Shale volume comes early in a log interpretation and quietly controls most of what follows. It sets the shale correction to porosity, the clay term in every shaly-sand saturation model, and usually one of the three net pay cut-offs. The gamma ray is the most common way to estimate it, and the estimate rests on two choices that are easy to make by habit: where to pick the clean and shale lines, and which transform turns the gamma-ray index into a volume.
The gamma-ray index
The starting point is a linear rescaling of the log between a clean-sand reading and a shale reading:
IGR = (GR − GR_clean) / (GR_shale − GR_clean)
Take a clean line at 30 API, a shale line at 120 API and a reading of 66 API:
IGR = (66 − 30) / (120 − 30) = 36 / 90 = 0.40
IGR is a ratio. Treating it directly as shale volume, the linear model, assumes the gamma ray rises in proportion to shale content. Several empirical relations say it does not, and all of them bend the index downwards in the middle of the range.
Four transforms, one reading
The common transforms, as given in standard references such as Asquith and Krygowski (2004), applied to IGR = 0.40:
Linear Vsh = IGR
= 0.400
Larionov, Tertiary rocks Vsh = 0.083 × (2^(3.7 × IGR) − 1)
= 0.083 × (2^1.48 − 1)
= 0.083 × (2.7895 − 1) = 0.149
Larionov, older rocks Vsh = 0.33 × (2^(2 × IGR) − 1)
= 0.33 × (2^0.8 − 1)
= 0.33 × (1.7411 − 1) = 0.245
Clavier Vsh = 1.7 − √(3.38 − (IGR + 0.7)²)
= 1.7 − √(3.38 − 1.21)
= 1.7 − √2.17 = 1.7 − 1.4731 = 0.227
Steiber Vsh = IGR / (3 − 2 × IGR)
= 0.40 / 2.2 = 0.182
All four agree at the ends, zero at IGR = 0 and close to one at IGR = 1, and disagree most in the middle, which is where shaly reservoir rock sits. Here the answers run from 0.15 to 0.40, a factor of more than 2.5 from the same log reading.
Larionov's two equations are for different rock ages: the Tertiary form for younger, less consolidated rock, and the older-rock form for consolidated, pre-Tertiary rock. Mixing them up is easy, because the names describe the rock, not the curve, and the difference at mid-range is large.
What the choice does downstream
Take the same sand with a total porosity of 0.24 and a shale porosity of 0.10, so that effective porosity is φe = φt − Vsh × φsh:
Linear 0.24 − 0.400 × 0.10 = 0.200
Larionov, older 0.24 − 0.245 × 0.10 = 0.216
Clavier 0.24 − 0.227 × 0.10 = 0.217
Steiber 0.24 − 0.182 × 0.10 = 0.222
Larionov, Tertiary 0.24 − 0.149 × 0.10 = 0.225
That is a spread of 2.5 porosity units from the shale model alone, about 12 percent of the pore volume, before saturation is computed. The saturation adds more, because every shaly-sand model takes Vsh as an input.
The cut-off is starker. With a Vsh cut-off of 0.35, the linear model rejects this interval as non-net and every other transform accepts it. Net pay can jump by whole intervals between transforms, and nothing on the log display says which answer is right.
The shale line matters as much
Move the shale pick from 120 API to 110 API, a judgement call on many logs:
IGR = 36 / 80 = 0.45
Larionov, Tertiary = 0.083 × (2^1.665 − 1) = 0.180
Larionov, older = 0.33 × (2^0.9 − 1) = 0.286
Move it to 130 API instead and IGR falls to 36 / 100 = 0.36 and the Tertiary transform gives 0.126. A 10 API change in the shale line moves Vsh by 0.02 to 0.04 with the Larionov transforms, and by up to 0.05 with the linear model, comparable to the gap between two neighbouring transforms. A few habits help.
- Pick by zone, not by well. Shale gamma-ray levels change with depth and with shale mineralogy. A single shale line through a long section is usually wrong somewhere, and a depth-varying trend is often better.
- Use the histogram, not the extreme. The cleanest and hottest readings are often a single bed or a spike; a high and a low percentile of the zone are steadier picks.
- Write the picks down. They are interpretation parameters with an uncertainty, not constants, and they belong in the sensitivity analysis.
When the gamma ray misleads
The gamma ray measures natural radioactivity, and shale is only one source of it.
- Feldspar and mica. Arkosic and micaceous sands contain potassium outside the clay and read hot. A clean arkose can look shaly.
- Uranium. Organic-rich shales, phosphatic beds and uranium carried by formation water raise the total gamma ray without adding clay. Spectral gamma-ray data let you use the computed gamma ray, thorium plus potassium, which excludes uranium.
- Heavy minerals. Zircon and monazite, which carry thorium and uranium and are concentrated in some sands, read as shale.
- Mud and hole. Potassium chloride in the mud adds a potassium signal, and hole size and mud weight change the count rate. The log should be environmentally corrected before it is rescaled.
In these rocks a second indicator is essential: the density–neutron separation, the SP, or the resistivity. Each indicator is pushed up by something other than shale, so where several are available, the minimum of them is a common, defensible estimate.
Shale volume is not clay volume
Shale is a rock, mostly clay minerals but with a large share of silt-sized quartz and other minerals. Clay volume is the volume of the clay minerals alone, and is smaller: if the local shale is about 60 percent clay minerals, a Vsh of 0.25 corresponds to a clay volume of about 0.15. The distinction matters because models differ in what they expect. Effective-porosity saturation models built on a shale resistivity want shale volume; models built on cation exchange capacity, and mineral solvers, want clay volume. Feeding one where the other is expected is a common, silent error.
The way to settle all of this is calibration: clay volume from core X-ray diffraction or thin sections, plotted against the index, shows which transform, if any, the rock follows. Without core, the honest course is to carry two transforms as the low and high cases and let the volumetric range show what the choice is worth.
The Lithology and Shale Modeling module of the Intermediate Petrophysics track covers shale-volume methods and mineral responses in more depth, and the Net Pay Construction module of the Basic track covers how the Vsh cut-off sits beside the porosity and saturation cut-offs.
In the platform
The Vsh workspace in Formation Evaluation applies the linear, both Larionov, Clavier and Steiber transforms to the gamma ray, with clean and shale lines that can follow a depth trend. Density, neutron, sonic, resistivity and SP indicators can be enabled alongside it and combined by their minimum, maximum or average. The selected transform and picks are saved with the case, so a reviewer can see what was used.
References
- Larionov, V. V. (1969). Borehole Radiometry. Moscow, Nedra (in Russian).
- Clavier, C., Hoyle, W., and Meunier, D. (1971). Quantitative interpretation of thermal neutron decay time logs: Part I. Fundamentals and techniques. Journal of Petroleum Technology, 23(6).
- Steiber, R. G. (1970). Pulsed neutron capture log evaluation in the Louisiana Gulf Coast. SPE 2961.
- Asquith, G., and Krygowski, D. (2004). Basic Well Log Analysis, 2nd edition. AAPG Methods in Exploration 16.