Oil Compressibility Correlations

Overview

Oil compressibility ($c_o$) is the isothermal change in oil volume per unit pressure change:

$$c_o = -\frac{1}{V} \left( \frac{\partial V}{\partial P} \right)_T = -\frac{1}{B_o} \left( \frac{\partial B_o}{\partial P} \right)_T$$

This property is essential for:

• Material balance calculations — determines oil expansion above bubble point
• Well testing interpretation — appears in diffusivity equation and total compressibility
• Reservoir simulation — required input for undersaturated oil reservoirs
• Production forecasting — affects primary recovery calculations

Physical Behavior

Oil compressibility behavior differs dramatically above and below the bubble point:

The effective or total oil compressibility below the bubble point includes gas evolution effects and is much larger than above $P_b$.

Undersaturated Oil Compressibility

Vasquez and Beggs (1980)

For pressures above the bubble point ($P > P_b$), oil behaves as a compressed liquid with relatively constant compressibility:

$$c_o = \frac{5 R_{sb} + 17.2 T - 1180 \gamma_g + 12.61 \gamma_{API} - 1433}{P \times 10^5}$$

Where:

• $c_o$ = oil compressibility, 1/psi
• $R_{sb}$ = solution gas-oil ratio at bubble point, scf/STB
• $T$ = temperature, °F
• $\gamma_g$ = gas specific gravity (air = 1.0)
• $\gamma_{API}$ = oil API gravity, °API
• $P$ = pressure, psia

Key Observations:

• Compressibility decreases with increasing pressure (1/P term)
• Higher temperature → higher compressibility
• Higher GOR → higher compressibility
• Lighter oil (higher API) → higher compressibility

Typical Values:

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Saturated Oil Compressibility

Villena-Lanzi (1985)

Below the bubble point ($P \le P_b$), the effective compressibility includes the effect of gas evolving from solution:

$$c_o = \exp \left[ -0.664 - 1.430 \ln(P) - 0.395 \ln(P_b) + 0.39 \ln(T) + 0.455 \ln(R_{sb}) + 0.262 \ln(\gamma_{API}) \right]$$

Where:

• $c_o$ = effective oil compressibility, 1/psi
• $P$ = current pressure, psia
• $P_b$ = bubble point pressure, psia
• $T$ = temperature, °F
• $R_{sb}$ = solution GOR at bubble point, scf/STB
• $\gamma_{API}$ = oil API gravity, °API

Key Observations:

• Compressibility increases rapidly as pressure drops below $P_b$
• Strong dependence on both $P$ and $P_b$
• Higher initial GOR → higher saturated compressibility

Physical Interpretation:

At saturated conditions, the "apparent" compressibility includes:

1. Liquid oil compression (small)
2. Gas liberation from solution (dominant)
3. Free gas expansion (after liberation)

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Total Compressibility

In reservoir engineering, the total system compressibility combines all phases:

$$c_t = S_o c_o + S_w c_w + S_g c_g + c_f$$

Where:

• $c_t$ = total compressibility, 1/psi
• $S_o, S_w, S_g$ = oil, water, gas saturations
• $c_o, c_w, c_g$ = phase compressibilities
• $c_f$ = formation (pore) compressibility

Relative Magnitudes (typical):

For undersaturated oil reservoirs with no free gas, oil compressibility often dominates $c_t$.

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Calculation Workflow

For Undersaturated Reservoirs ($P > P_b$)

Use CoUSatVasquezBeggs1980 directly with reservoir conditions:

co = CoUSatVasquezBeggs1980(Rsob, SGgas, SGoilAPI, T, P)

For Saturated Reservoirs ($P \le P_b$)

Use CoSatVillenaLanzi1985 with current and bubble point pressures:

co = CoSatVillenaLanzi1985(P, Pb, T, Rsob, SGoilAPI)

Pressure Depletion Scenarios

As a reservoir depletes:

1. Initial pressure > Pb: Use Vasquez-Beggs
2. Pressure = Pb: Transition point (either correlation)
3. Pressure < Pb: Use Villena-Lanzi (compressibility jumps significantly)

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Practical Considerations

Material Balance Applications

For undersaturated reservoirs, oil expansion above $P_b$ provides significant drive energy:

$$\Delta V = V_o \cdot c_o \cdot \Delta P$$

Example: 10 MMSTB of oil at $P = 4,000$ psia with $c_o = 15 \times 10^{-6}$ 1/psi:

If pressure drops to 3,000 psia ($\Delta P = 1,000$ psi):

$$\Delta V = 10 \times 10^6 \times 15 \times 10^{-6} \times 1000 = 150,000 \text{ STB}$$

This expansion contributes to production before the bubble point is reached.

Well Testing

Total compressibility $c_t$ appears in the diffusivity equation:

$$\frac{\partial^2 p}{\partial r^2} + \frac{1}{r} \frac{\partial p}{\partial r} = \frac{\phi \mu c_t}{k} \frac{\partial p}{\partial t}$$

Accurate $c_o$ is critical for:

• Calculating transmissibility from pressure buildup
• Estimating drainage area from drawdown tests
• Interpreting skin factor and wellbore storage

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Related Documentation

• Bubble Point Pressure (Pb) — defines transition pressure
• Oil Formation Volume Factor (Bo) — related to compressibility
• Solution Gas-Oil Ratio (Rs) — affects saturated behavior
• Dimensionless Variables — uses total compressibility

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References

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

2. Villena-Lanzi, M. (1985). "A Correlation for the Coefficient of Isothermal Compressibility of Black Oil at Pressures Below the Bubblepoint." M.S. Thesis, University of Tulsa.

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

4. Ahmed, T. (2019). Reservoir Engineering Handbook, 5th Edition. Gulf Professional Publishing. Chapter 2: Reservoir-Fluid Properties.