U.S. patent application number 12/270168 was filed with the patent office on 2009-03-12 for method and computer program product for estimating true intrinsic relaxation time and internal gradient from multigradient nmr logging.
This patent application is currently assigned to BAKER HUGHES INCORPORATED. Invention is credited to Songhua Chen.
Application Number | 20090066327 12/270168 |
Document ID | / |
Family ID | 46326765 |
Filed Date | 2009-03-12 |
United States Patent
Application |
20090066327 |
Kind Code |
A1 |
Chen; Songhua |
March 12, 2009 |
METHOD AND COMPUTER PROGRAM PRODUCT FOR ESTIMATING TRUE INTRINSIC
RELAXATION TIME AND INTERNAL GRADIENT FROM MULTIGRADIENT NMR
LOGGING
Abstract
A method and a computer program product for estimating the true
intrinsic relaxation time T.sub.2 and the internal gradient
G.sub.int for a multi-frequency nuclear magnetic resonance imaging
tool for well logging includes providing at least two frequencies
in a plurality of echo trains, evaluating the signal decay in each
echo train, quantifying the signal decay and correlating the signal
decay to the internal gradient.
Inventors: |
Chen; Songhua; (Katy,
TX) |
Correspondence
Address: |
CANTOR COLBURN LLP- BAKER ATLAS
20 Church Street, 22nd Floor
Hartford
CT
06103
US
|
Assignee: |
BAKER HUGHES INCORPORATED
Houston
TX
|
Family ID: |
46326765 |
Appl. No.: |
12/270168 |
Filed: |
November 13, 2008 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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11567828 |
Dec 7, 2006 |
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12270168 |
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11403255 |
Apr 13, 2006 |
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11567828 |
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Current U.S.
Class: |
324/303 ;
702/7 |
Current CPC
Class: |
G01R 33/3808 20130101;
G01R 33/5615 20130101; G01R 33/448 20130101; G01V 3/32 20130101;
G01N 24/081 20130101 |
Class at
Publication: |
324/303 ;
702/7 |
International
Class: |
G01V 3/32 20060101
G01V003/32; G01V 3/38 20060101 G01V003/38 |
Claims
1. A method for estimating an internal gradient of an earth
formation in response to a magnetic field, the method comprising:
applying the magnetic field to the earth formation; directing
pulsed RF energy for a first frequency to the earth formation and
acquiring a first signal and directing pulsed RF energy to the
earth formation for a second frequency and acquiring a second
signal; determining a first signal decay corresponding to the first
signal and a second signal decay corresponding to the second
signal; and using the first signal decay and the second signal
decay to estimate the internal gradient by solving a relationship
relating the internal gradient to the first signal decay and the
second signal decay.
2. The method as in claim 1, wherein at least one of the first
signal and the second signal comprise one of an echo-train and a
portion of an echo-train.
3. The method as in claim 1, wherein directing pulsed RF energy for
the second frequency comprises directing pulsed RF energy
comprising signal times that are proportionally related to signal
times of the pulsed RF energy for the first frequency.
4. The method as in claim 3, wherein each of the signal times
comprises inter-echo times.
5. (canceled)
6. (canceled)
7. (canceled)
8. The method as in claim 1, wherein a sensitive volume for the
estimating comprises at least one of water, salt water, drilling
fluid, minerals, clay, mud, oil and formation fluids.
9. A computer program product stored on machine readable media, the
product comprising instructions for estimating an internal gradient
of an earth formation in response to a magnetic field, the
instructions comprising instructions for: applying the magnetic
field to the earth formation; directing pulsed RF energy for a
first frequency to the earth formation and acquiring a first signal
and directing pulsed RF energy to the earth formation for a second
frequency and acquiring a second signal; determining a first signal
decay corresponding to the first signal and a second signal decay
corresponding to the second signal; using the first signal decay
and the second signal decay to estimate the internal gradient by
solving a relationship relating the internal gradient to the first
signal decay and the second signal decay; and providing the
estimation as an output.
10. The computer program product of claim 9, wherein at least one
of the first signal and the second signal comprise one of an
echo-train and a portion of an echo-train.
11. The computer program product of claim 9, wherein directing
pulsed RF energy for the second frequency comprises directing
pulsed RF energy comprising signal times that are proportionally
related to signal times of the pulsed RF energy for the first
frequency.
12. The computer program product of claim 11, wherein each of the
signal times comprises inter-echo times.
13. (canceled)
14. (canceled)
15. (canceled)
16. The computer program product as in claim 9, wherein a sensitive
volume for the estimating comprises at least one of water, salt
water, drilling fluid, minerals, clay, mud, oil and formation
fluids.
17. The computer program product as in claim 9, wherein providing
the output comprises providing output to at least one of a screen,
a printer, a memory, a network, a storage, a wireless link and a
direct link.
