The Compaction Correction

Part 5, Chapter 5: Sonic and Acoustic Logs

Learning objectives

Explain why Wyllie over-reads porosity in undercompacted sand
Use the adjacent shale transit time as a compaction gauge
Apply the compaction factor Cp = DTsh/100
Recognize when no compaction correction is needed

When Wyllie Lies

The Wyllie time average assumes the rock is well compacted, so the sound path is a clean matrix-plus-fluid mix. In young, shallow, unconsolidated sands the grains are not fully cemented, the pulse dawdles, and DT runs too high. Read straight off the time average, the porosity comes out too big, sometimes wildly so. The sonic, left uncorrected, is the most optimistic of the three porosity logs in soft rock.

The Shale Gauge

The trick is to let the rock tell you how much it is undercompacted. A well-compacted shale has a transit time near 100 us/ft; a slow, soft shale runs well above that. So the nearest shale is a compaction gauge, and the compaction factor is

C_p = \frac{DT_{sh}}{100}.

A shale at 120 us/ft gives $C_p = 1.2$ ; at 140, $C_p = 1.4$ .

Dividing It Down

The compaction factor divides the raw porosity back down:

\phi = \frac{DT - DT_{ma}}{DT_f - DT_{ma}}\cdot\frac{1}{C_p}.

In the figure the corrected line sits below the raw line, and the gap is the over-read the compaction caused. When the adjacent shale is fast (compacted, near 100), $C_p$ is one and the two lines coincide, no correction needed. This is why the sonic is best trusted in consolidated rock, and why in soft sands the density-neutron pair is usually the better porosity.

References

Asquith, G. and Krygowski, D. (2004). Basic Well Log Analysis, 2nd ed. AAPG Methods in Exploration 16.
Tiab, D. and Donaldson, E. (2015). Petrophysics, 4th ed. Gulf Professional Publishing.