Note: Descriptions are shown in the official language in which they were submitted.
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METHOD AND APPARATUS FOR SUBTERRANEAN FORMATION FLOW
IMAGING
FIELD OF THE INVENTION
The present invention relates to an apparatus and
techniques for determining characteristics of Earth
formations surrounding a borehole and, more particularly,
to an apparatus and method for nuclear magnetic resonance
(NMR) borehole logging further being capable of magnetic
resonance imaging (MRI) the formations surrounding the
borehole and determine other formation characteristics
such as porosity and permeability, as well as the
characterization of fluids in the formation.
BACKGROUND OF THE INVENTION
A major goal in the evaluation of hydrocarbon bearing
Earth formations is the accurate determination of the
volumes of oil and water in the pore space of sedimentary
rocks. Measurements made with signals from logging
instruments have been used to obtain estimates of these
volumes. The most credible measurement of producibility
of the fluid volumes is to actually produce fluids from
the formation; such as by using a drill stem test or by
using a logging device that extracts fluids from the
formations.
However, it is desirable to determine the nature of
the earth formation and make estimates of the bulk volume
of the fluids present in the formation, as well as their
producibility, prior to undertaking the measures set
forth above. Petrophysical parameters of a geological
formation which are typically used to determine whether
the formation will produce viable amount of hydrocarbons
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include the formation porosity, fluid saturation, the
volume of the formation and its permeability. Formation
porosity is the Dore volume per unit volume of formation;
it is the fraction of the total volume of a sample that
is occupied by pores or voids. The saturation of a
formation is the fraction of its Dore volume octupied by
the fluid of interest. Thus, water saturation is the
fraction of the Dore volume that contains water.
The water saturation of the formation can vary from 100
percent to a small value that cannot be displaced by oil,
and is referred to as irreducible water saturation. For
practical purposes it is assumed that oil or hydrocarbon
saturation of the formation is equal to one minus the
water saturation. Obviously, if the formation's pore
space is completely filled with water, such a formation
will not produce oil or gas and is of no interest.
Conversely, if the formation is at an irreducible water
saturation, it will produce all hydrocarbons and no
water. Finally, the permeability of a formation is a
measure of the ease with which fluids can flow through
the formation, i.e., it's producibility.
Traditional methods of determining these parameters
called for the use of wireline logging or logging while
drilling (LWD) techniques which generally include
resistivity, gamma, and neutron-density measurements,
commonly known as the "triple-combo." In the instance of
a wireline measurement, the tool is typically lowered
below the zone of interest on an armored multiconductor
cable, providing for power and communications, and moved
upwardly through the borehole while making the
measurements. In the instance of LWD logging, the
measurements are made while drilling is taking place, the
tools being mounted on specialized subs in the drilling
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string. Each of these methods has their advantages.
The wireline method is generally capable of providing a
more accurate measurement as well as more real time data.
,The LWD method, while being more susceptible to
'5 environmental effects, such as tool position within the
borehole, makes the measurements in a relatively new
borehole, generally prior to any invasion by components
of the drilling fluids into the formation. The triple
combo measurements are subject to a number of borehole
environmental effects. Resistivity tools respond to
conductive fluids, including moveable water, clay bound
water, capillary bound water and irreducible water.
While a number of models have been developed to estimate
the water saturation of the formation, the recognition of
pay zones within an earth formation is difficult because
no conductivity contrast exists between capillary-bound
water and moveable water. Further, the resistivity
measurement is subject to borehole rugosity and mudcake
effects. Similarly, the methods utilized to determine
porosity were lacking in detail in that neutron-density
measurements responded to all components within the
formation but are more sensitive to the formation matrix
as opposed to the fluids contained therein. Even after
cross plot corrections, borehole rugosity, mudcake,
lithology and other environmental effects can adversely
effect this measurement.
Nuclear magnetic resonance (NMR) logging is
relatively recent commercial method developed to
determine the above formation parameters, as well as
other parameters of interest, for a geological formation
and clearly has the potential to become the measurement
of choice for characterizing formation fluids. This is
due, at least in part, to the fact that unlike nuclear
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porosity logs, which utilize isotopic radioactive
sources, the NMR measurement is environmentally safe and
is less affected by variations in matrix lithology than
most other logging tools. The NMR logging method is
'5 based on the observation that when an assembly of
magnetic moments, each of which having a certain angular
momentum, are exposed to a static magnetic field they
tend to align at a certain angle to the direction of the
magnetic field, and will precess with the Larmor
frequency around the direction of the magnetic field.
The rate at which equilibrium is established upon
provision of a static magnetic-'field is characterized by
the parameter T1, known as the spin-lattice relaxation
time. Another related and frequently used NMR parameter
is the spin-spin relaxation time constant T2 (also known
as transverse relaxation time) which is an expression of
the relaxation due to dynamic non-homogeneities on
molecular length scales. Another measurement parameter
used in NMR well logging is the self-diffusion
coefficient of formation fluids, D. Generally, self-
diffusion refers to the random motion of atoms in a
gaseous or liquid state due to their thermal energy.
Since the molecular propagation of pore fluid molecules
is affected by pore geometry, the diffusion parameter D
offers much promie as a separate permeability indicator.
Diffusion causes atoms to move from their original
positions to new ones. In a uniform magnetic field,
diffusion has no effect on the decay rate of the measure
to NMR echoes. In a gradient magnetic field, however,
atoms that have diffused will acquire different phase
shifts compared to atoms that do not move, and diffusion
will thus contribute to a faster rate of relaxation.
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Recent advances in the NMR logging tool design and
interpretation have permitted users to obtain detailed
information regarding formation characteristics porosity,
fluid characterization and estimates of permeability.
.5 In particular, the MRILO tool manufactured and utilized
by the NUMAR product service line of Halliburton. Energy
Services and the CMRTm tool manufactured and utilized by
Schlumberger Oilfield Services represent significant
improvements in the field of NMR logging and are both
capable of making porosity, permeability and fluid
characterization measurements. Both tools utilize
permanent magnets to provide a static magnetic Bo field
and RF pulses to create a Bl fields as part of
Carr-Purcell-Meiboom-Gill (CPMG) experiment. Using
Tl and/or T2 echo information, one can determine a number
of formation properties. Fluid saturation (porosity) is
generally determined by means of signal intensity. Fluid
typing utilizes Tl , T2 and/or diffusion measurements and
is usually based on the viscosity of the fluid being
measured. The bulk volume index (BVI) and free fluid
index (FFI) are measured based on T2 and empirically
derived formulas. The formation permeability is also
based on Tl and/or T2 measurements and one of several
empirically derived models.
