Shale Volume from the Gamma Ray

Part 3, Chapter 3: Gamma Ray and Spontaneous Potential

Learning objectives

Explain why the linear model overestimates shale volume
Name the common nonlinear shale-volume models and their ordering
Apply Larionov for young versus older rocks
Quantify how the model choice affects net pay

From Index to Volume

The gamma ray index is not the same as the shale volume. Using IGR directly as $V_{sh}$ (the linear model) systematically overestimates clay, because a small amount of clay, especially dispersed in the pores, lifts the gamma ray out of proportion to its volume. The industry corrects this with a family of nonlinear models, all of which bend below the linear line and so report less shale for the same index.

The Nonlinear Models

The most common are the Larionov equations. For young, Tertiary rocks $V_{sh} = 0.083,(2^{3.7,I_{GR}} - 1)$ , which bends the most; for older, consolidated rocks $V_{sh} = 0.33,(2^{2,I_{GR}} - 1)$ , which bends less. Clavier and Steiber are simpler curves that fall between the two Larionov lines. At a mid-range index the linear and Larionov-Tertiary models can differ by nearly 30 shale-percent, the single biggest swing in a shale-volume calculation.

Choosing a Model

Pick by geology: Larionov-Tertiary for young, soft, Gulf-Coast-style sands; Larionov-older or Steiber for consolidated, older rocks. Better still, calibrate the choice to core or to a clean-sand interval of known mineralogy. And remember the safe default: the linear model gives the highest shale volume, so it is the conservative bound, the one to fall back on when the geology is uncertain and you would rather underestimate the pay than oversell it.

References

Asquith, G. and Krygowski, D. (2004). Basic Well Log Analysis, 2nd ed. AAPG Methods in Exploration 16.
Larionov, V. V. (1969). Borehole Radiometry. Nedra, Moscow.