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

GATE-2012

30. Based on acoustic log of a well, the transmit time in a water-bearing sandstone zone is found to be 75μs/ft. The transit time of acoustic wave through the sandstone matrix and water are 50μs/ft and 200μs/ft, respectively. Determine the porosity of the sandstone. ( Give answer up to 2 decimal places).

A)0.05                     B)0.10                     C) 0.12                 D)0.17

Solution:

Sonic logging is a well logging tool that provides a formation's interval transit time, designated as, which is a measure of a formation's capacity to transit seismic waves. Geologically, this capacity varies with lithology and rock texture, most notably decreasing with an increasing effective porosity.

$\bf \triangle t =\frac{\triangle t_{log}-\triangle t_{mat}}{\triangle t_{fluid}-\triangle t_{mat}}----(1)$
 

Δt_log = 75 μs/ ft

Δt_fluid= 200 μs/ ft

Δt_matrix= 50 μs/ ft

Φ = (75 -50) / (200-50 )

Φ = (25) / (150)

Porosity (Φ) =0.16