With respect to permeability, several models have
been used to estimate formation permeability. The first
method is based on Tl and/or T2 porosity and is estimated
by various oilfield service and oil exploration companies
according to equations 1-3 below:
k 01'12
[1]
k =C04T22Az
[2]
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k 027-12
[3]
Where k is permeability, (I) is porosity, C is an
empirically derived constant and T2ML is the logarithmic
mean of the T2 distribution.
Yet another model estimates formation permeability
based on the bound water information (often referred to
as the Coates model) according to equation 4 below:
k- W2(FT'-2)
LBW)
[4]
where FFI is the free fluid index, which is determined by
partitioning the total measured NMR response by the
T2cutoff, which is the value of T2 that is empirically
related to the capillary properties of the wetting fluid
for the specific formation lithology. The porosity
estimate below T 2cutoff is generally referred to as the
bound fluid porosity or bulk volume irreducible (BVI).
While estimates of T 2cutoff values have been made for
various types of mineralogy, the only accurate means of
determining T 2cutoff is by performing NMR measurements on
a core sample.
Another model for estimating formation permeability
is based on the restricted diffusion and pore size of the
formation as set forth in equation 5 below:
k 03 1(0-0Y i-(Y)2)
V
[5]
- where S/V is the pore surface to volume ratio and T is
the rock tortuosity.
Each of the above models has drawbacks in their
application. For instance, equation 4 (the Coates model)
might not be valid if gas is present in the sample or if
the estimate of the T 2cutoff is significantly in error.
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The Carman-Kozeny model set forth in equation 5 was
derived for an artificial lithology (glass beads) and has
yet to be verified over wide range of reservoir
lithology.
'5 Other techniques have been used to estimate formation
permeability. Primary among them is the use of formation
test tools to determine formation permeability.
A formation test tool is generally lowered into the
borehole and brought into contact with the formation
wall. A probe is inserted past the mud cake to come in
contact with the formation itself. Fluid is then
withdrawn from the formation using a pre-charge piston or
pumping means. This "draw down" period induces fluid
into the tool that may be diverted to sampling chambers
or, ultimately, discharged back into the borehole.
Following the draw down, formation pressure (and
generally temperature) is measured as it builds back up
to its natural formation pressure. There are a number of
models for estimating permeability based on the formation
pressure and temperature tool data. These models may
include a laminar or spherical model design. The use of
formation testers to determine permeability is well known
and U.S. Patents 6,047,239, 5,2447,830 and 4,745,802 set
forth exemplary formation test tools. As noted
previously, these formation test evaluation techniques
pre-suppose the use of a particular model, which in turn
pre-supposes the nature of the formation itself.
The formation may be thinly laminated near the test point
or have a large, consistent lithology. It will be
appreciated that models designed to work in a consistent
lithology will not yield as accurate a result where the
formation is thinly laminated with the layers each having
differing porosity and permeability characteristics.
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Formation test tools are generally incapable of measuring
anisotropic permeability, i.e., vertical versus
horizontal permeability. An additional downside to using
formation test tools is the fact that logging tool
movement must be stopped to permit the formation test
tool to come into contact with formation, perform the
draw down and permit the pressure to build back up.
It may require several minutes to hours to perform the
draw down and build up. It will be further appreciated
prior to wireline logging operations, the drill string
must be "tripped" or removed from the borehole to permit
logging. This results in an associated cost over and
beyond the cost of services associated with logging.
The triple-combo and NMR logging tools noted above are
used in continuous logging operations, that is, the
measurements are made as the tool is moved up or down the
borehole at rates exceeding three feet per minute.
Indeed, modern borehole logging speeds generally
exceed 30 feet per minute. Thus, while providing some
information regarding permeability, formation test tools
are costly to use when compared to NMR logging tools.
At the same time, NMR logging tools make certain
assumptions regarding permeability that may not be
accurate in light of actual formation conditions.
Recently, some efforts have been made to combine NMR
techniques with formation test tools. Halliburton,
Schlumberger and Baker Atlas have introduced techniques
in which fluid identification is performed on the fluid
withdrawn from the formation during one of the formation
tests. Examples on these types of techniques are set
forth in U.S. Patents 6,111,408 and 6,111,409.
In each
instance, the NMR experiment is performed on the fluid
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that is no longer in situ. As a result, it may undergo a
phase change.
Other methods of formation characterization include
in the use of imaging tools. These tools attempt to
create an image of the borehole wall as it surrounds the
tool: There are a number of different techniques
utilized in this area. Primary among them are the use of
acoustic or sonic information and microresistivity.
Borehole acoustic imaging tools typically utilize an
ultrasonic transducer to emit high frequency sonic energy
that is reflected back from the borehole. The reflected
signal is received by the transceiver and processed to
create an image. The microresistivity technique places
small electrodes against the side of the borehole wall
and current is forced into the formation. Based on the
return resistivity information, an image of the borehole
wall can likewise be created. Both of these techniques
have their drawbacks in that both require a great amount
of time to hold the tools stationary in the borehole in
order to make measurements. In the case of the
electrical technique, the electrodes must be in contact
with the borehole wall. Further, commonly used oil-based
drilling muds have an adverse effect on the use of the
microresistivity method. It will be appreciated that
both of these techniques significantly increase the
amount of time required for logging operations.
Moreover, they provide only a portion of the information
that may be sought in order to characterize the
reservoir.
Further, there exists a continued need for accurately
determining formation permeability at present, formation
permeability can be derived in a number of different
ways. One method utilizes a formation test tool wherein
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a small section of the borehole wall is isolated from the
borehole. A fluid channel between the formation and the
tool is created and fluid is drawn into the tool over a
period of time. Pressure, temperature and fluid volumes
are recorded and permeability is empirically derived
using various models. Permeability may also be
empirically derived utilizing NMR tools based on fluid
volumes and various models.
Thus, there exits a need for a means for directly
determining formation permeability, as well as providing
an image of the formation where the measurement is made.
Further, there exists a need for a means for determining
anisotropic permeability where vertieal permeability (kv)
differs from horizontal permeability (kH).
Summary of the Present Invention
The present invention is directed to a means for
measuring formation characteristics, including
determining formation porosity, permeability, fluid
characterization and imaging of the well borehole.
