Vclay from Sonic-Density

Summary

The sonic-density method estimates Clay volume from the position of the measured Bulk density and Compressional slowness relative to a clean-rock line and a clay point on the crossplot. It uses the same dual-clay form as the neutron-density method, with the sonic in place of the neutron. Use it when no neutron log is available and the sonic and density logs are good.

Inputs and outputs

Equations

The two clean points \(A\) and \(B\) define the clean-rock line on the bulk density-compressional slowness crossplot, and the clay point is the 100% clay end. The clay volume is the offset of the measured point from the clean line, as a fraction of the offset of the clay point:

and the result is clamped to the interval 0 to 1. The numerator and denominator are both proportional to a perpendicular distance from the clean line, so their ratio does not depend on the units or the scaling of either axis.

Single-value calculator

Behavior

Clay volume is a straight-line function of each measurement, so the plot lines are straight and are clipped to 0 and 1. A higher slowness at the same density reads as more clay, and a denser rock at the same slowness also reads as more clay, because the clay point lies on the dense, slow side of the clean line. The slope is set by how far the clay point is from the clean line.

Parameter guidance

Six picks define the method: two points on the clean-rock line and one clay point. The clean line starts at the matrix point (for example 2.65 g/cm³ and about 55 µs/ft for sandstone) and a second point is read from the cleanest water-bearing sand in the zone. The clay point is read from a thick shale. The general principles are in the Clay Volume page.

Worked example

A measured point of 2.50 g/cm³ and 80 µs/ft. The clean line runs through (2.65, 55.5) and (2.20, 92.0), and the clay point is (2.45, 100.0):

A, B, clay = (2.65, 55.5), (2.20, 92.0), (2.45, 100.0)   # (density, slowness)
rhob, dt = 2.50, 80.0
num = (B[0] - A[0]) * (dt - A[1]) - (rhob - A[0]) * (B[1] - A[1])
den = (B[0] - A[0]) * (clay[1] - A[1]) - (clay[0] - A[0]) * (B[1] - A[1])
vcl = min(1.0, max(0.0, num / den))
print(f"numerator = {num:.4f}, denominator = {den:.4f}")
print(f"Vcl = {vcl:.3f}")

Output

numerator = -5.5500, denominator = -12.7250
Vcl = 0.436

Assumptions and limitations

• The clean points lie on a single straight line. Lithology changes move the clean line.
• The sonic reads the matrix slowness of the clean rock. Compaction and cementation change the slowness at constant porosity, so unconsolidated rock reads slower than the picks.
• There is no gas. Gas raises the slowness and lowers the density, which biases the clay volume.
• The logs are good. Cycle skipping on the sonic, and washouts on the density, move the point without a change in clay.
• The clay point lies off the clean line. If it lies on the clean line the denominator is zero and the method is undefined.

QC checks

• The result is between 0 and 1 without relying on the clamp.
• Clean, water-bearing sands read near zero.
• Spikes in clay volume that line up with sonic cycle skips or caliper spikes are log quality problems, not clay.
• Compare with the gamma-ray clay volume and, if available, the neutron-density clay volume.

Going Deeper

The sonic responds to porosity and to rock compaction, so the clean-rock line from a Wyllie-type relation is a better description of consolidated rock than of young, unconsolidated sand. In unconsolidated formations the clean line is better read directly from the data than computed from matrix and fluid values. The method is mostly used as a fallback when a neutron log is missing.

References

References will be added once verified.

Python reference implementation

Related methods

• Vclay from GR (Linear Index)
• Vclay from GR (Larionov, Tertiary)
• Vclay from GR (Larionov, Older Rocks)
• Vclay from GR (Clavier)