Electricity: measuring and testing – Particle precession resonance – Using well logging device
Reexamination Certificate
2002-08-20
2004-03-09
Fulton, Christopher W. (Department: 2862)
Electricity: measuring and testing
Particle precession resonance
Using well logging device
Reexamination Certificate
active
06703833
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to the field of nuclear magnetic resonance (NMR) measurements and methods of measurement. Specifically, the present invention provides improved apparatus for sensing the NMR response of rock formations surrounding a wellbore deep in the earth using a device located in the wellbore although the improved sensing methods are not limited to use in a wellbore.
2. Background and Description of the Prior Art
A variety of techniques have are utilized in determining the presence and estimation of quantities of hydrocarbons (oil and gas) in earth formations. These methods are designed to determine formation parameters, including among other things, the resistivity, porosity and permeability of the rock formation surrounding the wellbore drilled for recovering the hydrocarbons. Typically, the tools designed to provide the desired information are used to log the wellbore. Much of the logging is done after the well bores have been drilled. More recently, wellbores have been logged while drilling of the wellbores, which is referred to as measurement-while-drilling (“MWD”) or logging-while-drilling (“LWD”).
One recently evolving technique involves utilizing Nuclear Magnetic Resonance (NMR) logging tools and methods for determining, among other things porosity, hydrocarbon saturation and permeability of the rock formations.
Stable nuclei have a quantized angular momentum Ih where the nuclear spin quantum number I is an integer multiple of ½ and Planck's constant h=2&pgr;h. When I is not zero, the nucleus has an associated nuclear dipole magnetic moment &mgr;=g&mgr;
h
I where &mgr;
h
is the nuclear magneton defined below. This equation defines g, the nuclear gyromagnetic ratio, which is unique for each nuclear isotope. Since both protons and neutrons of which each nucleus is composed are fermions with spin ½, I is non-zero whenever the number of protons or the number of neutrons in the nucleus is odd.
It has long been known (i.e. since 1946) that the nuclear dipole magnetic moments of individual nuclei in a sample of matter align themselves with any externally applied steady state or static magnetic field, H
0
, so that their projections along the axis of the field direction are quantized in one of 2I+1 states with magnitudes m=I, I−1, . . . −I. This produces a bulk magnetization along the direction of the applied magnetic field if the populations of the different magnetic substates differ as they normally do since the states are populated according to a Maxwell-Boltzmann distribution function. The magnitude of this bulk magnetization is thus proportional to the asymmetry in the populations of the magnetic substates with values of m equal in magnitude but opposite in sign and this asymmetry in turn is proportional to the energy difference between these substates which itself depends directly on the strength of the field H
0
. Thus the bulk magnetization is proportional to H
0
. The energy eigenvalues E
m
of these magnetic substates are given by the interaction of &mgr; with the static field by the relation
E
m
=
-
μ
→
·
H
→
0
=
-
μ
I
I
→
·
H
0
=
-
g
μ
h
I
→
·
H
→
0
=
-
m
g
μ
h
H
0
(
1
)
and transitions are allowed between neighboring states so that the nuclei may absorb or emit energy quanta with E=hv=g&mgr;
h
H
0
. Thus, if the different states are not equally populated, by irradiating the sample with an oscillating magnetic field of frequency v=g(&mgr;
h
/h)H
0
, energy can be transferred to the system and this phenomenon is known as nuclear magnetic resonance or NMR for short since only at this frequency will energy be absorbed. The system behaves as a classical system in which the nuclear spins maintain fixed angles with the static field direction and precess about that direction with an angular frequency &ohgr;
1
=2&pgr;v=g(&mgr;
h
/h)H
0
known as the Larmor precession frequency, where the nuclear magneton, &mgr;
h
, is simply a scaling constant given by &mgr;
h
=(eh)/(2M
&rgr;
c)=5.051 10 joules per gauss, M
&rgr;
being the rest mass of the proton, e its charge and c the speed of light in a vacuum.
Since the resonance frequency is proportional to g, different nuclei precess about the static field direction at different frequencies. The nucleus with the largest g factor is the single proton which is the nucleus of the hydrogen atom for which g(&mgr;
h
/h)=26,752 radians/gauss/sec and these nuclei precess at the highest Larmor frequency in the presence of any given static magnetic field. For strong static fields typically employed in NMR logging devices, protons process at radio frequencies.
For example, with H
0
=0.1T=1,000 gauss, v=4.2577 MHz.
When the radio frequency perturbing field is applied orthogonally to the static field, it exerts a coherent force on the nuclei selected with its frequency which is orthogonal to both the static field and perturbing field directions. If this perturbing field is applied for only a precisely appropriate time, the spins of the nuclei selected with this frequency will be rotated through an angle of 90° in the plane orthogonal to the direction of the radio frequency field. Such a finite length radio frequency (RF) perturbing field is called a &pgr;/2 or 90° pulse since it rotates the nuclear spins by exactly 90°. The field strength required for this 90° rotation may be very small compared to the static field strength since &thgr;=&pgr;/2=g(&mgr;
h
/h)H
1
t
p
where H
1
is the RF field strength, &thgr; is the angle through which the nuclear spins are rotated by H
1
and t
p
is the length of time the RF field H
1
must be applied to rotate the bulk magnetization through the angle &thgr; For protons, a mere 1 gauss H
1
will produce a &pgr;/2 rotation in only t
p
=58.7 usec. When this 90° pulse ends, the nuclear spins gradually relax and return to their original alignment with the static magnetic field. The characteristic time for this process, T
1
, which is called the longitudinal decay time in the art, is related to interactions between the nuclear spins of interest and the “lattice” in which they are held or the material in which they are imbedded and thus may be related to water saturation and rock permeability among other petrophysical parameters in the case of proton resonance in natural rock formations. This signal can in principal be detected by the same coil or antenna used to apply the perturbing 90° RF pulse: it would be the decay time of the strength of the RF signal observed at the Larmor frequency of the selected nuclei (i.e. hydrogen) as a function of time.
There are, however, difficulties in measuring T
1
directly by simple observation of the magnetization decay following such a pulse because other processes can contribute to the decay of the observed signal following a single 90° pulse which is known in the art as the free induction decay or FID signal. In particular, dipole-dipole interactions between the spins of neighboring nuclei may occur, significantly reducing the decay time. The characteristic time for relaxation by this process, T
2
, is called the transverse decay time in the art and this too can be related to petrophysical quantities of interest such as producible or movable porosity, permeability to fluid flow, irreducible water saturation and fluid diffusion coefficients. In addition, local magnetic field inhomogeneities within the macroscopic sample examined whether caused by the geometry or asymmetry of the magnets producing the static field or by local magnetic property variations within the sample can produce a static distribution of precession frequencies for a given nuclear isotope also resulting in a much faster decay of the signal. The observed characteristic relaxation time of the FID signal is called T
2
* a
Gonsoulin Bryan L.
Thompson Larry W.
Wisler Macmillan M.
Baker Hughes Incorporated
Fulton Christopher W.
Madan Mossman & Sriram P.C.
Vargas Dixomara
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