It relates more particularly to a method and apparatus
for measuring a property relating to fluid flow in an
earth formation, more specifically to directly measuring
formation permeability. The present invention provides a
method for determining the permeability of a hydrocarbon
bearing earth formation, which method comprises the steps
of:
(a) locating a tool at a selected position in a
borehole penetrating the earth formation;
(b) inducing a flow of fluid within the earth
formation to said tool;
(c) creating at least two MRI images of said fluid
while flowing within the earth formation to said tool,
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said at least two images being created at different
times;
(d) determining displacement of said fluid within
the earth formation relative to said different times,
using the at least two MRI images;
characterized in that:
the at least two MRI images are created utilizing
Time of Flight angiography pulsed field gradient
experiments or Phase Encoding angiography; and the
method further comprises:
(e) determining in situ the earth formation
permeability from the displacement of said fluid,
wherein the step of creating said at least two MRI
images further includes the steps of:
(cl) creating a static magnetic field in the earth
formation to polarize and align selected nuclei within
said fluid;
(c2) applying a 90 sinc radio frequency pulse and
a first pulsed gradient magnetic field to the earth
formation, said radio frequency pulse being applied
perpendicular to said static magnetic field and said
first pulsed gradient field being generally aligned with
said static magnetic field;
(c3) applying a second and a third pulsed gradient
magnetic field to the earth formation following
termination of the radio frequency pulse and said first
pulsed gradient magnetic field, and said first, second
and third pulsed gradient magnetic fields being mutually
orthogonal;
(c4) applying a 90 square radio frequency pulse to
the earth formation;
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(c5) applying the third pulsed field gradient again
to the earth formation together with a second 900 sinc
radio frequency pulse;
(c6) receiving a spin echo signal from said nuclei
within said fluid;
(c7) creating an image from said signal; and
(c8) repeating steps (c3)-(c7) for each MRI image
created.
In accordance with another aspect of the present
invention, there is provided an apparatus for
determining permeability of a hydrocarbon bearing earth
formation by creating at least two MRI images for fluid
flow within the earth formation, the apparatus
comprising:
(a) means for inducing fluid flow within the earth
formation to the apparatus;
(b) at least one permanent magnet to create a
static magnetic field in a remote region in the earth
formation to polarize and align selected nuclei within
said fluid, said magnet having a longitudinal axis and a
magnetization vector;
(c) a first electromagnetic coil to create a first
variable magnetic field in said remote region the first
variable magnetic field being a 90 sinc radio frequency
and a first pulsed gradient magnetic field applied to
the earth formation, said coil having a magnetization
vector parallel to the magnetization vector of said
permanent magnet and said radio frequency pulse is
applied perpendicular to the static magnetic field and
the first pulsed gradient field being generally aligned
with said static magnetic field;
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(d) a second electromagnetic coil to create a
second variable magnetic field in said remote region the
second magnetic field being a second pulsed gradient
magnetic field applied to the earth formation following
termination of the radio frequency pulse and said first
pulsed gradient magnetic field, said second coil having
a magnetization vector substantially perpendicular to
the magnetization vector of said permanent magnet;
(e) a third electromagnetic coil to create a third
variable magnetic field in said remote region the third
magnetic field being a third pulsed gradient magnetic
field applied to the earth formation following
termination of the radio frequency pulse and said first
pulsed gradient magnetic field, said third coil having a
magnetization vector lying in a plane orthogonal to said
permanent magnet longitudinal axis and perpendicular to
the magnetization vector of said permanent magnet,
wherein third magnetic field being the third pulsed
gradient magnetic field applied to the earth formation
with a second 900 sinc radio frequency pulse;
wherein said first, second and third pulsed
gradient magnetic fields being mutally orthogonal;
(f) a radio frequency (RF) transmitter apparatus
for selectively transmitting a RF magnetic field in said
remote region the RF magnetic field being a 900 square
radio frequency pulse applied to the earth formation
exciting nuclei in said remote region; and
(g) a receiver for receiving nuclear magnetic
resonance signals for receiving a spin echo signal from
said nuclei within said fluid from said excited nuclei,
thereby creating the at least two MRI images of fluid
flow within said formation at different times from which
the permeability of said formation is derived.
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In one embodiment, the present invention utilizes
one or more small NMR imaging sensors in conjunction with
a formation test tool, the sensors being in or proximate
to the borehole wall during the formation test
procedures.
The present invention is thus capable of performing
fluid typing of the fluid in situ as it flows toward the
formation test tool probe. This permits a determination
of the formation based on the displacement of the
hydrogen atoms within the formation. It is, thus, further
an objective of the present invention to provide for a
more accurate determination of permeability, including,
anisotropic permeability measured in situ.
According to the present invention there is further
provided an apparatus for use within a borehole within
an earth formation for imaging fluid flow within the
earth formation, comprising:
(a) means for inducing fluid flow from the
formation;
b) at least one permanent magnet to create a static
magnetic field in said remote region in the earth
formation, said magnet having a longitudinal axis and a
magnetization vector;
(c) a first electromagnetic coil to create a
variable magnetic field in said remote region, said coil
having a magnetization vector parallel to the
magnetization vector of said permanent magnet;
llc
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(d) a second electromagnetic coil to create a
variable magnetic field in said remote region, said coil
having a magnetization vector substantially perpendicular
to the magnetization vector of said permanent magnet;
(e) a third electromagnetic coil to create a variable
magnetic field in said remote region, said coil having a
magnetization vector lying in a plane orthogonal to said
permanent magnet longitudinal axis and perpendicular to
the magnetization vector of said permanent magnet;
(f) a radio frequency (RF) transmitter apparatus for
selectively transmitting a RF magnetic field in said
remote region thereby exciting nuclei in said remote
region; and
(g) a receiver for receiving nuclear magnetic
resonance signals from said excited nuclei, thereby
providing information regarding the properties and
characteristics of the formation, from which may be
derived a petrophysical property of said formation and an
image of fluid flow within said formation.
The apparatus of the present invention further is
capable of creating a 3 dimensional image of the
borehole. Unlike prior part techniques, which utilize
Free Induction Decay (FID) CPMG experiments and/or
Saturation Recovery techniques, the present invention is
capable of utilizing a Pulsed Field Gradient (PFG) pulse
sequence to measure single point echo information to
derive spin density for a myriad of "voxel" or scan
positions at the borehole wall and into the formation.
