(1)	$\begin{array}{l}\displaystyle \frac{1}{R_t} = \phi_t^m s_{wt}^n \, \left[ \frac{1}{R_w} +\frac{1}{s_{wt}} \frac{1}{R_{sh}} \right]\end{array}$

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

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
$\begin{array}{l}R_t\end{array}$	total measured resistivity from OH logs
$\begin{array}{l}R_w\end{array}$	formation water resistivity
$\begin{array}{l}R_{sh}\end{array}$	wet clay resistivity
$\begin{array}{l}A\end{array}$	dimensionless constant, characterising 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

In some practical cases, the clay resisitvity $\begin{array}{l}R_{sh}\end{array}$ can be expressed as:

(5)	$\begin{array}{l}\displaystyle \frac{1}{R_{sh}} = B \cdot Q_V\end{array}$

where

$\begin{array}{l}B\end{array}$	conductance per cat-ion (mho · cm²/meq)
$\begin{array}{l}Q_V\end{array}$	Cation Exchange Capacity (meq/ml)

and both can be measured in laboratory.

The other model parameters still need calibration on core data.

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