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:

 

Given data

Diameter of the cylinder (d) = 0.02 m

So, radius of the cylinder (r) = 0.01 m

Cylinder cross sectional area (A) = Π* r²

 

                                                                   = 3.14* (0.01)²

                                                                   = 0.000314 m²

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)

Radius (r)=0.01 m

length of the cylinder (l) = 0.04 m

Resistance (R)= 500Ω

R_w - Saturated water resistivity

                         (or)

Resistivity of the brine solution (R_w)=0.5 Ωm

Resistance (R) = (ρ *l) /A

Resistivity (ρ) = (R * A) / l

                             = (500 * 0.000314) / 0.04

R₀ – Resistivity of porous medium saturated with water.

                         (or)

Resistivity of the water ( ρ) = R₀

R₀ = 3.925 Ωm

Therefore , F = R₀ /R_w

                            = 3.925 / 0.5

                            =7.85