Voxel is a commonly used term to denote a volume picture
element, which is used as smallest division of a three-
dimensional space or image. This spin density information
is used to create an image of the formation at depths
exceeding that of near surface images. In one
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embodiment, the apparatus of the present invention
utilizes a series of permanent magnets and electromagnets
to create a static magnetic field and a pulsed magnetic
field to perform the PFG experiment. The electromagnets
are under independent programmable control and may be used
to control the magnetic field at each of the voxel
positions. This control feature may be used to create a 3-
D grid of voxels, thereby providing a 3-D image of the
formation surrounding borehole wall.
In another alternative embodiment, this present
invention may be utilized in conjunction with a
formation test tool to create an image of the formation
fluid flowing into the test tool to determine fluid
characteristics, including self-diffusion.
In yet another alternative embodiment, the present
invention provides for utilizing existing NMR tool
structures and designs modified to include
electromagnetic coils in addition to permanent magnets.
In this embodiment, the present invention may be
utilized with a separate formation test tool, or may be
run on a stand-alone basis and derive permeability from
known models. The addition of electromagnetic coils
permit carrying out the PFG experiment for the purpose
of imaging, as well as any CPMG experiments to determine
other formation characteristics such as porosity,
permeability (using existing models), and fluid typing.
In still another alternative embodiment, the
present invention provides an apparatus for determining
the permeability of a hydrocarbon bearing earth
formation comprising:
(a) means for inducing fluid flow within the earth
formation to the apparatus;
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(b) at least one permanent magnet to create a
static magnetic field in a remote region in the earth
formation, said magnet having a longitudinal axis and a
magnetization vector;
(c) a first electromagnetic coil to create a
variable magnetic field in said remote region, said coil
having a magnetization vector parallel to the
magnetization vector of said permanent magnet;
(d) a second electromagnetic coil to create a
variable magnetic field in said remote region, said coil
having a magnetization vector
substantially
perpendicular to the magnetization vector of said
permanent magnet;
(e) a third electromagnetic coil to create a
variable magnetic field in said remote region, said coil
having a magnetization vector lying in a plane
orthogonal to said permanent magnet longitudinal axis
and perpendicular to the magnetization vector of said
permanent magnet;
(f) a radio frequency (RF) transmitter apparatus
for selectively transmitting a RF magnetic field in said
remote region thereby exciting nuclei in said remote
region; and
(g) a receiver for receiving nuclear magnetic
resonance signals from said excited nuclei, thereby at
least two MRI images of fluid flow within said formation
at different times from which the permeability of said
formation is derived.
In yet another alternative embodiment, the present
invention provides for a centralized NMR apparatus
including both permanent and electromagnets to create an
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azimuthal image of the borehole wall. In this particular
embodiment, the tool is not measuring flow formation and
known techniques for estimating permeability based on
NMR data may be used. At the same time, the embodiment
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includes a combination of permanent magnets and
independently controllable electromagnets to create
voxels in the sensitive volume and carry out the
necessary PFG experiments to provide a 3D image of the
borehole. As with the embodiment noted above, this
embodiment is capable.of utilizing existing CPMG
techniques to determine porosity, permeability and fluid
characterization. -
The present invention thus provides the user the
ability to accurately determine formation parameters as
well as obtain a 3-D image of the formation past the
borehole wall. This image information can be used in
conjunction with other logging information to provide the
user with the information required to make decisions
regarding the completion and production of wells.
Brief Description of the Drawings
A better understanding of the present invention may
be had by reference to the detailed description of the
preferred embodiment and the Figures referenced therein
in which:
Figure 1 is an illustration of a logging system;
Figure 2 is an illustration of a formation test tool
deployed in a well borehole;
Figures 3A and 3B are illustrations of a formation
test tool utilizing NMR spectroscopy sensors;
Figures 4A and 4B are illustrations of embodiments of
the NMR spectroscopy magnet .and antenna configuration of
the present invention;
Figure 5 is an illustration of a known NMR apparatus
modified to provide the functionality of the present
invention;
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Figure 6 is an illustration of yet another known NMR
apparatus modified to provide the functionality of the
present invention;
Figure 7 is a block diagram of the NMR control system
of the present invention;
Figure 8 is an illustration of the rotating frame of
reference used in NMR/MRI techniques;
Figure 9A is a sequence diagram of a projection
reconstruction pulse sequence and signal;
Figure 9B is a sequence diagram of a Projection
Reconstruction pulse sequence and signal, wherein a sinc
.RF pulse is utilized;.
Figure 10A is a sequence diagram of a two-dimensional
Fourier Imaging pulse sequence and signal;
Figure 10B is the method used for sampling k-space
when using the Fourier Imaging sequence;
Figures 11A - 11D are illustrations of the reaction
of spin packets to the presence of the BO magnetic field
and phase encoding and frequency/read gradient magnetic
fields;
Figure 12 is a sequence diagram of a sequence used in
conjunction with multislice imaging techniques;
Figure 13 is a sequence diagram for a multifrequency
multislice imaging sequence;
Figure 14 is a sequence diagram for a basic spin echo
sequence;
Figure 15 is a sequence diagram for an inversion
recovery sequence;
Figure 16 is a sequence diagram for a gradient
recalled imaging sequence;
Figures 17A - 17B are sequence diagram and depiction
of a multifrequency, multislice, angiography imaging
technique and the manner of slice selection;
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Figure 18 is a sequence diagram of a single.frequency
angiography sequence;
Figure 19 is a sequence diagram of a phase encoding
angiography sequence;
.5 Figure 20 is a PGSE pulse sequence that may be used
to detect fluid flow;
Figure 21 is a depiction of the behavior of the
conditional probability functions PS for the behavior of
particles in response to Brownian motion and flow;
Figure 22 is a depiction of the FAST SSP sequence
that may be used for image acquisition;
Figures 23A and 23B are depictions of two different
SPRITE sequence techniques that may be used for image
acquisition;
Figures 24A and 24B are depictions of the "thirteen
interval" sequence that may be used to suppress
background gradient information;
Figures 25A and 25B is a depiction of sequences
utilizing bipolar pulsed field gradients to encode and
obtain information related to POSXY and VEXSY experiments
to determine fluid displacement, velocity and
acceleration; and
Fig. 26 is a depiction of an exemplary thirteen
interval sequence utilizing bipolar pulsed field
gradients.
