Electricity: measuring and testing – Particle precession resonance – Using well logging device
Reexamination Certificate
1999-09-16
2003-05-06
Lefkowitz, Edward (Department: 2862)
Electricity: measuring and testing
Particle precession resonance
Using well logging device
Reexamination Certificate
active
06559639
ABSTRACT:
BACKGROUND
This invention relates to estimating permeability.
Nuclear magnetic resonance (NMR) measurements typically are performed to investigate properties of a sample. For example, an NMR wireline or logging while drilling (LWD) downhole tool may be used to measure properties of subterranean formations. In this manner, the typical downhole NMR tool may, for example, provide a lithology-independent measurement of the porosity of a particular formation by determining the total amount of hydrogen present in fluids of the formation. Equally important, the NMR tool may also provide measurements that indicate the dynamic properties and environment of the fluids, as these factors may be related to petrophysically important parameters. For example, the NMR measurements may provide information that may be used to derive the permeability of the formation and viscosity of fluids contained within the pore space of the formation. It may be difficult or impossible to derive this information from other conventional logging arrangements. Thus, it is the capacity of the NMR tool to perform these measurements that makes it particularly attractive versus other types of downhole tools.
Typical NMR logging tools include a magnet that is used to polarize hydrogen nuclei (protons) in the formation and a transmitter coil, or antenna, that emits radio frequency (RF) pulses. A receiver antenna may measure the response (indicated by a received RF signal) of the polarized hydrogen to the transmitted pulses. Quite often, the transmitter and receiver antennae are combined into a single transmitter/receiver antenna.
The NMR techniques employed in current NMR tools typically involve some variant of a basic two step sequence that includes a polarization time and thereafter using an acquisition sequence. During the polarization time (often referred to as a “wait time”), the protons in the formation polarize in the direction of a static magnetic field (called B
0
) that is established by a permanent magnet (of the NMR tool). The growth of nuclear magnetization M(t) (i.e., the growth of the polarization) is characterized by the “longitudinal relaxation time” (called T
1
) of the fluid and its equilibrium value (called M
0
). When the specimen is subject to a constant field for a duration t
p
, the longitudinal magnetization is described by the following equation:
M
(
t
p
)
=
M
0
(
1
-
ⅇ
-
tp
T
1
)
(
Eq
.
1
)
The duration of the polarization time may be specified by the operator (conducting the measurement) and includes the time between the end of one acquisition sequence and the beginning of the next. For a moving tool, the effective polarization time also depends on tool dimensions and logging speed.
Referring to
FIG. 1
, as an example, a sample (in the formation under investigation) may initially have a longitudinal magnetization
10
(called M
Z
) of approximately zero. The zero magnetization may be attributable to a preceding acquisition sequence, for example. However, in accordance with Equation (Eq.) 1, the M
Z
magnetization
10
(under the influence of the B
0
field) increases to a magnetization level (called M(tp(
1
))) after a polarization time tp(
1
) after zero magnetization. As shown, after a longer polarization time tp(
2
) from zero magnetization, the M
Z
magnetization
10
increases to a higher M(tp(
2
)) magnetization level.
An acquisition sequence (the next step in the NMR measurement) typically begins after the polarization time. For example, an acquisition sequence may begin at time tp(
1
), a time at which the M
Z
magnetization
10
is at the M(tp(
1
)) level. At this time, RF pulses are transmitted from a transmitter antenna of the NMR tool. The pulses, in turn, produce spin echo signals
16
that appear as a RF signal to the NMR tool. A receiver antenna (that may be formed from the same coil as the transmitter antenna) receives the spin echo signals
16
and stores digital signals that indicate the spin echo signals
16
. The initial amplitudes of the spin echo signals
16
indicate a point on the M
Z
magnetization
10
curve, such as the M(tp(
1
)) level, for example. Therefore, by conducting several measurements that have different polarization times, points on the M
Z
magnetization
10
curve may be derived, and thus, the T
1
time for the particular formation may be determined.
As a more specific example, for the acquisition sequence, a typical logging tool may emit a pulse sequence based on the CPMG (Carr-Purcell-Meiboom-Gill) pulse train. The application of the CPMG pulse train includes first emitting a pulse that rotates the magnetization, initially polarized along the B
0
field, by 90° into a plane perpendicular to the B
0
field. A train of equally spaced pulses, whose function is to maintain the magnetization polarized in the transverse plane, follows. In between the pulses, magnetization refocuses to form the spin echo signals
16
that may be measured using the same antenna. Because of thermal motion, individual hydrogen nuclei experience slightly different magnetic environments during the pulse sequence, a condition that results in an irreversible loss of magnetization and consequent decrease in successive echo amplitudes. This rate of loss of magnetization is characterized by a “transverse relaxation time” (called T
2
) and is depicted by the decaying envelope 12 of FIG.
1
. This may be referred to as a T
2
-based experiment.
The relaxation times may be used to estimate the permeability of a downhole formation. In this manner, the magnetic resonance relaxation-time of a water filled pore (of the formation) is proportional to a volume-to-surface ratio of the pore. A high surface-to-volume ratio indicates either the presence of clay minerals in the pore space or microporosity, both of which impede fluid flow. Therefore, there is a correlation between the magnetic resonance relaxation times and permeability.
Obtaining T
2
times from magnetic resonance logs is an ill-posed problem. Either the precision or the resolution of the decay-time spectrum is severely limited by the signal to-noise ratio of the measurements. Quite often, magnetic resonance logs are depth-stacked before signal processing to improve the signal-to-noise ratio of the data. Depth stacking increases the signal-to-noise ratio (SNR) by adding, or stacking, the amplitudes of corresponding spin echo signals that are obtained from different NMR measurements. For example, the amplitude of the tenth spin echo signal from a first CPMG measurement may be combined with the amplitude of the tenth spin echo signal from a second CPMG measurement. Because the tool may be moving, the CPMG measurements are performed at different depths.
The above-described depth stacking increases the signal-to-noise ratio by a factor of {square root over (N)}, where “N” represents the number of measurements that are combined in the depth stacking.
A problem with depth stacking is that the stacking reduces the vertical resolution of the NMR measurements. Furthermore, the NMR tool that is used to obtain the measurements for the depth stacking may move between measurements. Thus, in thinly laminated sand-shale sequences, the measurements for sand and shale layers may be stacked together, thereby making it difficult to distinguish a shaley sand from a sequence of shales and highly producible sands. There are several techniques that may used to estimate the permeability of a formation, and these techniques may include fitting the NMR signal to a model function, a technique that may increase the statistical error in the derived permeability estimator. For example, one technique to derive a permeability estimator includes representing the amplitude of each spin echo signal by a summation, as described below:
echo
(
n
)
≈
∑
j
A
j
ⅇ
-
n
TE
T
2
,
j
,
(
Eq
.
2
)
where “TE” represents the echo spacing, and “A
j
” represents the amplitude of components having a relaxation time T
2,j
. A histogram
17
of the A
j
coefficients defines a T
2
distribution, as depicted i
Cao Minh Chanh
Heaton Nicholas J.
Sezginer Abdurrahman
Fetzner Tiffany A.
Jeffery Brigitte L.
Lefkowitz Edward
McEnaney Kevin P.
Ryberg John J.
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