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# Calculating Shale Volume from Gamma Ray: Larionov, Clavier and Stieber models

Estimating the rock's shale volume VSH linearly from the gamma ray log still remains the first preferred approach to become with a preliminary shaliness indicator. The procedure is easy and straightforward, and might give reasonable results for some deep reservoirs. The equation (1) shown below defines an IGR shaliness index as a function of the GR gamma ray log signal: It only needs to record the response of the gamma ray log for a nearby known shale body and a nearby known clean rock.

However, quite often the linear IGR shaliness indicator yields an over-estimation of rock's volume of shale (specially for shallow, young reservoirs), producing an overall pessimistic scenario of the reservoir quality. To overcome this, several empirical formulations have been developed to correct and reduce the rock's shale volume Vshale as direct functions of IGR, that is VSH = f (IGR), trying to adjust the clay minerals total radioactive response.

Ordered from the most pessimistic shale indicator IGR (more VSH), to the most optimistic one, the Larionov VSH equation for young, tertiary rocks (less VSH), the equations show the Linear VSH IGR indicator, the Larionov model for older rocks, the Clavier model, the Stieber model, and the Larionov model for tertiary rocks:

The figure below, shows the different vshale corrections VSH = f (IGR), as functions of the IGR index. The corrections are particularly important for medium IGR values around 0.4 - 0.7:

What's the best model to choose? There is no a closed answer. Instead of computing all the 5 equation models, we suggest to compute only the extremes pessimistic linear IGR, and the optimistic Larionov for tertiary rocks to derive a custom weighted combination:

VSH_geoloil (IGR, w) = w*IGR + (1-w)*VSH_larionovTertiary

where w is a weight blend term in the range (0,1). The closer w is to 1.0, the more weight is given to IGR, the closer w is to 0.0, the less weight is given to IGR.

How to choose a value for w?, again there is no a closed answer, the petrophysicist or geologist interpreter might pick a value from his/her judgement, experience, and nature of the reservoir. The interpreter should compute also different estimates of VSH that don't depend upon the gamma ray log to aid the decision, like the neutron porosity to density porosity difference technique.

Below we show a log from a case study for a shallow Wyoming reservoir. In this particular case, the linear IGR index yielded a clearly pessimistic, over-estimation of rock's shale content:

The blue "Zone 2" on the GeolOil plotter log's bottom panel, shows a pay zone with a deep resistivity around 30-40 Ohm.m. The magenta "Zone 1" on the top log's plot panel shows a resistivity of around 30 ohm.m. According to the linear IGR VSH, the zone 1 shaliness (dashed red curve) is more 0.50 V/V units. It is quite difficult to believe that such high resistivity zone, could come from a very shaly sand body. Both the Larionov tertiary rock VSH estimate and the VSH estimate from the Neutron Porosity to Density Porosity distance yield more reasonable lower VSHALE values around 0.25 - 0.30 V/V, allowing hydrocarbon accumulations.

The figure below compares three VSH estimates: the Linear IGR index (red), Larionov (green) and Neutron-Density difference (blue).

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