Page 181 - Introduction to Petroleum Engineering

168 WELL LOGGING
and transfer some of their energy to the electrons. The remainder of the energy is
scattered as lower‐energy gamma‐ray photons. The density logging tool then detects
some of these scattered photons. The gamma‐ray count rate at the tool depends on
formation electron density, which is proportional to formation bulk density ρ .
b
Combining ρ from the density log with rock matrix density ρ and fluid density
b
ma
ρ yields porosity ϕ:
f
ρ − ρ
φ = ma b (9.1)
ρ ma − ρ f
Formation bulk density ρ can be obtained by rearranging Equation 9.1:
b
ρ = (1 − φ ρ ) ma + φρ f (9.2)
b
Results of the density tool are presented in three tracks on a log: bulk density,
density correction, and porosity. The density correction track shows corrections to
the bulk density due to irregularities in wellbore diameter. It is an indication of the
quality of the bulk density response. For density corrections greater than 0.2 g/cm ,
3
the bulk density values are suspect. The depth of investigation for the density tool is
typically 1–2 ft.

Example 9.2 Density Log

A density log shows that the bulk density ρ of a formation is 2.30 g/cc. The
b
density of the rock matrix ρ is 2.62 g/cc and the density of the fluid ρ in the
f
ma
formation is 0.869 g/cc. Calculate porosity.
answer
ρ − ρ 2622.
− 30
.
Use φ = ma b = = 0 183 or 18.3%
.
ρ ma − ρ f 2620 .
− 869
.
9.3.2 acoustic Logs
The elapsed time to propagate a sound wave from a source on a logging tool through
the formation and back to a receiver on the tool depends on formation porosity. The
tool that sends and receives sound waves is called an acoustic log or sonic log.
Sound waves are vibrations in a medium like air or rock. The speed of sound in a
medium depends on the density of the medium. In the case of rock, density depends
on the density of rock matrix and the density of the fluids occupying the pore space
in the rock. Fluid density is usually much smaller than matrix density. Consequently,
the bulk density of a formation with relatively large pore volume is less than the bulk
density of a formation with relatively small pore volume if the fluids in the pore
volume are the same in both formations.