18. A method for typing a material using diffusion based nuclear
magnetic resonance (NMR) techniques, the method comprising:
applying a magnetic field to the material; directing pulsed RF
energy for a first frequency to the earth formation and acquiring a
first signal and directing pulsed RF energy to the earth formation
for a second frequency and acquiring a second signal; determining a
first signal decay corresponding to the first signal and a second
signal decay corresponding to the second signal; using the first
signal decay and the second signal decay to estimate an internal
gradient by solving a relationship relating the internal gradient
to the first signal decay and the second signal decay; and
estimating a material type for the material based on the internal
gradient.
19. The method as in claim 18, wherein the material comprises at
least one of fresh water, salt water, drilling fluid, minerals,
clay, mud, oil and a formation fluid.
20. The method as in claim 19, wherein the minerals comprise at
least one of detrital minerals comprising SiO.sub.2,
Ca.sub.2CO.sub.3, Mn.sub.2O.sub.3 and secondary minerals comprising
at least one of a type of clay mineral and a type of evaporate
mineral.
21. The method as in claim 18, wherein the material comprises: an
earth formation.
22. The method as in claim 21, wherein at least one of the first
signal and the second signal comprise one of an echo-train and a
portion of an echo-train.
23. The method as in claim 21, wherein directing pulsed RF energy
for the second frequency comprises directing pulsed RF energy
comprising signal times that are proportionally related to signal
times of the pulsed RF energy for the first frequency.
24. The method as in claim 21, wherein each of the signal times
comprises inter-echo times.
25. (canceled)
26. (canceled)
27. (canceled)
Description
CROSS REFERENCE TO RELATED APPLICATION
[0001] This application is filed under 35 U.S.C. 120 and 37 CFR
.sctn.1.53(b) as a Continuation-In-Part of copending U.S. patent
application Ser. No. 11/403,255, filed Apr. 13, 2006 and claims
priority thereto. The disclosure of U.S. patent application Ser.
No. 11/403,255 is incorporated by reference herein in its
entirety.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] The invention relates to geological exploration techniques
and more specifically to estimation of geologic properties from
well logging data.
[0004] 2. Description of the Related Art
[0005] Various instruments applying Nuclear Magnetic Resonance
(NMR) imaging technology are useful for measuring certain
petrophysical properties of earth formations. NMR well logging
instruments typically include a magnet for polarizing nuclei in the
earth formations surrounding a wellbore. The polarizing typically
occurs along a static magnetic field through use of at least one
antenna for transmitting radio frequency ("RF") energy pulses into
the formations. The RF pulses reorient the spin axes of certain
nuclei in the earth formations in a predetermined direction. As the
spin axes precess and reorient themselves into alignment with the
static magnetic field, RF energy is emitted and can be detected by
the antenna. The magnitude of the RF energy emitted by the
precessing nuclei and the rate at which the magnitude changes are
related to certain petrophysical properties of interest in the
earth formations.
[0006] A typical embodiment of an NMR logging tool for
characterization of geologic deposits includes a side-looking or
centralized NMR logging tool. Typically, the tool operates using a
gradient magnetic field and multiple frequencies. One example of
such a tool is the MX Explorer.sup.SM provided by Baker Hughes,
Inc. of Houston Tex. (referred to as the "MREX tool," the "logging
tool" or simply as the "tool" herein).
[0007] There are several principal operating parameters in NMR well
logging which should be optimized for efficient operation of an NMR
well logging instrument. These parameters include the logging speed
(speed of motion of the instrument along the wellbore), the average
and the peak power supplied to the instrument and transmitted as RF
pulses, and the signal-to-noise ratio ("SNR"). Other parameters of
interest include the vertical resolution of the instrument and the
radial depth of investigation of the measurements made by the
instrument within the formations surrounding the wellbore.
[0008] Physical parameters of particular interest to wellbore
operators are the fractional volume of pore spaces in the earth
formations ("porosity"), the texture of the rock and connectivity
of the pore spaces, and the nature of the fluids contained in the
pore spaces. In petroleum bearing earth formations, the pore spaces
will typically contain some fractional volume of water and some
fractional volume of hydrocarbons. Since hydrocarbons generally
have different NMR relaxation properties than water, various NMR
relaxometry techniques have been developed to qualitatively
determine the nature of the fluids present in certain earth
formations.
[0009] One method, for example, enables discriminating between gas
and oil, and light oil and water. This method includes performing
NMR spin-echo experiments using two different "wait times",
T.sub.w. The wait time T.sub.w is the delay between individual
Carr-Purcell-Meiboom-Gill ("CPMG") spin echo measurement sequences.
See S. Meiboom et al, Rev. of Sci. Instr. v. 29, p. 6881 (1958).
