Vclay from GR (Larionov, Older Rocks)

Summary

The Larionov relation for older rocks converts the Gamma ray index to Clay volume with a milder exponential curve than the Tertiary relation. It is intended for older, more consolidated formations. Use it when only a gamma ray is available and the rock is pre-Tertiary.

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 Larionov relation for older rocks then gives the clay volume:

Single-value calculator

Behavior

The curve lies between the linear index and the Tertiary relation. At an index of 0.5 it gives 0.33, compared with 0.22 for the Tertiary relation and 0.50 for the linear index. At an index of 1 it gives 0.99, which is close to but not exactly 1.

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. The constants 0.33 and 2 are part of the published relation and are not normally changed.

Worked example

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

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 = 0.33 * (2 ** (2 * igr) - 1)
print(f"IGR = {igr:.3f}")
print(f"Vcl = 0.33 x (2^(2 x {igr:.3f}) - 1) = {vcl:.3f}")
print(f"Vcl at IGR = 1: {0.33 * (2 ** 2 - 1):.3f}")

Output

IGR = 0.450
Vcl = 0.33 x (2^(2 x 0.450) - 1) = 0.286
Vcl at IGR = 1: 0.990

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 is older and consolidated. Applying it to young, unconsolidated rock will over-predict clay volume relative to the Tertiary relation.

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 result at an index of 1 is 0.99. Clamp the output if a value of exactly 1 is needed in shales.

Going Deeper

This is the second of the two relations Larionov published. The older-rock curve is less aggressive than the Tertiary curve because consolidated rocks tend to have gamma ray responses closer to linear in clay content. As with the Tertiary relation, the age split is an empirical proxy, so the choice should be tested against core or an independent clay indicator.

References

1. Larionov, V.V., 1969. Borehole Radiometry (Radiometriya skvazhin). Nedra, Moscow (in Russian).

Python reference implementation

Related methods

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