TOC from Faust

Summary

The Faust method predicts the sonic slowness that the resistivity and depth imply, and reads the excess of the measured slowness over that prediction as organic matter. The difference in sonic porosity is scaled to Total organic carbon with a multiplier fitted to core. Use it where a sonic log, a resistivity log and depth are available and a core calibration is possible.

Inputs and outputs

Equations

Faust's empirical relation predicts the compressional slowness from deep resistivity and depth:

Both the measured and the predicted slowness are converted to sonic porosity with the time-average relation, limited to the interval 0.0001 to 1:

TOC is the scaled difference, limited to the interval 0 to 100 wt%:

Single-value calculator

Behavior

TOC is zero while the measured slowness is at or below the predicted value and rises in a straight line above it. A higher resistivity predicts a lower slowness, so the same measured slowness gives more TOC. The three curves show this: at a measured slowness of 100 µs/ft and a depth of 8000 ft, TOC rises from about 1.9 to 3.4 to 4.8 wt% as the resistivity goes from 5 to 10 to 20 ohm·m.

Parameter guidance

Matrix slowness and Fluid slowness are the matrix and fluid slowness, typically 47 to 60 and 180 to 200 µs/ft. The multiplier Faust multiplier has no physical value: it is the scale between the porosity separation and TOC, and it should be fitted so that the result matches core TOC. The depth must be true vertical depth in feet and resistivity in ohm·m. If the sonic is in other units, convert it first, as covered in Stage 1. Calibration is covered on the TOC Analysis page.

Worked example

A slowness of 95 µs/ft and a resistivity of 10 ohm·m at 8000 ft, with a matrix of 55.5 µs/ft, a fluid of 189 µs/ft and a multiplier of 0.21:

dt, rt, tvd, dt_ma, dt_w, f_m = 95.0, 10.0, 8000.0, 55.5, 189.0, 0.21
dt_faust = 1e6 / (1948 * (tvd * rt) ** (1 / 6))
clip = lambda x: min(1.0, max(0.0001, x))
ps = clip((dt - dt_ma) / (dt_w - dt_ma))
psf = clip((dt_faust - dt_ma) / (dt_w - dt_ma))
toc = max(0.0, 100 * f_m * (ps - psf))
print(f"Faust sonic = {dt_faust:.1f} us/ft")
print(f"sonic porosity: measured {ps:.3f}, Faust {psf:.3f}")
print(f"TOC = 100 x {f_m:g} x ({ps:.3f} - {psf:.3f}) = {toc:.2f} wt%")

Output

Faust sonic = 78.2 us/ft
sonic porosity: measured 0.296, Faust 0.170
TOC = 100 x 0.21 x (0.296 - 0.170) = 2.64 wt%

Assumptions and limitations

• Faust's relation describes normally compacted, non-organic rock at the depth and resistivity given. It is a general empirical trend, so it is only a reference for the formation being studied.
• The excess of the measured slowness over the predicted one is attributed to organic matter. Overpressure and under-compaction raise the slowness for the same reason and are read as TOC. So does gas.
• The fluid and matrix slowness are constant, and the multiplier is constant over the interval.
• The resistivity responds to the rock and not to hydrocarbons in a reservoir, and the sonic is free of cycle skips and washouts.

QC checks

• TOC is zero or close to zero in non-source rock, and the Faust sonic overlays the measured sonic there.
• TOC compares with core TOC. A systematic offset means the multiplier or the matrix and fluid slownesses need adjustment.
• TOC is high in an overpressured shale without a high resistivity. This is a compaction effect and not organic matter.
• The result does not spike where the sonic cycle-skips.

Going Deeper

Faust's 1953 paper related velocity to depth and resistivity for a set of sedimentary rocks. The same idea of using resistivity to predict the sonic is the basis of the sonic-resistivity overlay used in source-rock work, where the separation of a measured sonic from a resistivity-derived one is read as organic richness. The method here converts that separation to porosity units and fits a single multiplier to core. It is closely related to the sonic form of the Passey method and shares its weaknesses.

References

1. Faust, L.Y., 1953. A velocity function including lithologic variation. Geophysics, 18(2), 271–288.

Python reference implementation

Related methods

• TOC from Passey ΔlogR
• TOC from Schmoker
• TOC from Vernik
• Combining TOC Estimates
• Kerogen Volume and Maturity