Another technique, described in U.S. Pat. No. 5,498,960 issued to
Vinegar et al, uses two different inter-echo spacing times, TE, for
CPMG sequences measured in a gradient magnetic field. Typically,
the inter-echo spacing is the time between rephasing radio
frequency (RF) energy pulses applied to the logging instrument's
antenna to "rephase" precessing nuclei which are influenced by the
NMR survey. The rephasing RF pulses result in the "spin echoes"
whose amplitude is measured. Gas, oil and water generally have
different self-diffusivities, and these differences will be
reflected in differences in the apparent transverse relaxation time
T.sub.2 calculated for an earth formation between CPMG sequences
measured using different values of TE. The technique described in
the Vinegar et al '960 patent for discriminating types of fluids in
pore spaces of earth formations typically uses two values of
TE.
[0010] Another physical property of particular interest is the
viscosity of any oil which may be present in the pore spaces of the
earth formation. A relationship between an intrinsic transverse
relaxation time, T.sub.2int, for oil with respect to its viscosity,
.eta. is provided:
T 2 int = 1.2 T K 298 .eta. x ; ( 1 ) ##EQU00001##
where T.sub.K represents the absolute temperature (in .degree. K)
of the oil and x represents an empirical fit factor, typically
about equal to unity. A difficulty in determining oil viscosity
.eta. using this relationship is that it requires determining the
intrinsic transverse relaxation time T.sub.2int. For NMR logging
instruments that use a gradient static magnetic field, the
transverse relaxation time T.sub.2 calculated from spin-echo
amplitude measurements is affected by a self-diffusion effect
T.sub.2D. An apparent transverse relaxation time T.sub.2 calculated
from the spin echo amplitudes is related to the intrinsic
transverse relaxation time T.sub.2int in the following manner:
1 T 2 = 1 T 2 int + 1 T 2 D ; ( 2 ) ##EQU00002##
where the self-diffusion effect T.sub.2D can be determined by the
expression:
1 T 2 D = D ( .gamma. * TE * G 7 ) 2 12 ; ( 3 ) ##EQU00003##
where an inter-echo time TE is generally selected by the system
operator and has a known value; D represents a diffusivity of the
media; the gyromagnetic ratio .gamma. is unique for each nuclear
isotope; and the magnetic field gradient G.sub.z, is dependent upon
a frequency (f) and includes an internal gradient component
G.sub.int and an external gradient component G.sub.MREX. The
magnitude of the static magnetic field, B.sub.0, in which the CPMG
sequences are actually measured, is therefore controlled by
selection of a frequency for the RF pulses. Since the spatial
distribution of the static magnetic field amplitude and gradient
magnitude are known, the gradient of the static magnetic field in
the NMR excitation volume will also be known for any selected RF
excitation frequency. The actual magnetic field gradient within the
pore spaces of the earth formation may not be known, however, since
the field gradients internal to the pore spaces depend on
differences in magnetic susceptibility between the formation solids
("matrix") and the fluid in the pore spaces, as well as the
amplitude of the static magnetic field. See for example, U.S. Pat.
No. 5,698,979 issued to Taicher et al.
[0011] Determination of the internal gradient G.sub.int(f) of the
static magnetic field B.sub.0 is essential for accurate material
typing using diffusion-based NMR techniques. Since the internal
gradient G.sub.int(f) is related to the pore mineralogy and pore
geometry, the internal gradient G.sub.int(f) may also be used to
obtain additional information about properties of the porous
rock.
[0012] The internal gradient G.sub.int(f) in porous media arises
from differences in the magnetic properties between minerals in the
formation matrix and material (e.g., fluid) in pore spaces of the
formation. Mathematically, the internal gradient G.sub.int(f) is
described as:
G int .varies. .DELTA. .chi. B 0 r ; ( 4 ) ##EQU00004##
where 1/r represents the curvature of a pore within the formation,
where .DELTA..chi. represents magnetic properties in the formation
(also referred to as a "susceptibility difference" between the
matrix and the fluid) and B.sub.0 represents an applied static
magnetic field. Although .DELTA..chi. is theoretically a dispersive
quantity, for the low-frequency range of NMR logging interest, it
can be regarded as typically being frequency independent. The
internal gradient G.sub.int is therefore dependent upon the
static-field B.sub.0. Consequently, for a logging tool that makes
use of multiple frequencies to generate a gradient magnetic field,
the internal gradient G.sub.int is also frequency dependent.
[0013] The effective gradient along the field direction
G.sub.int(f) may therefore be described as:
G ( f ) = G z , int ( f ) + G MREX ( f ) = a 2 .pi. f .DELTA..chi.
.gamma. r + b f c ; ( 5 ) ##EQU00005##
Where G represents a radiofrequency (RF) field gradient strength; a
is substantially equal to unity, while b and c are two coefficients
dependent on aspects of the NMR logging instrument. For an MREX
logging tool, b is approximately 40 and c is approximately 1.5.
This function includes two operands, where the first operand
G.sub.z,int(f) represents the internal magnetic field gradient and
G.sub.MREX(f) represents the logging tool magnetic field gradient
(also referred to as an "external magnetic field gradient").
