedersen (1984, 1987)

Method

The Pedersen model uses a corresponding states principle with a reference fluid (methane):

$$\mu_{mix}(T, P) = \mu_{ref}\left(T_0, P_0\right) \cdot \frac{T_{c,mix}}{T_{c,ref}} \cdot \left(\frac{P_{c,mix}}{P_{c,ref}}\right)^{2/3} \cdot \left(\frac{M_{w,mix}}{M_{w,ref}}\right)^{1/2} \cdot \frac{\alpha_{mix}}{\alpha_{ref}}$$

Where the reference conditions are:

$$T_0 = T \cdot \frac{T_{c,ref}}{T_{c,mix}}, \quad P_0 = P \cdot \frac{P_{c,ref}}{P_{c,mix}}$$

Key Features

• Uses methane as reference substance (well-characterized viscosity)
• Includes a rotation coupling coefficient $\alpha$ for heavy components
• Better for wide molecular weight ranges than LBC
• Recommended for heavy oils ($\mu > 10$ cp)

Comparison with LBC

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Selection Guide

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Best Practices

1. Always validate viscosity predictions against measured PVT data
2. Tune to lab data — adjust LBC polynomial or Pedersen coupling coefficients
3. Check phase continuity — viscosity should vary smoothly across the two-phase region
4. Match dead oil viscosity first, then live oil, then undersaturated
5. Use EoS density for viscosity calculation — errors in density propagate directly

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Related Topics

• EoS Overview — Context for viscosity in compositional modeling
• Peng-Robinson EoS — Density predictions feeding viscosity models
• PVT Oil Viscosity — Empirical viscosity correlations for comparison

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References

1. Lee, A.L., Gonzalez, M.H., and Eakin, B.E. (1966). "The Viscosity of Natural Gases." Journal of Petroleum Technology, 18(8), 997-1000. SPE-1340-PA.

2. Lohrenz, J., Bray, B.G., and Clark, C.R. (1964). "Calculating Viscosities of Reservoir Fluids from Their Compositions." Journal of Petroleum Technology, 16(10), 1171-1176. SPE-915-PA.

3. Pedersen, K.S., Fredenslund, Aa., Christensen, P.L., and Thomassen, P. (1984). "Viscosity of Crude Oils." Chemical Engineering Science, 39(6), 1011-1016.

4. Pedersen, K.S. and Fredenslund, Aa. (1987). "An Improved Corresponding States Model for the Prediction of Oil and Gas Viscosities and Thermal Conductivities." Chemical Engineering Science, 42(1), 182-186.

5. Whitson, C.H. and Brule, M.R. (2000). Phase Behavior. SPE Monograph Vol. 20.