Detailed Description Preferred Embodiment
The present invention is intended to be used as an
NMR imaging device within a well borehole. Use of the
present invention within the well borehole is intended to
provide certain formation characteristics, including,
porosity, permeability, fluid characterization, flow
velocity and 3-D imaging of the formation of interest.
With reference to Figure 1, a well logging system is
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generally depicted. A well borehole 10 is seen as
penetrating earth formation 12, having been drilled using
known methods. A well logging tool 14 is seen as being
lowered into the well borehole and on an armored,
multiconductor cable 16. The tool 14 includes the
sensors required for the measurement(s) to be made, power
conditioning circuitry, tool control processors, and
telemetry circuitry to transmit the information back up
the cable 16. The cable 16 is lowered over shiv wheel
18, which is in turn supported by rig 20. The cable 16
is played out from a winch 22, controlled by an operator
within a well logging truck or skid (not shown).
The cable 16 includes conductors that provide for power,
control signals to and control and data information from
the tool 14. The conductors are thus connected to a
control system 24, which is generally includes a
processor for tool programming and operation, as well as
data reception and interpretation. The tool data, as
well as interpretations created, may be stored in
recorder 26 that may be disk, tape or other mass storage
system located at the logging site. Further, the
information may be visually displayed on a monitor, CRT,
log chart, or other visual means of display (not shown).
In addition or in the alternative, the tool data and
interpretation information may be communicated via
satellite or land lines (not shown) to a remote location
for further interpretation by persons having specialized
knowledge relevant to logging information or formation
characterization, including other interpretation software
or visualization software. The tool 14 is shown as being
a single tool being lowered on a wireline. It will be
appreciated that in practice, multiple tools may be
lowered on the wireline for a single run. The number of
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tools that may be included in any single run can be
limited by a number of factors, including compatibility,
power consumption, and telemetry requirements.
Figure 2 depicts tool 14 as being a modular formation
test tool. As noted above, the tool 14 is lowered on
armored cable 16 to the zone of interest. In the
instance of a formation test tool, the tool 14 is
stationary when it makes its measurements. The borehole'
is generally filled with a mud or other weighted fluid
10 used to control wellbore pressure. The mud also operates
to seal and support the borehole by forming a mud cake 28
on the borehole wall. The mud cake 28 also reduces
invasion of formation fluids into the borehole 10.
The formation test tool 14 of Fig. 2 is shown as being
comprised of several modules, 30, 32, 34A and 34B.
Recent developments in formation tester design have
resulted in "modular" testers that permit the user to
configure the tool 14 for the specific application.
It might include one or more control and power
section 30, a module for multiple sample chambers 32,
and, as depicted in Fig. 2, two sample
modules 34A and 34B. Tools of this type include
Schlumberger's MDT, Halliburton's RDT and Baker Atlas'
RCI formation test tools. Typically, the tool 14 is
eccentered in the borehole by the extension of
eccentering arms 46 that bring pad 44 in contact with the
borehole wall opposite the formation tool tester.
The eccentering arms 46 are typically hydraulically
actuated. As the tool 14 is eccentered in the borehole
10, the sampling apparatus is extended. The apparatus
typically consists of hydraulically actuated extension
arms 36 that push a typically elastomeric isolation pad
38 into contact with mud cake 28. A probe or
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snorkel 40 is mounted in the center of the pad and is
extended once pad 38 comes into contact with the mud
cake 28 to position snorkel 40 proximate to the
formation 12. The pad 38 is used to isolate probe 40
from borehole fluids that may adversely affect any
pressure readings and/or fluid characterization.
A number of techniques have been developed to isolate the
snorkel 40 from the borehole fluids and any influx of mud
from the mud cake 28. The snorkel 40 is in fluid
communications with transport tube 42, which is itself in
fluid communication with the pre-test piston or pump (not
shown), and/or fluid sampling chambers located in module
32. Temperature and pressure sensors are located in
sample modules 34A. Additional sensors for fluid
characterization, e.g., NMR spectroscopy units, acoustic
sensors, or optical sensors may be located in any of the
modules. Module 34B depicts the snorkel 40, isolation
pad 38 and eccentering pad 44 in the withdrawn position
to permit transit up or down the borehole 10.
The tool 14 is typically lowered to the desired test
depth with the sampling mechanism in the position
depicted in module 34B. The eccentering pad 44 and
isolation pad 38 systems are actuated to move the tool 10
into position against the borehole 10 wall. The snorkel
40 is then actuated to extend toward the formation 12 and
the programmed test program is carried out. It will be
appreciated that the test program will vary with the
parameters to be measured, the nature of the formation 12
and the number of samples (if any to be taken). The tool
sampling apparatus is then deactivated and the
eccentering pad 44 and isolation pad 38 return to the
positions shown in module 34B. The tool 14 may then be
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moved to a different depth for additional testing or
returned to the surface.
Permeability maybe derived from the formation tester
pressure and temperature according to several well-known
'5 models. One model utilizes a spherical flow model to
approximate fluid flow from the formation into the
snorkel 40. This technique is described
in U.S. Patent No. 5,703,286. Other models postulate
that the fluid flow to the snorkel 40 takes place in the
form of a generally laminar flow model. This technique
is described in U.S. Patent No. 4,427,944. There exist
other techniques for the determination of fluid
permeability directed to specific applications, e.g.,
tight (very low) porosity measurements, multiphase
techniques, etc. These techniques may be applied in
addition to the method and apparatus described in further
detail below.
Structural Embodiments For Carrying Out the Method of the
Present Invention
Figs. 3A and 33 illustrate one embodiment of the
present invention in which the NMR imaging sensors 50
(described in greater detail below) are used in
conjunction with a formation test tool. In Fig. 3A, two
NMR sensors 50 are depicted as being placed within the
isolation pad 38. As the isolation pad 38 is advanced
toward to formation 12, the sensors likewise come into
close proximity with the formation 12. As will be set
forth further below, the NMR sensor 50 of this embodiment
is intended to operate in close proximity to the
borehole 10 wall. In Fig. 3B, the NMR sensors 50 are
mounted adjoining isolation pad 38 as opposed to within
the pad 38 itself.
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The NMR sensor 50 embedded used in conjunction with a
formation tester as shown in Figs. 3A and 35 does not
represent the entire NMR imaging apparatus. The NMR
sensor 50 referred to is limited to the permanent magnet,
electromagnet and RF transmit/receive antenna design.