[0014] Eq. (5) shows that both the internal gradient G.sub.int(f)
and the tool gradient G.sub.MREX(f) are frequency dependent.
However, these dependencies are different. The internal gradient
G.sub.z,int(f) is linearly proportional to f, but the tool gradient
G.sub.MREX(f) generally depends upon frequency more than linearity.
In the prior art, typical diffusion based NMR fluid typing
techniques acquire multiple G(f)*TE echo trains for hydrocarbon
typing where G(f) has always been simplified to the tool gradient
G.sub.MREX(f) and a contribution by the internal gradient
G.sub.int(f) has been discounted. Inherently, this assumption
causes inaccuracies in results.
[0015] What is needed is a technique for accurately determining the
internal magnetic field gradient G.sub.z,int(f) of the earth
formation for a given NMR well logging tool and operating
frequency, which will in turn provide for accurate typing of
materials (fluids as well as minerals) of formations using
diffusion based NMR techniques.
BRIEF SUMMARY OF THE INVENTION
[0016] Disclosed is a method for estimating an internal gradient of
an earth formation in response to a magnetic field, that includes:
applying the magnetic field to the earth formation; directing
pulsed RF energy for a first frequency to the earth formation and
acquiring a first signal and directing pulsed RF energy to the
earth formation for a second frequency and acquiring a second
signal; determining a first signal decay corresponding to the first
signal and a second signal decay corresponding to the second
signal; and using the first signal decay and the second signal
decay to estimate the internal gradient.
[0017] Also disclosed is a computer program product for estimating
an internal gradient of an earth formation in response to a
magnetic field, that includes instructions for: applying the
magnetic field to the earth formation; directing pulsed RF energy
for a first frequency to the earth formation and acquiring a first
signal and directing pulsed RF energy to the earth formation for a
second frequency and acquiring a second signal; determining a first
signal decay corresponding to the first signal and a second signal
decay corresponding to the second signal; using the first signal
decay and the second signal decay to estimate the internal
gradient; and providing the estimation as an output.
[0018] In addition, a method for typing a material using diffusion
based nuclear magnetic resonance (NMR) techniques, is disclosed and
includes: determining an internal gradient of a magnetic field; and
estimating a material type for the material based on the internal
gradient.
[0019] Other systems, methods, and/or computer program products
according to embodiments will be or become apparent to one with
skill in the art upon review of the following drawings and detailed
description. It is intended that all such additional systems,
methods, and/or computer program products be included within this
description, be within the scope of the present invention, and be
protected by the accompanying claims.
BRIEF DESCRIPTION OF THE DRAWINGS
[0020] For detailed understanding of the present invention,
references should be made to the following Detailed Description of
the Invention, taken in conjunction with the accompanying drawings,
in which like elements have been given like numerals, wherein:
[0021] FIG. 1 depicts aspects of an NMR logging tool in a wellbore;
and
[0022] FIG. 2 depicts aspects of a method for estimating the
internal gradient G.sub.z,int of a magnetic field B.sub.0.
[0023] The detailed description explains the preferred embodiments
of the invention, together with advantages and features, by way of
example with reference to the drawings.
DETAILED DESCRIPTION OF THE INVENTION
[0024] FIG. 1 shows a well logging apparatus disposed in a wellbore
22 penetrating earth formations 23, 24, 26, 28 for making
measurements of properties of the earth formations 23, 24, 26, 28.
The wellbore 22 in FIG. 1 is typically filled with a fluid 34 known
in the art as "drilling mud." A "sensitive volume," shown generally
at 58 and having a generally cylindrical shape, is disposed in one
of the earth formations, shown at 26. The sensitive volume 58 is a
predetermined portion of the earth formations 26 in which nuclear
magnetic resonance (NMR) measurements are made, as will be further
explained.
[0025] In typical embodiments, the sensitive volume 58 includes
materials such as would be found within a wellbore 22 including a
mixture of liquids including water, (including fresh water and salt
water), drilling fluid, minerals, clay, mud, oil and formation
fluids that are indigenous to the formations 23, 24, 26, 28, or
introduced therein. NMR measurements may be used to determine a
variety of formation properties and other aspects of interest. For
example, aspects of mineralogy may be determined or surmised.
Consider the following.
[0026] An internal magnetic field gradient in a rock formation
arises from differing properties of the minerals that form the rock
matrix and the fluids that fill pore spaces. The magnetic
susceptibility X of water (H.sub.2O) is very small, and has been
reported to be about -12.97E-06 cgs at room temperature. The basic
minerals forming sandstones and carbonate rocks also have small
magnetic susceptibilities. For example, silicon dioxide (SiO.sub.2)
has a magnetic susceptibility .chi. value of about -19.6E-06 cgs
and calcium carbonate (CaCO.sub.3) has a magnetic susceptibility
.chi. value of about -38.2E-06 cgs. Both minerals have magnetic
susceptibility .chi. close to that of water. On the other hand,
manganese compounds, such as Mn.sub.2O.sub.3, have a magnetic
susceptibility .chi. value of thousand times higher than that of
water or quartz. Thus, the presence of manganese compounds can
strongly affect internal gradients measured in the rock formation.
