Vclay from GR (Clavier)

Summary

The Clavier relation converts the Gamma ray index to Clay volume with a smooth curve built from a circular arc. It gives a moderate reduction of the linear index and reaches exactly 0 and 1 at the clean and clay picks. Use it when only a gamma ray is available and a bounded, smooth transform is wanted.

Inputs and outputs

Equations

The gamma ray index scales the log between the clean and clay values and is clamped to the interval 0 to 1:

The Clavier relation then gives the clay volume:

Single-value calculator

Behavior

The curve starts with a slope close to 0.4 at an index of 0, steepens through the middle of the range and reaches 1 with a slope of about 2.4 at the clay pick. At an index of 0.5 it gives about 0.31, between the Stieber value of 0.25 and the linear value of 0.50. Unlike the Larionov relations, it returns exactly 0 and 1 at the endpoints.

Parameter guidance

The method has no parameters of its own. The result depends on the two gamma ray picks, Clean gamma ray and Clay gamma ray, which every gamma-ray-based method shares. How to pick them, and why to pick them per zone, is covered on the Clay Volume page under shared parameter picking.

Worked example

A reading of 65 gAPI, with a clean pick of 20 gAPI and a clay pick of 120 gAPI:

import math
gr, gr_clean, gr_clay = 65.0, 20.0, 120.0
igr = min(1.0, max(0.0, (gr - gr_clean) / (gr_clay - gr_clean)))
vcl = 1.7 - math.sqrt(3.38 - (igr + 0.7) ** 2)
print(f"IGR = {igr:.3f}")
print(f"Vcl = 1.7 - sqrt(3.38 - ({igr:.3f} + 0.7)^2) = {vcl:.3f}")

Output

IGR = 0.450
Vcl = 1.7 - sqrt(3.38 - (0.450 + 0.7)^2) = 0.266

Assumptions and limitations

• The gamma ray responds only to clay. Radioactive feldspars, micas, glauconite, uranium-rich organic matter and heavy-mineral sands raise the gamma ray without adding clay, so clay volume is overestimated.
• One pair of clean and clay picks applies across the zone. If clay mineralogy or the clean-sand response changes with depth, the picks must change too.
• The gamma ray is environmentally corrected and normalized across wells, as covered in Stage 1.
• The formation response is close enough to the fitted shape of the relation. Like the other transforms, it is an empirical curve and not a derived one.

QC checks

• The result is between 0 and 1, equal to 0 at the clean pick and close to 1 at the clay pick.
• A visibly clean sand reads close to zero, not a few percent.
• Compare with an independent clay indicator such as neutron-density in a clean and a shaly interval. If the gamma-ray result is consistently higher, suspect a radioactive mineral.
• Compare with the other gamma ray transforms. The ordering at a given index must be the same at every depth.
• The square-root argument must stay positive. It does for any index between 0 and 1, so a failure means the index was not clamped.

Going Deeper

The Clavier form is a fitted curve with a circular-arc shape, which is why it gives smooth behavior and exact endpoints. It sits between the linear index and the stronger exponential reductions of Larionov, so it is often chosen as a compromise. As with all gamma ray transforms, the shape should be validated against an independent clay estimate before it is adopted for a field.

References

1. Clavier, C., Hoyle, W. and Meunier, D., 1971. Quantitative interpretation of thermal neutron decay time logs. Journal of Petroleum Technology.
2. Clavier, C., Coates, G. and Dumanoir, J., 1977. The theoretical and experimental bases for the "dual water" model for the interpretation of shaly sands. SPE 6859, SPE Annual Fall Technical Conference and Exhibition, Denver.

Python reference implementation

Related methods

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