Waxman-Smits-Thomas Model (WST ) @model

One of the saturation from resistivity models:

(1)	$\begin{array}{l}\displaystyle \frac{1}{R_t} = \phi_t^m s_{wt}^n \, \Big[ \frac{1}{R_w} +\frac{B Q_V}{s_{wt}} \Big]\end{array}$

and saturation is given by

(2)	$\begin{array}{l}\displaystyle s_w = \frac{s_{wt} - s_{wb}}{ 1 - s_{wb}}\end{array}$

(3)	$\begin{array}{l}\displaystyle s_{wb}= \frac{V_{wb}}{V_t}\end{array}$

(4)	$\begin{array}{l}\displaystyle B Q_V = s_{wb} \left( \frac{1}{R_{wb}} - \frac{1}{R_w} \right)\end{array}$

where

$\begin{array}{l}s_w\end{array}$	formation water saturation
$\begin{array}{l}s_{wb}\end{array}$	bound water saturation
$\begin{array}{l}\phi_e\end{array}$	effective porosity
$\begin{array}{l}V_{sh}\end{array}$	shaliness
$\begin{array}{l}R_t\end{array}$	specific electrical resistivity from OH logs
$\begin{array}{l}R_w\end{array}$	specific electrical resistivity of formation water
$\begin{array}{l}R_{sh}\end{array}$	specific electrical resistivity of wet shales
$\begin{array}{l}A\end{array}$	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
$\begin{array}{l}m\end{array}$	formation matrix cementation exponent	1.5 ÷ 2.5, default value is 2
$\begin{array}{l}n\end{array}$	formation matrix water-saturation exponent	1.5 ÷ 2.5, default value is 2
$\begin{array}{l}B Q_V\end{array}$

In some practical cases, the laboratory data is available on $\begin{array}{l}B\end{array}$ and $\begin{array}{l}Q_V\end{array}$ separately, but the other model parameters still need calibration on core data.

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Waxman-Smits-Thomas Model (WST ) @model