LaTeX Math Block |
---|
| \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 LaTeX Math Block |
---|
| s_w = \frac{s_{wt} - s_{wb}}{ 1 - s_{wb}} |
LaTeX Math Block |
---|
| s_{wb}= \frac{V_{wb}}{V_t} |
LaTeX Math Block |
---|
| \frac{1}{R_{sh}} = s_{wb} \left( \frac{1}{R_{wb}} - \frac{1}{R_w} \right) |
where | formation 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: LaTeX Math Block |
---|
| \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.
|