Oil Formation Volume Factor (Bo)

Overview

The oil formation volume factor (Bo) is defined as the ratio of the volume of oil at reservoir conditions (including dissolved gas) to the volume of the same oil at stock-tank (surface) conditions. It is one of the most fundamental PVT properties used in reservoir engineering calculations.

$B_o = \frac{(V_R)_{T,P}}{(V_o)^{SC}}$

where:

• $V_R$ = Volume of oil and dissolved gas at reservoir temperature and pressure
• $V_o^{SC}$ = Volume of oil at standard conditions (60°F, 14.7 psia)

Key Concepts

• Always > 1.0: Oil swells when gas dissolves into it at reservoir conditions
• Pressure Dependent: Behavior differs above and below bubble point
• Correlation-Based: Multiple empirical correlations for different oil types
• Temperature Sensitive: Higher temperatures increase Bo

Bo Behavior with Pressure

Theory

Saturated Oil (P ≤ Pb)

Below the bubble point, the oil formation volume factor increases with pressure because more gas dissolves into the liquid phase. This behavior is modeled using empirical correlations that relate Bo to:

• Gas specific gravity (γg)
• Oil API gravity (γAPI)
• Solution gas-oil ratio (Rs)
• Temperature (T)

Undersaturated Oil (P > Pb)

Above the bubble point, all gas is dissolved and the oil behaves as a single-phase compressible liquid. The formation volume factor decreases exponentially with pressure increase:

$B_o = B_{ob} \cdot \exp\left[c_o(P_b - P)\right]$

where:

• $B_{ob}$ = Formation volume factor at bubble point (bbl/STB)
• $c_o$ = Isothermal oil compressibility (1/psi)
• $P_b$ = Bubble point pressure (psia)
• $P$ = Current pressure (psia)

Equations

Standing (1947) Correlation

Developed from California crude oils:

$B_o = 0.9759 + 0.000120 \cdot F^{1.2}$

where:

$F = R_s \cdot \sqrt{\frac{\gamma_g}{\gamma_o}} + 1.25 \cdot T$

Parameters:

• $R_s$ = Solution gas-oil ratio (scf/STB)
• $\gamma_g$ = Gas specific gravity (air = 1.0)
• $\gamma_o$ = Oil specific gravity = 141.5 / (131.5 + °API)
• $T$ = Temperature (°F)

Applicability:

• γg: 0.59 - 0.95
• °API: 16.5 - 63.8
• Rs: 20 - 1,425 scf/STB
• T: 100 - 258°F

Vazquez-Beggs (1980) Correlation

Based on worldwide data, with coefficients dependent on API gravity:

$B_o = 1 + A_1 R_s + A_2 (T - 60) \frac{\gamma_{API}}{\gamma_{gc}} + A_3 R_s (T-60) \frac{\gamma_{API}}{\gamma_{gc}}$

For API ≤ 30:

• $A_1$ = 4.677 × 10⁻⁴
• $A_2$ = 1.751 × 10⁻⁵
• $A_3$ = -1.811 × 10⁻⁸

For API > 30:

• $A_1$ = 4.670 × 10⁻⁴
• $A_2$ = 1.100 × 10⁻⁵
• $A_3$ = 1.337 × 10⁻⁹

Applicability:

• γg: 0.511 - 1.351
• °API: 15.3 - 59.5
• T: 75 - 294°F

Glasø (1980) Correlation

Developed from North Sea crude oils:

$B_o = 1 + 10^A$

where:

$A = -6.58511 + 2.91329 \log_{10}(B_o^*) - 0.27683 [\log_{10}(B_o^*)]^2$

$B_o^* = R_s \left(\frac{\gamma_g}{\gamma_o}\right)^{0.526} + 0.968 \cdot T$

Applicability:

• γg: 0.65 - 1.276
• °API: 22.3 - 48.1
• Rs: 90 - 2,637 scf/STB
• T: 80 - 280°F

Al-Marhoun (1988) Correlation

Developed from Middle East crude oils:

