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One of the saturation from resistivity models:

Excerpt




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s_w = \left[  \frac{\sqrt{\frac{1}{R_t}}}{ \frac{V_{sh}^{(1-0.5 \, V_{sh})}}{\sqrt{R_{sh}}} + \sqrt{ \frac{\phi_e^m}{A \, R_w}}}  \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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bodyA
 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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