Further, a spike in internal gradient values for a zone in the
formation may indicate some mineralogy variation within the
formation zone. Note that the magnetic susceptibility X values were
cited from the "CRC Handbook of Chemistry and Physics," 63.sup.rd
edition, CRC Press, 1982.
[0027] Exemplary minerals for typing include at least one of
detrital minerals comprising SiO.sub.2, Ca.sub.2CO.sub.3,
Mn.sub.2O.sub.3 and secondary minerals comprising at least one of a
type of clay mineral and a type of evaporate mineral.
[0028] The magnitude of the measured internal gradient is dependent
on other factors as well. For example, the internal gradient is
effected by the curvature of the interface between pore fluid and
the rock matrix surface. Thus, the internal gradient is also
related to pore geometry. More specifically, for identical
minerals, the smaller the pores, the larger the internal gradient.
This may provide for certain determinations. For example, for
carbonate rocks, the internal gradient may only be significant in
the intragranualar pores, and thus may be helpful for surveys of
the intragraualar pores.
[0029] Many sandstone formation rocks contain certain amount of
clay minerals. The distribution of clay minerals may affect the
pore geometry significantly. Therefore, the internal gradient is
significantly larger for dispersed clay minerals than for
structural clay distributions. This is because the former
introduces a great amount of surface area interfacing with pore
fluid and increases curvature on the interfaces. Thus, if the
amount of clay is determined by NMR clay-volumetric measurements or
other mineral-sensitive measurements, one will be able to use the
internal gradient estimates to predict the clay distributions.
[0030] NMR relaxation time distribution is often known to be
associated with the pore size distribution in rocks. This
association is valid if the surface relaxivity is relatively
uniform over different pore sizes. If different sized-pores are
confined by different minerals that have a different magnetic
susceptibility .chi., one needs first to correct the internal
gradient effect before the pore size distribution can be derived
from NMR relaxation time. Therefore, determination of the internal
gradient is essential for accurate determination of pore size
distributions.
[0031] Turning again to FIG. 1, a string of logging tools 32, which
can include an NMR apparatus according to the present invention, is
typically lowered into the wellbore 22 by a means of an armored
electrical cable 30. The cable 30 can be spooled and unspooled from
a winch or drum 48. The tool string 32 can be electrically
connected to surface equipment 54 by an insulated electrical
conductor (not shown separately in FIG. 1) forming part of the
cable 30. The surface equipment 54 can include one part of a
telemetry system 38 for communicating control signals and data to
the tool string 32 and computer 40. The computer may also include a
data recorder 52 for recording measurements made by the apparatus
and transmitted to the surface equipment 54. Typically, the
computer includes a variety of input/output devices and other
supporting devices to enhance the operation of the apparatus and
estimations performed by use thereof.
[0032] An NMR probe 42 can be included in the tool string 32. The
tool string 32 is typically centered within the wellbore 22 by
means of a top centralizer 56 and a bottom centralizer 57 attached
to the tool string 32 at axially spaced apart locations. The
centralizers 56, 57 can be of types known in the art such as
bowsprings.
[0033] Circuitry for operating the NMR probe 42 can be located
within an NMR electronics cartridge 44. The circuitry can be
connected to the NMR probe 42 through a connector 50. The NMR probe
42 is typically located within a protective housing 43 which is
designed to exclude the drilling mud 34 from the interior of the
probe 42. The function of the probe 42 will be further
explained.
[0034] Other well logging sensors (not shown separately for clarity
of the illustration in FIG. 1) may form part of the tool string 32.
As shown in FIG. 1, one additional logging sensor 47 may be located
above the NMR electronics cartridge 44. Other logging sensors, such
as shown at 41 and 46 may be located within or below the bottom
centralizer 57. The other sensors 41, 46, 47 can be of types
familiar to those skilled in the art and can include, but are not
limited to, gamma ray detectors, formation bulk density sensors or
neutron porosity detectors. Alternatively, parts of the NMR
electronics may be located within electronic cartridges which form
part of other logging sensors. The locations of the other sensors
41, 46, 47 shown in FIG. 1 are a matter of convenience for the
system designer and are merely exemplary.
[0035] Other aspects of the exemplary embodiment of the NMR probe
42 are provided in U.S. Pat. No. 5,712,566, entitled "Nuclear
Magnetic Resonance Apparatus and Method," issued Jan. 27, 1998 to
Taicher et al., and incorporated herein by reference in it's
entirety. Another non-limiting example is disclosed in U.S. Pat.
No. 4,710,713, also issued to Taicher et al, and incorporated by
reference herein in it's entirety. It should be recognized that
these embodiments of NMR tools are exemplary only, and not limiting
of the teachings herein.
