GATE-2018 (24) :Wyllie – Time average equation

 

Question:  Calculate the apparent resistivity in electrical logging, a current of 2000mA is passed through the electrodes C₁ and C₂ and a voltage of 1900mV is measured between the potential electrodes P₁ and P₂. The electrodes P₁ and C₁ being lowered into the borehole separated by a distance of 40 cm (Note P₂ and C₂ being grounded at the surface).

Solution:

 Given that

Current (I) = 2000mA = 2A

Voltage (ΔV) =1900mV=1.9V

Spacing (a) = 40 cm =0.4m

The apparent resistivity

$\rho _{a}=4\pi a(\frac{\triangledown V}{I})$

$\rho _{a}=(4)(3.14)(0.4)(\frac{1.9}{2})$

$\rho _{a}=4.7728ohm-m $