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One of the saturation from resistivity models:
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with specific electrical resistivity is defined as:| LaTeX Math Block |
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| anchor | SimandouxArchie |
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| alignment | left |
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| \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}w = \Big ( \frac{A R_w (1-V_{sh})}{2 \phi_e^m} \, \left(; \sqrt{ \left( \frac{VR_{sh}w}{R_{sht}} \rightBig)^2 + \frac{4\phi_e^m}{a R_t R_w (1-V_{sh}) } } - \frac{V_{sh}}{R_{sh}} \right)^{1/n} |
where
| specific electrical resistivity of formation water |
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| 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 |
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| formation matrix cementation exponent | 1.5 ÷ 2.5, default value is 2 |
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| formation matrix water-saturation exponent | 1.5 ÷ 2.5, default value is 2 |
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Archie model is usually used in: - high permeable clean sands with low or no shaliness
- high permeable clean limestones with low or no shaliness
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