Specific electrical resistivity or specific electrical conductivity of formations is defined by mineralization of the rock matrix and saturating fluids which depend on water-saturated shaliness , formation porosity and water saturation volumetric share .
Simandeux model suggest a more complicated correlation between resitvity and water saturation :
with default value .
The dual-water model accounts for the fact that different shales have different shale-bound water saturation :
\phi_t = \phi_e + \phi_t s_{wb} |
so that formation water saturation is related to total water saturation as:
s_w = \frac{s_{wt} - s_{wb}}{ 1 - s_{wb}} |
Rock volume is a sum of rock matrix volume and total pore volume :
where
Total pore volume is a sum of shale-bound water and free fluid volume (water and hydrocarbons):
where
and therefore:
Total volume of water is a sum of shale-bound water and free water :
and relates to as:
or
which gives an explicit formula for formation water saturation:
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Formation resistivity is given by the following correlation:
\frac{1}{R_t} = \phi_t^m s_{wt}^n \, \Big[ \frac{1}{R_w} + \frac{s_{wb}}{s_{wt}} \Big( \frac{1}{R_{wb}} - \frac{1}{R_w} \Big) \Big] \quad \Rightarrow \quad s_w = \frac{s_{wt} - s_{wb}}{ 1 - s_{wb}} |
where
shale-bound water saturation | |
total water saturation (shal-bound water and free-water) | |
specific electrical resisitvity of shale-bound water |
In simple case when all shales have the same properties, the shale-bound water saturation can be expressed through the shaliness as:
s_{wb} = \zeta_{wb} V_{sh} |
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