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One of the saturation from resistivity models:

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s_w = \left[  \frac{  \frac{1}{\sqrt{R_t}}  }{  \left(  \left   \frac{V_{sh}^{1- 0.5 \, V_{sh}}}{\sqrt(R_w)} \right) + sqrt{ \frac{\phi_e^m}{A \cdot R_w} }     \right ) } \right]^{2/n}

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\frac{1}{R_t} = \frac{\phi_e^m \, s_w^n }{A R_w} \quad \Rightarrow \quad s_w = \Big (  \frac{A}{\phi_e^m} \; \frac{R_w}{R_t} \Big) ^{1/n}

where constant 

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 is defined by formation shaliness 
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bodyV_{sh}
:

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\frac{1}{A} = 1 + \Big( \frac{V_{sh}^{2-V_{sh}}}{\phi_e} \, \frac{R_w}{R_{sh}}  \Big)^{1/2}  

where

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formation water saturation

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body\phi_e

effective porosity

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bodyV_{sh}

shaliness

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bodyR_t

specific electrical resistivity from OH logs

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bodyR_w

specific electrical resistivity of formation water

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bodyR_{sh}

specific electrical resistivity of wet shales

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bodym

formation matrix cementation exponent1.5 ÷ 2.5, default value is 2

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bodyn

formation matrix water-saturation exponent

1.5 ÷ 2.5, default value is 2


See Also

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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Petrophysics

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