reservoir · volumetrics
Pore Volume Compressibility
ct = So·co + Sw·cw + Sg·cg + cf
click formula to derive ↑
Inputs
fraction
fraction
fraction
μpsi⁻¹
μpsi⁻¹
μpsi⁻¹
μpsi⁻¹
Description
Computes total system compressibility as the saturation-weighted sum of oil, water, and gas compressibilities plus pore volume (rock) compressibility. Total compressibility ct is a key input to material balance and well test analysis.
Variables
| Symbol | Unit | Description |
|---|---|---|
| ct | μpsi⁻¹ | Total System Compressibility |
| So | fraction | Oil saturation of the interval. So + Sw + Sg should sum to 1.0. |
| Sw | fraction | Water saturation of the interval. |
| Sg | fraction | Free gas saturation of the interval — zero for an undersaturated oil reservoir above the bubble point. |
| co | μpsi⁻¹ | Oil compressibility in units of ×10⁻⁶ psi⁻¹. Typically 5-20 μpsi⁻¹, higher for undersaturated, lighter, or more gassy oils. |
| cw | μpsi⁻¹ | Formation water compressibility in units of ×10⁻⁶ psi⁻¹. Typically 3-4 μpsi⁻¹. |
| cg | μpsi⁻¹ | Free gas compressibility in units of ×10⁻⁶ psi⁻¹. Gas is far more compressible than oil or water and dominates ct when Sg is non-zero. |
| cf | μpsi⁻¹ | Formation (pore volume) compressibility in units of ×10⁻⁶ psi⁻¹, from a Hall-type correlation or core measurement. Typically 3-10 μpsi⁻¹. |
Assumptions
- Saturations (So, Sw, Sg) sum to approximately 1.0 and are representative of the interval being characterized
- Individual phase compressibilities are evaluated at representative reservoir pressure and temperature
- Rock (pore volume) compressibility is from a correlation or core test appropriate to the formation's lithology and stress state
Limitations
- Highly sensitive to Sg when free gas is present — a small error in gas saturation can significantly bias ct
- Compressibilities (co, cw, cg) vary with pressure, especially near the bubble/dew point — using a single-pressure value oversimplifies depletion-long material balance
- Pore volume compressibility correlations (e.g., Hall) are regionally calibrated and may not transfer well to unconsolidated or highly fractured rocks
Use Cases
- → Undersaturated oil material balance: Provide ct as the compressibility-drive term in the material balance equation for a reservoir above the bubble point.
- → Pressure transient (well test) analysis: Supply ct as an input to the skin factor and diffusivity equations used in drawdown/buildup test interpretation.
- → Depletion-drive sensitivity: Evaluate how ct (and therefore predicted pressure decline) increases sharply once free gas saturation develops below the bubble point.
Related Calculations
Region Notes
Permian Basin
Wolfcamp tight oil above the bubble point: ct dominated by co+cf, typically 15-25 μpsi⁻¹ total; once gas breaks out below Pb, ct rises sharply due to cg.
Eagle Ford
Volatile-oil and condensate windows show co at the high end (15-20 μpsi⁻¹) due to lighter, more compressible oil composition.
Gulf of Mexico
Unconsolidated Miocene/Pliocene sands have higher cf (8-15 μpsi⁻¹) than well-cemented rocks, reflecting greater pore volume sensitivity to effective stress changes.
Global
Always re-evaluate ct as a reservoir depletes below the bubble point — using an above-bubble-point ct in a solution-gas-drive material balance will significantly understate pressure decline.
References
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