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🪨 Calculators

Shale Volume from Gamma Ray (Larionov)

Estimates the shale volume of a formation from the gamma ray log, the first step in any petrophysical well evaluation. The calculation normalizes the zone reading between the cleanest sand and the most radioactive shale in the interval, giving the gamma ray index IGR = (GR − GR min) ÷ (GR max − GR min), and then applies the non-linear Larionov curve, Vsh = 0.083 × (2^(3.7 × IGR) − 1). The result is the fraction of rock volume occupied by clay, as a percentage: intervals above 30 to 40% are usually discarded as reservoir, and the value later feeds the porosity and water saturation corrections for shaly sands. The Larionov curve for Tertiary, poorly consolidated rocks was adopted, which is the usual one in young sedimentary basins; for Mesozoic or older rocks the literature uses Vsh = 0.33 × (2^(2 × IGR) − 1), which returns far larger volumes for the same IGR. Enter the zone gamma ray reading, the minimum reading and the maximum reading of the interval.

Result

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Shale Volume from Gamma Ray: Reading the Larionov Curve

Anyone opening a fresh wireline log starts at the same place: the gamma ray curve, and the same question — how much of each metre of the interval is clay? That figure comes before porosity, before saturation, before any net pay count, because clay holds bound water, biases the density log and pushes Archie saturation toward values that never match the formation test. Skip it and an interval that should have been dropped ends up inside the pay footage, with an inflated oil volume riding on top of it.

The calculation runs in two steps. First the gamma ray index, IGR = (GR − GRmin) ÷ (GRmax − GRmin), which normalizes the zone reading between the cleanest sand and the hottest shale in the same interval — roughly 15 to 30 API in sand and 100 to 150 API in shale. Then the Larionov curve for Tertiary rocks, Vsh = 0.083 × (2^(3.7 × IGR) − 1): the 0.55 index from the sample values returns 25.72% clay rather than the 55% a linear reading would hand you. We use the Tertiary version because it suits young, poorly consolidated basins; for Mesozoic rocks the literature applies Vsh = 0.33 × (2^(2 × IGR) − 1), worth 37.74% at that same point.

Normalization is the fragile part. GRmin and GRmax must come from the same interval and the same logging run; uranium-rich shale, or sand carrying potassium feldspar and mica, shifts the whole scale, and a uranium-free curve from a spectral gamma tool makes a better input there. The calculator rejects readings outside the two endpoints, since an index below zero or above unity carries no physical meaning. Keep in mind too that Vsh means bulk volume of clay in the rock, distinct from clay content measured on core and from the shale fraction a geologist logs in cuttings.

Frequently asked questions

Why 25.72% when the index sits mid-scale?
Gamma ray and clay content are not linearly related. With a 75 API reading, a 20 API minimum and a 120 API maximum, the index lands on 0.55 — precisely what a linear reading would call 55% clay. The Larionov curve corrects a known bias: in poorly consolidated Tertiary rock the clay sits dispersed and reads hotter per unit volume, so a mid-range gamma ray value corresponds to far less clay than the proportion suggests. Hence 25.72%. If you want the linear figure for comparison, it equals the index multiplied by 100.
When should I switch to the Mesozoic curve instead?
Whenever the formation is old and consolidated, typically a well cemented Mesozoic or Palaeozoic sandstone. The expression becomes 0.33 × (2^(2 × IGR) − 1) and always runs more conservative: at the 0.55 index of the example it returns 37.74% instead of 25.72%. When in doubt, run both and treat the pair as a range. If completing or abandoning the interval hinges on which value you pick, the case calls for core calibration or a density-neutron crossplot rather than a blind choice of curve.
The tool rejected my numbers. What should I check?
It only accepts a zone reading inside the interval, with the maximum above the minimum and the minimum at zero or higher. The reason is arithmetic: outside those bounds the index turns negative or exceeds unity, and the curve would report a clay volume below zero or above 100%. When that happens the trouble usually lies in the endpoints, not in the zone reading. If a cleaner sand or a hotter shale showed up anywhere in the log, update both endpoints with the full interval in view and rerun every zone on one scale.

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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.