Calculation of true thickness of the bed

 Q.) If the resistivity of the formation 100% water-saturated is 5Ωm and resistivity of the formation water is 0.5Ωm. Then calculate the porosity (φ %) in consolidated sandstone?

(If m-Cementation factor =2, a-tortuosity factor)

Solution:

Formation factor (F) $=\frac{\rho_{0}}{\rho_{w}}$

${\rho_{0}}$ – Resistivity of formation 100% water saturated

$\rho_{w}$ – Resistivity of formation water

$F=\frac{\rho_{0}}{\rho_{w}}$

 $F=\frac{5}{0.5}$

 $F=10$

The relation between formation factor and porosity is given below,

$F=\frac{0.81}{\phi^m}$ For consolidated sandstones

Cementation factor $m=2$

$\phi^2 =\frac{0.81}{F}$

$\phi^2 =\frac{0.81}{10}$

$\phi^2 =0.081$

$\phi =\sqrt{0.081}$

$\phi =0.284$

$\phi$ =28.4%