The electronics and power section for the operation of
the tool of the present invention would reside in the
tool body 14 and within the surface system 24.
On embodiment of the NMR sensor capable of performing
known NMR, Pulsed Field Gradient (PFG) NMR, and MRI
imaging experiments is depicted in Fig. 4A, which is a
top view of the NMR sensor 50.
The sensor is encased in
a protective package 52 designed to protect the sensor
antenna and magnet structure from ambient conditions,
including fluids, pressure and shock. Two permanent
magnets 54a and 54b are being disposed in the sensor 50,
the axes of the magnets 54a and 54b (between the poles
for each respective magnet) being coplanar. The magnets
54a and 54b are oriented such that the North pole of
magnet 54a is adjacent to the South pole of magnet 54b.
The permanent magnets 54a and 54b are used to form the Bo
field for the NMR experiments to be carried out with the
present invention. Each of the permanent magnets 54a
and 54b has a coil 56a and 56b wound about the magnet.
Coil 56a has leads 58a and 60a to provide power to the
coil to create an electromagnet (EM coil) when powered.
Likewise, coil 56b has leads 58b and 60b to provide power
to the coil to create an electromagnet. The EM coils 56a
and 56b may be independently energized and are used to
provide the Gs (slice selection) magnetic field gradient
utilized in one embodiment of the present invention.
A radio frequency (RF) coil 62, having leads 64a and 64b
is shown as being disposed between magnets 54a and 54b,
=
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The radio frequency coil 62 is designed such that its
magnetic field is oriented orthogonal to the direction of
the effective magnetic field created by the permanent
magnets 54a and 54b and coils 56a and 56b.
Two EM coils
66a and 66b, having leads 68a, 69a(not shown) and 68b,
69b(not shown), respectively are shown as being disposed
between magnets 54a and 54b. The coils 66a and 66b may
be comprised of multiple winding or may consist of a
single EM coil, the coil(s) lying in a plane that is
parallel to the axes of magnets 54a and 54b and
substantially orthogonal to the plane of the coils of the
RF antenna 62. The EM coils 66a and 66b may be
independently energized and are used to provide the G4>
(phase encoding) magnet gradient field. They may also be
used to provide frequency encoding along depth by the
time invariant gradient. Yet another EM coil 70a having
leads 72a and 74a is shown in Fig. 4A. Not shown is a
corresponding coil 70b, having leads 72b and 74b, which
is disposed below the magnets 54a and 54b and is
similarly positioned. The coils 70a and 70b may be
independently energized and are used to provide the Gf
(frequency encoding) magnet field gradient utilized in
the present embodiment. EM coils 56a and 56b are shown
as being wound about magnets 54a and 54b. It will be
appreciated that EM coils 56a and 56b may instead be
wound about ferrite cores disposed in parallel to magnets
54a and 54b to provide the Gs magnetic field gradient.
The magnet/antenna structure set forth in Fig. 4A is
capable of performing known CPMG experiments to determine
various formation characteristics, including porosity,
permeability, and fluid typing.
An alternative embodiment of NMR sensor 50 is shown
in Fig. 45 The sensor is comprised of a non-magnetic
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body 150, having an axis 151. A plurality of bar
magnets 152 are circumferentially deployed about
body 150, having a common polarity orientation, the axes
of the bar magnets 152 being parallel to the axis 151 of
body 152. The bar magnets provide the static Bo field.
Four electromagnets, 154a, 154b, 154c and 154d, are
embedded in the body 152 and may be energized as
explained in the discussion of Fig. 7. These magnets
provide one orthogonal component to the gradient field.
An electromagnetic coil 156 is wrapped around the body
150 and when energized creates a magnetic vector
essentially perpendicular to the axis of body 150 and bar
magnets 152. A second electromagnetic coil 158 is
wrapped around body 152 and when energized, creates a
magnetic vector that is orthogonal to the Bo vector and
the magnetic vector created by coil 156. Lastly, a RF
coil 160 is mounted on the face of the body to provide
for the Bl field. Thus, the bar magnets 152 create a
static Bo field, the electromagnets 154a-d, 156 and 158
may be used to create a selective gradient field and
coil 160 may be used for RF pulses to carry out the NMR
and MRI activities within the present invention.
While the embodiments set forth in Figs. 4A and 4B
describe concentrically wound coils or individual
magnets, Fig. 5 is an illustration of a modification of a
known NMR apparatus to provide the functionality of the
present invention, in particular the imaging capability.
The NMR logging that may be modified in accordance with
the present invention is disclosed in
U.S. Patent 5,796,252 and is a variant of Schlumberger's
CMR tool. While the apparatus disclosed therein is
capable of performing both PFG and CPMG experiments, it
is incapable of addressing individual voxels with the
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pulsed magnetic field for the purposes of imaging.
Fig. 5 is an sectional view of a CMR tool which has been
modified to perform various CPMG experiments as are known
in the art of oilfield logging, as well as the PFG
imaging experiments of the present invention as well.
In Fig. 5, the CMR tool 200 modified to provide the
functionality of the present invention is generally
described. The tool 200 is comprised of a tool body 202
having magnets 204 and 206 disposed therein. In Fig. 5,
magnets 204 and 206 appear to be bar magnets. In fact,
they are slab magnets, having a longitudinal axes, one
pole of the magnet being located on one edge of the slab
and the opposite pole of the magnet on the opposite edge
of the slab. The magnetization directions of both
magnets 204 and 206 are perpendicular to the axes of the
magnets. The tool body 202 further includes a cavity 218
in which is disposed a RF antenna 220 having a semi-
circular cross section. An EM coil 210 is shown as being
disposed on the face 208 of the tool body 202.
The EM coil 210 is energized to provide the Gs gradient
magnetic field within the present invention. The
embodiment further includes EM coils 214a and 214b, each
of which may be independently energized, to provide the
G(1) gradient magnetic field in the present invention.
The coil(s) of EM coils 214a and 214b lie in a plane that
is substantially parallel to the magnetization direction
of magnets 204 and 206. Lastly, two independently
energizable EM coils 216a and 216b (not shown) are shown
as being disposed in a plane that is orthogonal to the
magnets 204 and 206 longitudinal axes and substantially
parallel to the magnetization direction of magnets 204
and 206. It will be appreciated that EM coil 216b is
located beneath bar magnets 204 and 206. EM coils 216a
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and 216b are energized to provide the Gf magnetic field
gradient utilized in the present invention as further
described below. The embodiment of Fig. 5, while
illustrated in the context of an eccentered self-standing
probe could be combined with a formation test tool as
shown in Figs. 3A and 3B or continue to be used on a
stand-alone basis. Where used as a self standing tool,
it can derive permeability of the formation utilizing the
models described above. Moreover, it may be used in
conjunction with a formation test tool to provide
additional information.
