petrophysics · nmr
NMR Permeability (SDR and Coates)
kSDR = C·φ⁴·T2lm² | kCoates = (φ/C)²·(FFI/BVI)²
click formula to derive ↑
Inputs
fraction
ms
fraction
fraction
—
—
Description
NMR-based permeability uses the T2 relaxation time distribution to estimate k without core, exploiting the correlation between pore-body size (T2) and permeability (SDR model) or the ratio of free to bound fluid volumes (Coates model). Running both models together provides a crosscheck and highlights intervals where the NMR response is unusual.
Variables
| Symbol | Unit | Description |
|---|---|---|
| kSDR | mD | NMR Permeability (SDR) |
| kCoates | mD | NMR Permeability (Coates) |
| φ | fraction | Total NMR porosity including all T2 components. This is the most reliable NMR-derived input because it is directly calibrated against formation volume. |
| T2lm | ms | Geometric mean of the T2 distribution (T2 log-mean) in milliseconds. Typical values: < 4 ms (clay-bound water), 4–33 ms (capillary-bound water), 33–300 ms (moveable water), > 300 ms (light oil or gas). |
| FFI | fraction | Free fluid index — fraction of total rock volume occupied by fluids with T2 > T2 cutoff (typically 33 ms for sandstones, 92 ms for carbonates). Represents moveable fluids. |
| BVI | fraction | Bound volume irreducible — fraction of total rock volume occupied by fluids with T2 < T2 cutoff. Includes clay-bound water and capillary-bound water; these fluids are immovable. |
| CSDR | — | Empirical constant in the SDR equation; ~4 for sandstones, ~0.1–1 for carbonates. Must be calibrated against core permeability in the specific formation being evaluated. |
| CCoates | — | Empirical constant in the Coates equation; ~10 for sandstones; varies by formation. Calibrate against core permeability. |
Assumptions
- T2lm is the geometric mean of the full T2 distribution (not a simple arithmetic mean) and is computed before any depth shifting or filtering
- The empirical constants C_SDR and C_Coates are calibrated to core permeability in the same formation — default values (4 and 10) are valid only as a starting point
Limitations
- Both models break down in light hydrocarbon zones (gas or very light oil) where the hydrocarbon T2 overlaps with the water T2; hydrocarbon correction of the NMR log is required first
- Fracture permeability is not captured — NMR k represents matrix permeability only; comparison with pressure-transient derived k is essential in naturally fractured reservoirs
Use Cases
- → Uncored interval permeability prediction: Apply NMR k models to all uncored wells once constants are calibrated from cored wells; NMR permeability is the best available continuous permeability log in complex lithologies.
- → Producibility screening: Compare FFI/φ (moveable fraction) across the pay interval: zones with FFI/φ > 0.6 are highly producible; zones with FFI/φ < 0.3 are likely at or near irreducible water saturation.
- → Facies and flow unit identification: Map T2lm and FFI/BVI logs as continuous indicators of pore geometry; rapid changes in these logs identify facies boundaries and flow unit transitions that are not always visible on conventional logs.
Related Calculations
Region Notes
Permian Basin
Wolfcamp tight oil: T2lm typically 5–25 ms, FFI/BVI ratio 0.5–2.0 in productive benches; SDR and Coates both give k 0.001–0.1 mD, consistent with plug data. C_SDR ≈ 2–6 from Permian Basin core calibration.
Gulf of Mexico
Unconsolidated GOM sands: T2lm 100–500 ms, FFI/BVI > 5 in clean, high-porosity sands; C_SDR ≈ 4 gives k 10–500 mD consistent with DST rates.
Eagle Ford
Tight oil: T2lm < 10 ms typical; Coates model is unreliable here because BVI ≈ FFI (low FFI/BVI), making the ratio sensitive to noise; SDR is preferred.
North Sea
Brent Group: T2lm 50–150 ms in good-quality sands; C_SDR calibrated from Statfjord and Brent core is 3–5; Coates model works well with T2 cutoff of 33 ms.
Global
Always calibrate C_SDR and C_Coates against at least 30 core plug measurements spanning the full permeability range in the formation; the default constants can be off by 5–10× without calibration.
References
Primary source
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