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

GATE-2016

Q.41: A Cylindrical sandstone core sample of diameter 0.02m and length 0.04m is fully saturated with brine solution of resistivity 0.5 ohm m. The resistance of the saturated sample measured in the laboratory is 500 ohm. The formation factor of the sample is...........(use pi=3.15)

Solution:

The ratio of the resistivity of a rock filled with water (R₀) to the resistivity of that water (R_w).

Formation Factor (F)= R₀/R_w----------------------(1)

Diameter (d)= 0.02 m

Radius (r)=0.01 m

Height (h)= 0.04 m

Resistance (R)= 500Ω

Resistivity of the brine solution (R_w)=0.5 Ωm

Resistance (R) = (ρ *l) /A

Resistivity (ρ) = (R * A) / l

                        = (500 * 0.00314) / 0.04

                      R₀  = 39.25 Ωm

Therefore , F = R₀/R_w

                        = 39.25 / 0.5

                         =78.5