Fig. 6 is another embodiment which modifies an
existing NMR device to perform the intended CPMG
experiments, as well as the PFG MRI imaging of the
present invention. U.S. Patent 4,710,713 (Figs. 1 and 2)
describes the magnet and antenna structure that is
utilized in the Halliburton/NUMAR MRIL tool. Unlike the
CMR tool, which is eccentered and located adjacent to the
borehole wall during operation, the MRIL tool is a
centralized design. Thus, the magnet and RF antennae
structures are not located against the borehole wall.
While it will be appreciated that improvements may have
been made to the antenna and magnet design, it remains
the basic structure. A variation of the MRIL tool that
added electromagnets to the Bo field activation is
disclosed in U.S. Patent 4,717,877 (Figs. 1 and 2), also
assigned to Halliburton/NUMAR. The modifications to the
magnet and antenna structure of U.S. Patent 4,717,877 are
set forth in Fig. 6. Fig. 6 is an oblique view of the
modified MRIL tool 250 in keeping with the present
invention. A permanent magnet 252 is shown having a
magnetization direction that is essentially perpendicular
to the magnet 252 longitudinal axis 253. The permanent
CA 02465809 2004-05-03
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magnet 252 is used to create the Bo field.
The embodiment further includes EM coils 254a and 254b,
which may be independently energized to create the Gs
magnetic field gradient. As depicted in Fig. 6, EM coils
254a and 254b are wound about magnet 252, such that the
coils lie in a plane substantially orthogonal to the
magnetization direction of magnet 252. The structure
further includes RF antennae 256a and 256b (not shown)
disposed along the side of magnet 252 used to propagate
the RF pulse to create the Bl field for the MRIL tool.
Additional EM coils 258a and 258b are shown as being
generally disposed above and below magne-E. 252 and may be
energized independent of each other. EM coils 258a
and 258b, when energized, are used to Provide the G4)
magnetic field gradient used within the present
invention. Lastly, EM coils 260a and 260b (not shown)
are disposed about permanent magnet 252, in a manner
similar to the RF antennae 256a and 256b. EM coils 260a
and 260b may be independently energized and, when
energized, provide the Gf magnetic field gradient of the
present invention. It should be further noted that the
recent MRIL-Prime version of this tool is capable of
performing multi-frequency NMR experiments.
See, e.g., U.S. Patent 5,936,405 and 6,111,408.
Utilizing the multiple frequencies, multiple sensitive
volumes at varying radial distances may be investigated
utilizing a single Bo field. Accordingly, it will be
appreciated that the volumes for imaging may likewise be
extended further into the formation.
As depicted in Fig. 6, the MRI apparatus of the
present invention is capable of providing and image for
the formation past the borehole wall in a specific volume
only where the resultant Bo, B1, Gs, G4) and Gf fields are
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operative to permit imaging. It does not provide an
azimuthally resolved picture of the formation.
The present invention further contemplates providing
azimuthally resolved images of the formation. One means
of providing an azimuthally resolved image is similar to
the technique utilized in microresistivity imaging, using
tools such as Schlumberger's FRITM, Halliburton's EMITM
and Baker Atlas' STARTm tools. Typically, a multi-arm
dipmeter, well known in the art, includes multiple
microresistivity buttons or electrodes on each dipmeter
pad to provide a derived image of the borehole wall.
The dipmeter provides information as to the relative
position of the arms, the tool within the borehole and
the formation inclination or dip. Thus, an image of the
borehole wall is generated from the resistivity
information. In an azimuthally resolved imaging
embodiment of the present invention, NMR sensors of the
type disclosed in Fig. 4 may likewise be mounted on the
dipmeter arm pads to provide known NMR formation
characterization information as well as imaging'
information which may be resolved to provide an
azimuthally resolved image of the formation past the
borehole wall.
Another means of providing an azimuthally resolved
image would be to rotate the structure set forth in
Fig. 6. This may be accomplished in a wireline
environment by providing a rotating tool head, such that
the magnet/antenna structure is free to rotate with
respect to the tool electronics and the remainder of the
wireline tool string. Such a system would further
require an orientation package to correlate NMR imaging
data with the tool azimuth and position. Known
techniques utilizing 3-axis accelerometers, gyroscopes.
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magnetometers or other directional sensing equipment may
be used to correlate the imaging data with the tool
position in the borehole, including tool azimuth (face).
Another alternative means of providing an azimuthally
resolved NMR image would be to mount the structure of
Fig. 6 as part of a LWD logging string sub.
The structure would be positioned where logging
information is desired and the drill string rotated to
provide azimuthal resolution. While a drill string
undergoes torque displacement over its length, the
navigation package typically utilized in LWD apparatus
includes magnetometers, accelerometers and other known
sensors to establish the position of the tool face.
By establishing the tool face and the position of the NMR
tool relative to the tool face, one can establish azimuth
during the logging position to obtain azimuthally
resolved NMR images. While NMR logging is typically a
continuous operation, the use of tools to provide MRI
information will require a cessation of tool movement for
the time required to form the image. As discussed below,
the faster the image can be obtained, the less time
required for logging operations.
Fig. 7 is a block diagram of the system of an
apparatus for carrying out the present invention and
consists of the control section 80, power section 100 and
MRI sensor 50. It will be appreciated that the control
80 and power 100 sections may be located at the surface
= or, in the case of power section 100, within the tool 14
itself. To the extent portions of the system may be
located at the surface, a telemetry system (not shown) is
utilized to transfer control and data between elements
located in the borehole 10 is incorporated in the tool 14
and control system 24. The control section includes
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processor 82 that is utilized for overall signal
processing, tool control and RF and electromagnetic
control. The user may program the processor 82 to
specify various pulse sequences. The processor 82 is in
communications with an RF pulse programmer 84 used to
create the RF pulse sequence utilized in the MRI
experiment. The RF Pulse Programmer 84 signal is also
provided to an RF Source 86, the output of which is
provided to the RF Driver 88, the Phase Shifter 92 and
back to the RF Pulse Programmer 84 for verification.
