Oil Viscosity Correlations

Overview

Oil viscosity ($\mu_o$) is a critical fluid property that governs flow behavior in reservoirs and production systems:

• Inflow performance — affects productivity index and deliverability
• Pressure transient analysis — appears in dimensionless time and mobility calculations
• Relative permeability — influences fractional flow and displacement efficiency
• Artificial lift design — determines pump performance and gas lift requirements
• Pipeline hydraulics — controls pressure drop and flow regime

Oil viscosity depends strongly on:

• Pressure — behavior differs above and below bubble point
• Temperature — viscosity decreases exponentially with temperature
• Dissolved gas content — gas in solution reduces viscosity
• Oil composition — heavier oils have higher viscosities

Viscosity Behavior vs. Pressure

The viscosity-pressure relationship exhibits three distinct regimes:

Three-Stage Viscosity Calculation

Petroleum Office uses a three-stage approach to calculate viscosity at any pressure:

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Correlation Equations

Dead Oil Viscosity — Egbogah (1983)

Dead oil is crude oil with no dissolved gas at atmospheric pressure. The Egbogah correlation predicts viscosity from API gravity and temperature:

$$\log_{10}[\log_{10}(\mu_{od} + 1)] = 1.8653 - 0.025086 \, \gamma_{API} - 0.5644 \, \log_{10}(T)$$

Solving for viscosity:

$$\mu_{od} = 10^{10^{1.8653 - 0.025086 \, \gamma_{API} - 0.5644 \, \log_{10}(T)}} - 1$$

Where:

• $\mu_{od}$ = dead oil viscosity, cP
• $\gamma_{API}$ = oil API gravity, °API
• $T$ = temperature, °F

Applicability:

• Light to heavy oils ($5 < \gamma_{API} < 50$)
• Standard reservoir temperatures ($60 < T < 300$ °F)
• Atmospheric pressure (no dissolved gas)

Physical Basis:

• Heavier oils (lower API) have higher viscosity
• Viscosity decreases exponentially with temperature
• The double-logarithmic form captures the exponential temperature sensitivity

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Saturated Oil Viscosity — Beggs and Robinson (1975)

When gas dissolves in oil, the viscosity decreases. The Beggs and Robinson correlation accounts for this effect:

$$A = 10.715 \, (R_s + 100)^{-0.515}$$$$B = 5.44 \, (R_s + 150)^{-0.338}$$$$\mu_o = A \, \mu_{od}^B$$

Where:

• $\mu_o$ = saturated oil viscosity at pressure $P \le P_b$, cP
• $\mu_{od}$ = dead oil viscosity from Egbogah or equivalent, cP
• $R_s$ = solution gas-oil ratio at pressure $P$, scf/STB

Applicability:

Physical Basis:

• As $R_s$ increases, both $A$ and $B$ decrease
• The power-law relationship captures how dissolved gas lightens the oil
• At $R_s = 0$, the equation reduces to $\mu_o = \mu_{od}$

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Undersaturated Oil Viscosity — Vasquez and Beggs (1980)

Above the bubble point, oil is single-phase liquid. Compression causes viscosity to increase with pressure:

$$m = 2.6 \, P^{1.187} \, \exp(-11.513 - 8.98 \times 10^{-5} \, P)$$$$\mu_o = \mu_{ob} \left( \frac{P}{P_b} \right)^m$$

Where:

• $\mu_o$ = oil viscosity at pressure $P > P_b$, cP
• $\mu_{ob}$ = oil viscosity at bubble point pressure, cP
• $P$ = reservoir pressure, psia
• $P_b$ = bubble point pressure, psia

Physical Basis:

• Liquid compression increases molecular packing density
• The exponential term in $m$ moderates growth at high pressures
• The power-law form on $(P/P_b)$ ensures $\mu_o = \mu_{ob}$ when $P = P_b$

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Calculation Workflow

At Pressures Below Bubble Point ($P \le P_b$)

1. Calculate dead oil viscosity: $\mu_{od} = f(\gamma_{API}, T)$ using Egbogah
2. Determine $R_s$ at pressure $P$ (from Rs correlation)
3. Calculate saturated viscosity: $\mu_o = f(\mu_{od}, R_s)$ using Beggs-Robinson

At Pressures Above Bubble Point ($P > P_b$)

1. Calculate dead oil viscosity: $\mu_{od} = f(\gamma_{API}, T)$ using Egbogah
2. Determine $R_{sb}$ at bubble point (maximum dissolved gas)
3. Calculate bubble point viscosity: $\mu_{ob} = f(\mu_{od}, R_{sb})$ using Beggs-Robinson
4. Calculate undersaturated viscosity: $\mu_o = f(\mu_{ob}, P, P_b)$ using Vasquez-Beggs

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Related Documentation

• Bubble Point Pressure (Pb) — required for undersaturated calculations
• Solution Gas-Oil Ratio (Rs) — required for saturated calculations
• Oil Formation Volume Factor (Bo) — related PVT property
• Dimensionless Variables — viscosity used in mobility calculations

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References

1. Egbogah, E.O. (1983). "An Improved Temperature-Viscosity Correlation for Crude Oil Systems." Annual Technical Meeting, Petroleum Society of Canada.

2. Beggs, H.D. and Robinson, J.R. (1975). "Estimating the Viscosity of Crude Oil Systems." Journal of Petroleum Technology, 27(9), pp. 1140-1141.

3. Vazquez, M. and Beggs, H.D. (1980). "Correlations for Fluid Physical Property Prediction." Journal of Petroleum Technology, 32(6), pp. 968-970.

4. McCain, W.D. Jr. (1990). The Properties of Petroleum Fluids, 2nd Edition. PennWell Books. Chapter 3: Crude Oil Properties.

5. Santos, R.G., Silva, J.A., Mehl, A., and Experiment, P.E. (2019). "Comparison of PVT Correlations with PVT Laboratory Data from the Brazilian Campos Basin." Brazilian Journal of Petroleum and Gas, 13(3), pp. 129-157.