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
$\rho_{w}$
– 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%
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