Wyllie Time Average Equation

Reference

The Wyllie time average equation treats a rock as fluid and matrix in series, giving porosity from a sonic log.

The equation

1/V = φ/Vf + (1 – φ)/Vm
  • φ is porosity, dimensionless
  • Vf is fluid velocity, near 1500 meters per second for brine
  • Vm is matrix velocity, near 5500 for sandstone

Worked example

A sandstone with porosity 0.20 saturated with brine gives 1/V = 0.2/1500 + 0.8/5500, so V = 3587 meters per second. Invert the logic on a measured sonic and you read porosity straight off the log.

When to use it

Behaves well in clean consolidated sandstones at moderate porosity. It underestimates velocity in unconsolidated sands and overestimates porosity in gas zones, where the fluid term collapses.

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