petrophysics · permeability
Permeability (Timur-Coates)
k = [C × φ⁴ × (1−Swirr) / Swirr]²
click formula to derive ↑
Inputs
fraction
fraction
—
Description
Estimates matrix permeability from porosity and irreducible water saturation using the Timur/Coates family of NMR-based transforms. It provides a continuous permeability log without requiring core plugs, but the empirical constant C must be calibrated locally.
Variables
| Symbol | Unit | Description |
|---|---|---|
| k | mD | Permeability |
| φ | fraction | Total porosity, ideally from NMR total porosity (TCMR) for consistency with the Swirr term. |
| Swirr | fraction | Irreducible water saturation, typically read from the NMR T2 cutoff (bound volume irreducible / total porosity). |
| C | — | Empirical constant — about 10 for sandstone but varies widely (5-15+) by formation. Calibrate against core permeability whenever possible. |
Assumptions
- Porosity and Swirr are derived consistently (same NMR T2 cutoff and total porosity definition)
- Pore system is dominated by intergranular porosity similar to the rocks used to calibrate C
- No significant fracture or vug permeability that this matrix-based transform would miss
Limitations
- Highly sensitive to C — an uncalibrated default can be off by an order of magnitude versus core permeability
- Breaks down in dual-porosity systems (fractured carbonates, vuggy dolomite) where fracture flow dominates
- NMR T2 cutoff used to derive Swirr must be appropriate for the formation's pore fluid and wettability
Use Cases
- → Continuous NMR permeability log: Generate a permeability curve over the logged interval where core data is sparse, for use in completion design and reservoir modeling.
- → Reservoir quality ranking: Compare permeability across zones or wells to rank completion targets and identify flow units.
- → Flow simulation input: Provide a first-pass permeability distribution for static/dynamic models pending core or DST calibration.
Related Calculations
Region Notes
Permian Basin
Wolfcamp benches: C≈1-5 (much lower than the conventional sandstone default of 10) is often needed because matrix permeability is in the microdarcy to low-millidarcy range.
Gulf of Mexico
Unconsolidated turbidite sands: C≈10 (Coates original sandstone default) is a reasonable starting point, refined with core from nearby wells.
Global
Always cross-plot calculated k against core permeability on a log scale and adjust C until the trend passes through the core data — a single C rarely holds across facies changes.
References
Primary source
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