\frac{1}{R_t} = \phi_t^m s_{wt}^n \, \left[ \frac{1}{R_w} +\frac{1}{s_{wt}} \frac{1}{R_{sh}}
\right] |
and saturation is given by
s_w = \frac{s_{wt} - s_{wb}}{ 1 - s_{wb}} |
s_{wb}= \frac{V_{wb}}{V_t} |
\frac{1}{R_{sh}} = s_{wb} \left( \frac{1}{R_{wb}} - \frac{1}{R_w} \right) |
where
| formation water saturation | ||
bound water saturation | ||
| effective porosity | ||
| shaliness | ||
| total measured resistivity from OH logs | ||
| formation water resistivity | ||
| wet clay resistivity | ||
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 | |
| formation matrix cementation exponent | 1.5 ÷ 2.5, default value is 2 | |
| formation matrix water-saturation exponent | 1.5 ÷ 2.5, default value is 2 |
In some practical cases, the clay resisitvity can be expressed as:
\frac{1}{R_{sh}} = B \cdot Q_V |
where
conductance per cat-ion (mho · cm2/meq) | |
Cation Exchange Capacity (meq/ml) |
and both can be measured in laboratory.
The other model parameters still need calibration on core data.