petrophysics · porosity
Sonic Porosity (Wyllie)
φ = (ΔT − ΔTma) / (ΔTfl − ΔTma)
click formula to derive ↑
Inputs
μs/ft
μs/ft
μs/ft
Description
Wyllie's time-average equation computes porosity from compressional sonic slowness by linear interpolation between zero-porosity (matrix) and 100%-porosity (fluid) end-members. It is reliable in consolidated, normally pressured, liquid-filled formations but requires a compaction correction in unconsolidated or overpressured sections.
Variables
| Symbol | Unit | Description |
|---|---|---|
| φs | fraction | Sonic Porosity |
| ΔT | μs/ft | Compressional sonic slowness from the log at the depth of interest, in μs/m canonical. Typical values: 131–164 μs/m in tight carbonates, 164–262 μs/m in tight to moderate-porosity sandstones, 262–490 μs/m in high-porosity unconsolidated sands. |
| ΔTma | μs/ft | Sonic slowness of the rock matrix (zero porosity). Common values in μs/m: sandstone 182.1 (55.5 μs/ft), limestone 156.2 (47.6 μs/ft), dolomite 142.7 (43.5 μs/ft). |
| ΔTfl | μs/ft | Sonic slowness of the pore fluid. Use 620 μs/m (189 μs/ft) for fresh mud filtrate (water). Gas invasion can lower this dramatically — most sonic-porosity tools assume borehole-invasion-flushed conditions (water filtrate). |
Assumptions
- Formation is consolidated and normally compacted — Cp = 1.0 applies (no compaction correction needed)
- Pore fluid in the flushed zone is water (mud filtrate), not gas, so ΔTfl ≈ 620 μs/m is valid
- Single-mineral matrix of known slowness dominates the rock frame
Limitations
- Overestimates porosity in unconsolidated or overpressured zones (slow shales) unless a compaction correction factor is applied
- Underestimates porosity in gas-bearing zones because gas slows the sonic wave and requires a separate gas correction
- Not reliable in vuggy or fractured carbonates where the sonic bypasses some of the porosity (cycle-skipping)
Use Cases
- → Porosity in tight carbonates (no neutron log): When a neutron log is unavailable, sonic porosity with a limestone or dolomite DTma is the best available option for carbonate porosity evaluation in consolidated reservoirs.
- → Crossplot QC with density porosity: Compare sonic porosity against density porosity (phi_den) — they should agree in water-bearing, clean formations; divergence signals gas, lithology error, or cycle-skipping.
- → Compaction correction for overpressured sections: In HPHT wells, track shale sonic through the overpressured section and derive a local Cp to correct sonic porosities in adjacent sands before using them in Sw and volumetric calculations.
Related Calculations
Region Notes
Permian Basin
Wolfcamp and Spraberry: DTma ≈ 175–185 μs/m appropriate for silty sandstone matrix; limestone interbeds need 156 μs/m. Compaction correction rarely needed at typical Permian Basin depths (<5000 m TVD).
Gulf of Mexico
Unconsolidated Plio-Pleistocene sands require compaction correction (Cp = ΔTshale/340 typically); without correction, sonic porosity is 5–10 pu too high relative to core.
Eagle Ford
Use DTma 162–168 μs/m (mixed carbonate-clay) rather than pure limestone; the wax-like organic matrix slightly lowers the rock-frame slowness.
Haynesville
Deep overpressured shale gas; compaction correction is critical — shale DT often 330–380 μs/m vs. normal-trend ~290 μs/m, implying Cp ≈ 1.14–1.31.
North Sea
Brent Group sandstones (consolidated, normally pressured at typical reservoir depths) give reliable Wyllie porosities with DTma = 182.1 μs/m and no compaction correction.
Global
Always run a crossplot of sonic vs. density porosity over a known water-bearing interval to calibrate DTma before applying sonic porosity to the full well.
References
Primary source
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