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)

$\alpha$ : Clay Distribution Factor (dimensionless)

$\beta$ : Clay Distribution Factor (dimensionless)

$R_{t}$ : Rock Resistivity (ohm m)

\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}

Bassiouni, Z., 1994, Theory, Measurement, and Interpretation of Well Logs. SPE Textbook Series Vol. 4. Chapter 1, Page: 16.