Page 182 - Introduction to Petroleum Engineering

POROSITY LOGS 169
An estimate of the speed of sound v in a formation is given by Wyllie’s equation.
If we write the speed of sound in fluids occupying the pore volume of a rock as v and
f
the speed of sound in the rock matrix as v , Wyllie’s equation is
ma
−
1 = φ ( 1 φ) (9.3)
+
ν ν f ν ma
where ϕ is rock porosity. We can write the speed of sound in each medium as the
distance traveled divided by the transit time. If we assume the distance traveled is the
same in each medium, then Wyllie’s equation can be written as

∆t = φ ∆t +(1 −φ ∆t ) ma (9.4)
f
where Δt is transit time in the bulk volume, Δt is transit time in the interstitial fluid,
f
and Δt is transit time in the rock matrix. Porosity in the bulk volume is obtained by
ma
rearranging Equation 9.4:
∆t − ∆t
φ = ma (9.5)
∆t f − ∆t ma
In addition to providing a measurement of porosity, acoustic logs can be used to
calibrate seismic measurements. The comparison of acoustic and seismic transit time
measurements in a formation can improve the accuracy of converting seismic transit
times to depths.
The depth of investigation for sonic logs is typically 1–4 ft.

Example 9.3 Acoustic Log

−
An acoustic log measured the transit time of 75µs = 7510 s in a formation.
×
6
×
The formation matrix has a transit time of 50µs = 50 10 s, and the fluid
−
6
transit time is 185µs = 185 10 s. Use Equation 9.5 to calculate porosity.
−
×
6
answer
∆t − ∆t 75 − 50
Use φ = ma = = 0 185. or 18.5%
∆t − ∆t 185 − 50
f ma
9.3.3 Neutron Logs
The neutron log provides information about the formation by emitting neutrons
from a radioactive source in the logging tool. The emitted neutrons lose energy as a
result of collisions with atomic nuclei in the formation to become slower thermal
neutrons. Slower neutrons can be captured by nuclei in the formation. Hydrogen
nuclei are especially effective at capturing thermal neutrons. Reservoir fluids (oil,
water, and hydrocarbon gas) contain hydrogen while formation rock usually does
not. Consequently, the detection of captured neutrons by the neutron logging tool
indicates porosity.