[0036] The techniques disclosed herein provide for improved
estimations where the formations 23, 24, 26, 28 are macroscopically
uniform within a depth of interest within sensitive volume 58 the
NMR logging tool. That is, pore geometry and mineralogy may vary
microscopically, but on average, each depth of interest within the
sensitive volume 58 has considerably similar mineralogy and pore
geometry effect, or can be represented with an effective pore
geometry and mineralogy for a given depth in the wellbore 22.
[0037] FIG. 2 provides a summary of aspects of an exemplary
embodiment of a method for determining the internal gradient
G.sub.int. Internal gradient G.sub.int estimation 60 first calls
for selecting frequencies 61. Using the selected frequencies
(f.sub.1, f.sub.2, . . . ), directing RF energy and acquiring echo
trains 62 is performed. Directing RF energy and acquiring echo
trains 62 involves, among other things, generating and directing
pulses of radiofrequency (RF) energy into the earth formations 23,
24, 26, 28 and then acquiring and resolving the pulsed RF energy as
the echo trains.
[0038] It should be recognized that use of an "echo train" is
merely illustrative. That is, it should be recognized that a
portion of an echo train may be used in support of the teachings
herein. Accordingly, while use of the first echo train and the
second echo train may be typically called for, in some embodiments,
only the portion is used. Therefore, acquiring an echo train 62
should be construed to mean acquiring any signal or portion of a
signal (corresponding to the directing of the RF energy) that
provides for determining decay 63.
[0039] When the signals from the echo trains are detected, the
signals are evaluated and determining decay 63 for the signals is
completed. By using the determination information, estimating
internal gradient 64 is completed. As selecting frequencies 61 as
well as directing RF energy and acquiring an echo train 62 are
generally understood by users of multi-frequency NMR probes 42,
further discussion is not warranted. However, steps to determining
decay 63 and estimating internal gradient 64 are described in
greater detail below.
[0040] As a matter of convention, one should note that the
variables used herein are not redefined, and appear throughout the
disclosure. Accordingly, previously defined variables are generally
not reintroduced. For convenience of referencing, the following
representations are some of the definitions applied herein: B.sub.0
represents static field strength; B.sub.1 represents RF field
strength; D represents diffusivity; e,E represents echo amplitude
with and without noise included; f represents frequency; G
represents RF field gradient strength; L represents echo length
(N.sub.ET.sub.E); M represents echo magnetization amplitude;
N.sub.E represents a number of echoes in an echo train; S.sub.E
represents a sum of echoes; T.sub.1 represents a longitudinal
relaxation time; T.sub.2 represents a transverse relaxation time;
T.sub.2B represents a bulk fluid transverse relaxation time;
T.sub.2cutoff represents a dividing time; T.sub.2diff represents an
extra decay time factor due to diffusion; T.sub.2int represents an
intrinsic relaxation time; T.sub.2surf represents a surface
relaxation time; T.sub.E represents an interecho time; T.sub.W
represents a wait time; and t.sub.k represents the time at the
formation of the k.sup.th echo.
[0041] First, a derivation of the internal field gradient
G.sub.z,int(f) is provided. Using the above relationship of Eq.
(5), the internal gradient G.sub.z,int(f) and the tool gradient
G.sub.MREX(f) are squared to obtain:
G.sup.2(f)=(G.sub.int+G.sub.MREX).sup.2=G.sub.int.sup.2+G.sub.MREX.sup.2-
+2{right arrow over (G)}.sub.int{right arrow over (G)}.sub.MREX
(6);
and, on the average, the cross term (2G.sub.intG.sub.MREX) cancels
out to account for random orientation. Thus:
G.sup.2(f).apprxeq.G.sub.int.sup.2+G.sub.MREX.sup.2 (7).
[0042] Plugging Eq. (7) into Eq. (3), one obtains:
1 T 2 D = D ( .gamma. G int TE ) 2 12 + D ( .gamma. G MREX TE ) 2
12 . ( 8 ) ##EQU00006##
[0043] One skilled in the art will recognize that multiple
measurements of inter-echo times TE do not provide for
determination of the internal gradient G.sub.z,int(f) and the tool
gradient G.sub.MREX(f) directly. Accordingly, Eq. (2) is rewritten
using Eq. (8) as:
T 2 - 1 = T 2 , int - 1 + D ( .gamma. G int TE ) 2 12 + D ( .gamma.
G MREX TE ) 2 12 = [ T 2 , int - 1 + D ( .gamma. G MREX TE ) 2 12 ]
+ D ( .gamma. G int TE ) 2 12 . ( 9 ) ##EQU00007##
[0044] The method as disclosed herein includes at least two
measurements completed by selecting at least two frequencies f and
two different inter-echo times TE. In these measurements, the
product of tool gradient G.sub.MREX and the inter-echo time TE is
held constant. This relationship is expressed as:
G.sub.MREX(f)*TE.sub.1=G.sub.MREX(f.sub.2)*TE.sub.2 (10).
