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CSIR-NET 2019 DEC

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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


\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


S_{h}=95%



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