One of the saturation from resistivity models: where
R_t
R_w
A dimensionless constant, characterizing the rock matrix contribution to the total electrical resistivity 0.5 ÷ 1, default value is 1 for sandstones and 0.9 for limestones
m
n 1.5 ÷ 2.5, default value is 2
(1)
\frac{1}{R_t} = \frac{\phi_e^m \, s_w^n}{A R_w (1-V_{sh})} + \frac{V_{sh}}{R_{sh}} s_w^{n/2}
\quad \Rightarrow \quad s_w^{n/2} = \frac{A R_w (1-V_{sh})}{2 \phi_e^m} \, \left( \sqrt{ \left( \frac{V_{sh}}{R_{sh}} \right)^2 + \frac{4\phi_e^m}{a R_t R_w (1-V_{sh}) } } - \frac{V_{sh}}{R_{sh}} \right)
specific electrical resistivity from OH logs specific electrical resistivity of formation water formation matrix cementation exponent 1.5 ÷ 2.5, default value is 2 formation matrix water-saturation exponent
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