Page 87 - Well Logging and Formation Evaluation

Advanced Log Interpretation Techniques 77

The basic principle by which the tool operates is as follows. The tool
is assumed to respond only to hydrogen nuclei (in water, oil, and gas) in
the porespace. The hydrogen nuclei (which are just protons) in the pore-
fluids have a spin and magnetic moment that may be affected by an exter-
nal magnetic field. In the absence of an atomic field, these moments are
aligned randomly. When an external field (B 0) is applied, a process occurs
whereby the orientation of the nuclei changes so that a proportion of them
align in the direction of the applied field H. The reason they do not all
immediately align in the direction of the field is that two adjacent nuclei
are in a lower energy state when they are aligned in opposite directions.
The nuclei do not immediately align in the direction of H, but their
spins precess around B 0 at a frequency given by Larmor:

w Larmor = gB 0

where g is the gyromagnetic ratio (42.58Mhz/T for hydrogen) and B 0 is
the strength of the external field, in Tesla.
After a time a proportion of the nuclei have “relaxed” to be aligned
with B 0. The resulting magnetization of the formation is given by M v , and
will vary according to:

-
M v µ(1 exp - ( t T )
1
where T 1 is the longitudinal relaxation time. In the absence of any further
fields being applied to the horizontal magnetic components, the individ-
ual nuclei will be randomly distributed and sum to zero.
Now consider what happens if, after a period denoted by T w (wait time),
a horizontal magnetic field is applied at a frequency equal to the Larmor
frequency. The nuclei’s horizontal magnetic moments will start to align
themselves in the direction of the horizontal pulse. After a time given by t
(the echo time), a pulse is given at 180 degrees to the direction of B 0 (called
a p pulse). The nuclei start to align themselves in the opposite direction.
However, because of differences in their horizontal relaxation times, the
magnetic moment building up in the opposite direction will be less than
during the first pulse. A third pulse is then applied in the original direction
of B 0 with correspondingly even less buildup of moment. The process is
continued for a finite number of “echoes” until the horizontal signal (which
can be detected in the tool’s coils) dies away to zero. The decay of the hor-
izontal signal is called the transverse relaxation, and the magnetization
detected (denoted by M h, ignoring diffusion) will vary according to: