...
One of the saturation from resistivity models:.
Excerpt |
---|
The dual-water model accounts for the fact that different shales have different shale-bound water saturation LaTeX Math Inline |
---|
body | s_{wb}= \frac{V_{wb}}{V_t} |
---|
| : LaTeX Math Block |
---|
| \phi_t = \phi_e + \phi_t s_{wb} |
so that formation water saturation is related to total water saturation LaTeX Math Inline |
---|
body | s_{wt} = \frac{V_{wb} + V_w}{V_t } |
---|
| as: LaTeX Math Block |
---|
| s_w = \frac{s_{wt} - s_{wb}}{ 1 - s_{wb}} |
Expand |
---|
| Rock volume is a sum of rock matrix volume and total pore volume : LaTeX Math Block |
---|
| V = V_m + V_t = (1-\phi_t) V + \phi_t V
|
where LaTeX Math Block |
---|
| \phi_t = \frac{V_t}{V} |
Total pore volume is a sum of shale-bound water and free fluid volume (water and hydrocarbons): LaTeX Math Block |
---|
| V_t = \phi_t V = V_e + V_{wb} = \phi_e V + s_{wb} V_t |
where LaTeX Math Block |
---|
| V_e = V_t (1 - s_{wb}) |
and therefore: LaTeX Math Block |
---|
| \phi_e = \phi_t (1 - s_{wb}) |
Total volume of water is a sum of shale-bound water and free water : LaTeX Math Block |
---|
| V_{wt} = V_{wb} + V_{wf} |
and relates to as: LaTeX Math Block |
---|
| s_{wt} V_t = s_{wb} V_t + s_w V_e = s_{wb} V_t + s_w V_t (1 - s_{wb}) |
or LaTeX Math Block |
---|
| s_{wt} = s_{wb} + s_w (1 - s_{wb}) |
which gives an explicit formula for formation water saturation: LaTeX Math Block |
---|
| s_w = \frac{s_{wt} - s_{wb}}{ 1 - s_{wb}} |
|
Formation resistivity is given by the following correlation: LaTeX Math Block |
---|
| \frac{1}{R_t} = \phi_t^m s_{wt}^n \, \Big[ \frac{1}{R_w} + \frac{s_{wb}}{s_{wt}} \Big( \frac{1}{R_{wb}} - \frac{1}{R_w} \Big) \Big] \quad \Rightarrow \quad s_w = \frac{s_{wt} - s_{wb}}{ 1 - s_{wb}} |
where LaTeX Math Inline |
---|
body | s_{wb} = \frac{V_{wb}}{V_t} |
---|
|
| shale-bound water saturation |
---|
LaTeX Math Inline |
---|
body | s_{wt} = \frac{V_{wb} + V_w}{V_t} |
---|
|
| total water saturation (shal-bound water and free-water) |
---|
| specific electrical resisitvity of shale-bound water |
---|
In simple case when all shales have the same properties, the shale-bound water saturation can be expressed through the shaliness as: LaTeX Math Block |
---|
| s_{wb} = \zeta_{wb} V_{sh} |
| 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.
|
...