[0045] If it is assumed that:
G.sub.MREX(f.sub.1)=2G.sub.MREX(f.sub.2) (11); and
TE.sub.1=0.5TE.sub.2 (12),
then, according to Eq. (5),
f 1 f 2 = 2 1 / c ; ( 13 ) ##EQU00008##
where, for the MREX tool having a value for c that is approximately
1.5, the frequency ratio (f.sub.1/f.sub.2) is approximately 1.59. A
corresponding change in the internal gradient G.sub.int (for the
two frequencies) may be described as:
G.sub.int,1=(f.sub.1/f.sub.2)G.sub.int,2=1.59G.sub.int,2 (14);
and,
(G.sub.int,1TE).sub.1/(G.sub.int,2TE.sub.2).apprxeq.0.795 (15).
[0046] If the internal gradient G.sub.int effect is much smaller
than the external (tool) gradient G.sub.MREX, then both echo trains
(one for each of the selected frequencies f.sub.1, f.sub.2) should
produce nearly identical results. On the other hand, if the
internal gradient G.sub.int dominates, the echo train with
G.sub.int,2TE.sub.2 decays faster than the echo train with
G.sub.int,2TE.sub.2. For each echo train, echo decay E.sub.k may be
described as:
E k = M 0 exp ( - t k T 2 ) = M 0 exp ( - ( 1 T 2 int + D ( .gamma.
G MREX TE ) 2 12 ) t k ) exp ( - D ( .gamma. G int TE ) 2 t k 12 )
; ( 16 ) ##EQU00009##
and can be quantified and related to the value for the internal
gradient G.sub.int. That is, in Eq. (16), only the exponential
factor
( - D ( .gamma. G int TE ) 2 t k 12 ) ##EQU00010##
is different for the measurements taken at f.sub.1, f.sub.2. Note
that in Eq. (16) M.sub.0 represents an initial echo magnetization
amplitude and t.sub.k represents time at the formation of the
k.sup.th echo.
[0047] Consequently, the internal gradient G.sub.int is quantified
by a difference in the decay rate. For instance, a ratio of the
echo decay E.sub.k,1 and echo decay E.sub.k,2 measurements is
described as:
E k , 1 E k , 2 = exp ( - D ( .gamma. G int , 1 TE 1 ) 2 t k 12 ) /
exp ( - D ( .gamma. G int , 2 TE 2 ) 2 t k 12 ) = exp ( + .xi. D (
.gamma. G int , 2 TE 2 ) 2 t k 12 ) . ( 17 ) ##EQU00011##
where .xi. represents a configuration coefficient that is generally
dependent upon the selection of the tool gradient G.sub.MREX and
the inter-echo time TE. In embodiments where the parameters of Eq.
(11) and Eq. (12) are used, the configuration coefficient .xi. is
0.368. More specifically, the configuration coefficient .xi.=0.368
if G.sub.MREX(f.sub.1)=2G.sub.MREX(f.sub.2) and
TE.sub.1=0.5TE.sub.2.
[0048] Accordingly, Eq. (17) provides one exemplary and
non-limiting calculation for estimating internal gradient 64. That
is, after the computer 40 has completed signal processing and other
steps to complete determining decay 63, Eq. (17), as an example,
may be used to derive the internal gradient G.sub.int.
[0049] For a given fluid having a diffusion constant D, whose
properties are known, the only unknown in Eq. (17) is the internal
gradient G.sub.int. Those skilled in the art will recognize that
using a ratio to solve the Eq. (17) is not the only approach. In
another approach, Eq. (12) and Eq. (17) can be solved
simultaneously to obtain the internal gradient G.sub.int.
Furthermore, a similar approach can be extended to multiple
transverse relaxation time T.sub.2 components where an inversion
technique is applied to obtain the distribution of apparent
transverse relaxation time T.sub.2 (Eq. (2)) values for the two
measurements. As an example, two incremental transverse relaxation
time T.sub.2 distributions are defined as distribution
P.sub.1(T.sub.2int, T.sub.2D(G.sub.int,1)) and distribution
P.sub.2(T.sub.2int,T.sub.2D(G.sub.int,2)), respectively. Using
these distributions, one can compute the log-mean transverse
relaxation time T.sub.2LM from distribution P.sub.1 and
distribution P.sub.2, and consequently the overall internal
gradient G.sub.int can be computed from Eq. (2) as:
1 T 2 LM , 1 - 1 T 2 LM , 1 = .xi. D ( .gamma. TE 2 G int , 2 ) 2
12 . ( 18 ) ##EQU00012##
[0050] If different fluids can be separated from the incremental
transverse relaxation time T.sub.2 distributions, the log-mean
transverse relaxation time T.sub.2 can be computed for individual
fluids and materials. Consequently, values for the internal
gradient G.sub.int can then be obtained from Eq. (18).
