Q)
A sandstone formation
has porosities varying from 10-30%. The 100% water saturated sand
with 10% porosity has a formation resistivity of 0.5 Ωm. what is
the hydrocarbon saturation (%) in the sand formation with 20%
porosity and formation resistivity of 50 Ωm( assume a=1,n=2)
(Thanks to Chandrasekhar, ANU)
Solution:
Given
that porosity varies \phi=10-30%
Formation
resistivity (\rho_ {0} ) = 0.5 Ωm when porosity (\phi) is 10%
Then
resistivity of water (\rho_ {w} ) =?
Formation factor
F=\frac{\rho_{0}}{\rho_{w}}
\frac{1}{\phi^{2}}=\frac{\rho_{0}}{\rho_{w}}
\rho_{w}=\phi^{2}\times\rho_{0}
\rho_{w}=(0.1)^2\times
(0.5)
\rho_{w}=0.005
For
the calculation of hydrocarbon saturation we need to calculate the
saturation of water
S_{h}+S_{w}=1
S_{w}=\sqrt{\frac{F
\rho_{w}}{\rho_{t}}}
S_{w}=\sqrt{\frac{\rho_{w}}{\phi^{2}\times\rho_{t}}}
Here
\phi=
20%
=0.2
=0.2
\rho_{w}=0.005
\rho_{t}=50
Substitute
these values in the above equation
We
get,
S_{w}=\sqrt{\frac{\rho_{w}}{\phi^{2}\times\rho_{t}}}
S_{w}=\sqrt{\frac{0.005}{(0.2)^{2}\times(50)}}
S_{w}=\sqrt{\frac{0.005}{2}}
S_{w}=0.05
The relation between water saturation and hydrocarbon saturation is given that,
S_{h}+S_{w}=1
S_{h}=1-S_{w}
S_{h}=1-0.05
S_{h}=0.95
Excellent, Both did great job
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