GATE_2018
79) A 15 Volt power supply
is applied across a cylindrical container (diameter = 0.20 m and
length = 0.50 m). Currents of 750 mA and 500 mA are measured when the
container is filled with (i) brine only, and (ii) rock sample fully
saturated with brine, respectively. The formation factor of the rock
sample is __________.
(Thanks to Chandra Sekhar, ANU)
Solution:
The formula for the
Formation Factor is (F) = $\frac{\rho_{0}}{\rho_{w}}$---------(1)
where $\rho_{0}$ is the
apparant resisitivity for the rock smaple with fully saturated with
brine.
$\rho_{w}$ is the apparent
resisitivity for the brine only
Given that
V = 15 volts
$I_{0}$ = 500 mA
$I_{w}$= 750mA
by substituting the given
values in the equation (1) then
$F
=\frac{\rho_{0}}{\rho_{w}}$
= $\frac{\frac{R_{0}\times
A}{L}}{\frac{R_{w}\times A}{L}}$
=$ \frac{R_{0}}{R_{w}}$
=$\frac{\frac{V}{I_{0}}}{\frac{V}{I_{w}}}$
=$\frac{I_{w}}{I_{0}}$
=$\frac{750}{500}$
F =1.5
The Formation factor of the
rock sample is 1.5
Reference: Petrophysics by Djebbar Tiab and Erle C.Donaldson.
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