[0051] As discussed herein, an "echo train" refers to the series of
echoes corresponding to a selected frequency f.sub.x. Manipulation
of the inter-echo times TE for each echo train (that is, between at
least two selected frequencies f.sub.1,f.sub.2), as discussed in
the foregoing example, provide for comparison of results and the
derivation of the internal field G.sub.int.
[0052] The above approach can be extended to include varying pairs
of echo trains having inter-echo times TE.sub.1 and TE.sub.2. In
one embodiment, both inter-echo times TE.sub.1 and TE.sub.2 are
increased proportionally. For example, consider inter-echo times
TE.sub.3=3TE.sub.1 and TE.sub.4=3TE.sub.2, such that Eq. (10) and
Eq. (12) remain valid. Because long inter-echo times TE effectively
excluded the shortest relaxation components, one will be able to
compute the internal gradient G.sub.int that corresponds to
non-clay bound water components (i.e., the effective internal
gradient G.sub.int for sands).
[0053] In another embodiment, it is assumed that the echo trains
from the above embodiments are related as follows:
TE.sub.2=2TE.sub.1, TE.sub.3=3TE.sub.1 and TE.sub.4=6TE.sub.1. Note
that in this example, the ratios of 1:2, 1:3, and 1:6 used here are
arbitrary and other numbers are possible, subject to the operating
frequencies for the logging tool.
[0054] In this example, the initial echoes from the inter-echo
times TE.sub.1, TE.sub.2, and TE.sub.3 are discarded so that all
first useful echoes in the data processing starts at inter-echo
time TE.sub.4. Thus, substantial sensitivity for the same range of
components in the transverse relaxation time T.sub.2 is realized.
Accordingly, this relationship may be expressed as:
G.sub.int,1TE.sub.1:G.sub.int,2TE.sub.2:G.sub.int,1TE.sub.3:G.sub.int,2T-
E.sub.4=0.796:1:2.38:3. (19).
[0055] Another embodiment calls for adjusting estimations of the
internal gradient G.sub.int without varying the inter-echo time TE.
In this embodiment, the only limitation is that the ratio of change
in the inter-echo time TE is limited by a useful range of the tool
and thus, the external gradient G.sub.MREX variation range.
[0056] Those familiar with the technology will recognize that
varying the combination of the inter-echo times TE and selected
frequencies (f) can provide for cross-checking of estimations,
improved results, and provide other such advantages.
[0057] Effects from the internal gradient G.sub.int are typically
important when the strength of internal gradient G.sub.int is
comparable to or larger than the tool gradient G.sub.MREX. Thus,
the technique described is useful for the range of internal
gradient G.sub.int as encountered in well logging.
[0058] The teachings herein provide for separating the internal
magnetic field gradient G.sub.z,int(f) effects from the external
magnetic field gradient G.sub.MREX effects using a method that
takes advantage of unique aspects of a multi-frequency NMR probe
42. By separately determining the internal gradient G.sub.z,int(f)
a true intrinsic relaxation time T.sub.2,int can be estimated.
[0059] The teachings herein provide for, among others, embodiments
in the form of computer-implemented processes and apparatuses for
practicing those processes. In exemplary embodiments, the invention
is embodied in computer program code executed by one or more
network elements. Embodiments include computer program code
containing instructions embodied in tangible media, such as floppy
diskettes, CD-ROMs, hard drives, or any other computer-readable
storage medium, wherein, when the computer program code is loaded
into and executed by a computer, the computer becomes an apparatus
for practicing the invention. Embodiments include computer program
code, for example, whether stored in a storage medium, loaded into
and/or executed by a computer, or transmitted over some
transmission medium, such as over electrical wiring or cabling,
through fiber optics, or via electromagnetic radiation, wherein,
when the computer program code is loaded into and executed by a
computer, the computer becomes an apparatus for practicing the
invention. When implemented on a general-purpose microprocessor,
the computer program code segments configure the microprocessor to
create specific logic circuits. Output may be directed to a variety
of devices as are known in the art, including, as non-limiting
examples, at least one of a screen, a printer, a memory, a network,
a storage, a wireless link and a direct link.
[0060] Further, while the invention has been described with
reference to exemplary embodiments, it will be understood by those
skilled in the art that various changes may be made and equivalents
may be substituted for elements thereof without departing from the
scope of the invention. In addition, many modifications may be made
to adapt a particular situation or material to the teachings of the
invention without departing from the essential scope thereof.
Therefore, it is intended that the invention not be limited to the
particular embodiment disclosed as the best mode contemplated for
carrying out this invention, but that the invention will include
all embodiments falling within the scope of the appended claims.
Moreover, the use of the terms first, second, etc. do not denote
any order or importance, but rather the terms first, second, etc.
are used to distinguish one element from another. Furthermore, the
use of the terms a, an, etc. do not denote a limitation of
quantity, but rather denote the presence of at least one of the
referenced item.
* * * * *