$B_o = 0.497069 + 8.62963 \times 10^{-4} \cdot (T + 460) + 1.82594 \times 10^{-3} \cdot F + 3.18099 \times 10^{-6} \cdot F^2$

where:

$F = R_s^{0.74239} \cdot \gamma_g^{0.323294} \cdot \gamma_o^{-1.20204}$

Applicability:

• γg: 0.752 - 1.367
• °API: 19.4 - 44.6
• Rs: 26 - 1,602 scf/STB
• T: 74 - 240°F

Petrosky-Farshad (1993) Correlation

Developed from Gulf of Mexico crude oils:

$B_o = 1.0113 + 7.2046 \times 10^{-5} \cdot F^{3.0936}$

where:

$F = R_s^{0.3738} \cdot \left(\frac{\gamma_g^{0.2914}}{\gamma_o^{0.6265}}\right) + 0.24626 \cdot T^{0.5371}$

Applicability:

• γg: 0.5781 - 0.8519
• °API: 16.3 - 45
• Rs: 217 - 1,406 scf/STB
• T: 114 - 288°F

Dindoruk-Christman (2004) Correlation

Developed for Gulf of Mexico deepwater reservoirs with high GOR:

A complex 14-coefficient correlation suitable for high-pressure, high-GOR systems.

Applicability:

• γg: 0.6017 - 1.027
• °API: 14.7 - 40
• Rs: 133 - 3,050 scf/STB
• T: 117 - 276°F

Functions Covered

See each function page for detailed parameter definitions, Excel syntax, and usage examples.

Applicability & Limitations

Correlation Selection Guidelines

Regional Performance

Based on Mangili & Ahón (2019) comparison for Campos Basin (Brazilian pre-salt):

Physical Constraints

• $B_o > 1.0$ always (oil swells with dissolved gas)
• $B_o$ typically ranges from 1.0 to 2.5 bbl/STB
• Maximum Bo occurs at bubble point
• Bo decreases above Pb due to liquid compression

Limitations

1. Correlation Extrapolation: Using correlations outside their development ranges reduces accuracy
2. CO₂-Rich Fluids: High CO₂ content (like Brazilian pre-salt) affects Bo; standard correlations may underpredict
3. Compositional Effects: Black-oil correlations don't account for unusual compositions
4. Temperature Range: Most correlations developed for T < 300°F

References

1. Standing, M.B. (1947). "A Pressure-Volume-Temperature Correlation for Mixtures of California Oils and Gases." Drilling and Production Practice, API, p. 275-287.

2. Vazquez, M.E. and Beggs, H.D. (1980). "Correlations for Fluid Physical Property Prediction." Journal of Petroleum Technology, 32(6): 968-970. SPE-6719-PA.

3. Glasø, Ø. (1980). "Generalized Pressure-Volume-Temperature Correlations." Journal of Petroleum Technology, 32(5): 785-795. SPE-8016-PA.

4. Al-Marhoun, M.A. (1988). "PVT Correlations for Middle East Crude Oils." Journal of Petroleum Technology, 40(5): 650-666. SPE-13718-PA.

5. Petrosky, G.E. and Farshad, F.F. (1993). "Pressure-Volume-Temperature Correlations for Gulf of Mexico Crude Oils." SPE Reservoir Evaluation & Engineering, 1(5): 416-420. SPE-51395-PA.

6. Dindoruk, B. and Christman, P.G. (2004). "PVT Properties and Viscosity Correlations for Gulf of Mexico Oils." SPE Reservoir Evaluation & Engineering, 7(6): 427-437. SPE-89030-PA.

7. Mangili, P.V. and Ahón, V.R.R. (2019). "Comparison of PVT Correlations for Predicting Crude Oil Properties: The Brazilian Campos Basin Case Study." Brazilian Journal of Petroleum and Gas, 13(3): 129-157.