Resistivity of a partially saturated shaly sand with hydrocarbons (Vsh models)
Input(s)
\(S_{w}\): Water Saturation (fraction)
\(R_{w}\): Formation Water Resistivity (ohm m)
\(V_{s h}\): Bulk Volume Fraction of Shale (fraction)
\(R_{s h}\): Shale Resistivity (ohm meter)
F: Formation Resistivity Factor (dimensionless)
Output(s)
\(\alpha\): Clay Distribution Factor (dimensionless)
\(\beta\): Clay Distribution Factor (dimensionless)
\(R_{t}\): Rock Resistivity (ohm m)
Formula(s)
\[
\begin{gathered}
\alpha=\frac{V_{s h}}{R_{s h}} \\
\beta=1 / F \\
\frac{1}{R_{t}}=\left(\alpha * S_{w}\right)+\frac{\beta *\left(S_{w}\right)^{2}}{R_{w}}
\end{gathered}
\]
Reference(s)
Bassiouni, Z., 1994, Theory, Measurement, and Interpretation of Well Logs. SPE Textbook Series Vol. 4. Chapter 1, Page: 16.