Mathematical model of rock shaliness.
The shales contain much higher concentration of radioactive minerals comparing to clean sands and carbonates (see Table 1 below).
This is why the most common way to quantify the shale content is the intensity of the natural gamma-ray (GR) emission.
The fist step is to normalize the actual GR-tool readings to the reference values in clean rocks and pure shales which is called Shale Index:
I_{GR}(l) = \frac{GR_{log}(l) - GR_m}{GR_{sh} - GR_m} |
where – along-hole depth.
The model parameters and are calibrated for each facies individually.
The shale Index is varying between 0 (for non-shally rocks) and 1 (for pure shales) but the actual shaliness may behave non-linearly between these extremes (especially for shallow, young reservoirs).
This can be calibrated based on the available core data.
The table below summairzes some popular shaliness models:
# | Equation | Author | Rock Type | Correlation database |
---|---|---|---|---|
1 | ||||
2 | Larionov (1969) | Tertiary Jurassic rocks | West Siberia | |
3 | Clavier (1971) | |||
4 | Stieber (1970) | |||
5 | Larionov (1969) | Older Rocks | West Siberia |
The graphic image of different shales volume models is brought on Fig. 1.
Table 1. GR values for popular minerals | ||||
Rock Type | GR, API | |||
1 | Halite (NaCl) | 0 | ||
2 | Coal | 0 | ||
3 | Limestone | 5 – 10 | ||
4 | Sandstone | 10 – 20 | ||
5 | Dolomite | 10 – 20 | ||
6 | Shale | 80 – 140 | ||
7 | Mica | 100 – 170 | ||
8 | Silvite (KCl) | 500 | ||
Fig. 1. Shale Volume Models. |
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