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

GATE-2007

66. If the saturation exponent in Archie's equation is 2 , the bulk resistivity of 50% water saturated formation increases in comparsion to that of a fully water saturated formation by a factor of

A) 4                        B) 8                    C)16                  D)32

Solution:

Saturation exponent n=2

water saturation (S_w) = 50 / 100 = 0.5

Formula :

S_wⁿ= (√R₀/ R_t) -------------------------(1)

R₀- Resistivity of rock fully saturated with water

R_t- Resistivity of rock partially satureated with water

Substitute water saturation value in eq (1)

R₀/ R_t = (0.5)²

R₀/ R_t = 0.25

R_t/ R₀ = (1/ 0.25)

Therefore, R_t=4 R₀