# 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.