The RF driver 88, which, together with input from the RF
Source 86 is utilized to create the signal that is
applied to the RF power supply 102, within the power
section 100 of the system. The RF signal is communicated
to the Transmit/Receive matching circuit 104. The signal
is then communicated to the RF Antenna 60 within MRI
sensor 50.
The processor 82 is also used to provide programming
information for the electromagnet system. The processor
82 is in signal communications with the EM Coil Pulse
Programmer 90. The signal output for the electromagnetic
coils is provided to the EM Coil Power supply 108 within
the Power section 100. The output from the EM Coil Power
supply is then applied to the EM Coils within the MRI
sensor 50. It will be appreciated that the power
supplied to the EM coils would be applicable to any of
the above embodiments described above.
Following the programmed pulse sequence, the
Transmit/Receive Matching circuit 104 goes into a receive
mode, and is in signal communications with
the RF Antenna 60. The RF Antenna 60 receives the
spin-echo(s) resulting from the NMR experiment and
receives the spin-echo as an analog signal that is
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transmitted through the Transmit/Receive matching
circuit 104 to the Receiver Preamplifier 106 within the
power section 100. The spin-echo signal is then
forwarded to the Receiver 94, together with the reference
phase information provided by the Phase Shifter 92, the
Receiver 94 then forwards the signal to the
Analog/Digital Converter 96 which converts the signal and
provides same to Processor 82 for further interpretation.
Imaging Techniques
As previously noted, the use of NMR techniques in the
logging of a well borehole is well known by those of
ordinary skill in the art. New techniques and apparatus
are continually being developed in the wireline and LWD
NMR logging fields. With a few exceptions, e.g.,
U.S. Patents 4,717,877 and 5,796,252, all of the tools
use some variant of CPMG experiments. The aforementioned
'877 and '252 patents utilize a pulsed field gradient in
conjunction with a CPMG experiment. Even so, the
PFG/CPMG experiments described therein are incapable of
providing a MRI image. There exist a number of differing
techniques that may be used to image the formation
surrounding the borehole, many of them finding their
genesis in the medical MRI field. In the following
discussion, the spin characteristics of hydrogen nuclei
are discussed in terms of a frame of reference, with X, Y
and Z axes being depicted as in Fig. 8. In reality, the
frame of reference is rotating about the Z axis at the
Larmor frequency for the nuclei being studied - in this
instance, hydrogen. The rotating frame of reference in
the transverse plane is referred to herein as X' and Y'
which, again, rotates at the Larmor frequency. Nuclei
spinning faster than the Larmor frequency appear to
precess the rotating frame of reference while those
CA 02465809 2004-05-03
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spinning slower appear to fall behind the movement of the
rotating frame of reference. This difference in spin
velocities results in the dephasing of the rotating
nuclei.
1.Imaging Principles
a. FID and Back Projection Techniques
The basic principles in a NMR experiment begins with
the resonance equation, in which the resonance frequency
of a spin is proportional to the Bo magnetic field:
7130
v= [6]
where y is the gyromagnetic ratio for the nuclei
being studied In the field of MRI, one employs
additional linear magnetic gradient field , smaller than
the Bo, which has the effect of modifying the Larmor
frequency as a function of the combined magnetic field at
the point being studied:
v0=7.130 +7G.r
[7]
where G is the gradient of the magnetic field, Bo,
and r is the vector of the particular nuclear spin
coordinates with respect to the isocenter of the Bo
field. Therefore, if a linear gradient field is applied
to the volume of investigation, each region will
experience a differing magnetic field. The amplitude of
the signal is proportional to the number of spins in a
plane perpendicular to the applied gradient.
The thickness of this plane depends on the intensity of
the field gradient and the duration of the radio
frequency pulses. The discrimination of positions can be
achieved by means of frequency encoding or phase
encoding. The basic technique behind frequency encoding
is set forth in Fig. 28a. Therein, following application
of the Bo field, the B1 field (TX) is applied, followed
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by the Hahn echo (RX) . The Gy gradient is applied for t1
followed by the application of the Gx gradient for time
t2=n2At2 . In frequency encoding, one varies n2, with the
resultant signal being:
4172) = exp(-- [1/ T2 + ir(Ba + n2 At2)
[8]
where n2 counts the numbers of data points along
the x direction. The spatial resolution of the frequency
encoding technique is limited by:
lyGxA 2 / 7;
Ac 112 and [9A]
1/ Ax = 7; yGx /2 = Gx I Awl/2 [9B]
The technique used to perform phase encoding is
depicted in Fig. 28b. Therein the amplitude of the Gy
field is varied to step through k space. The resulting
signal may be expressed as:
s(ni) = exp(--[1 I T2 + iy(.130 + n1AGy yUti)
[10]
where n1 counts the number of data points along
the y direction. In this instance, the spatial resolution
increases using phase encoding with n1, MAX:
lynio,fAxAGyAytil< 27z. and
[11A]
1/ Ay = ?holm, 7A Gy I 27r
[11B]
The variation of the local magnetic field brought
about by a field gradient pulse of intensity G and
duration t adds an additional phase 11) to a magnetic
moment precessing at location r:
co = 21G = r [12]
MRI imaging pulse sequences are typically based on
the acquisition of spin-echoes. Spin echoes occur when
the dephasing of rotating magnetic moments has been
compensated for by use of refocusing radio frequency
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pulses. Spin-echo imaging pulse sequences comprise at
least two identical magnetic field gradient pulses, one
of which is applied prior to, the other one after the
refocusing RF pulse. It will be appreciated that these
field gradient pulses can be realized using a constant
field gradient and a refocusing RF pulse. In that case,
the duration of the first field gradient pulse is given
by the time from the beginning of the pulse sequence to
the beginning of the RF pulse, and the duration of the
second field gradient pulse is equal to the time from the
end of the RF refocusing pulse to the peak of the spin
echo.
If the magnetic moments have not changed their
position r during the time between the two field gradient
pulses, the second field gradient pulse will exactly
compensate for the additional phase that was added to the
precessing spins by the first field gradient pulse.
However, if the magnetic moments have propagated over a
certain distance Ar during that time interval, each
precessing spin will have acquired a phase difference AO
after the second field gradient pulse:
Ap=i4GAr =
[13]
The measured intensity of the acquired spin echo is a
superposition of the projections of the magnetic moments
onto the x' (real part of the signal) and y' (imaginary
part of the signal) axes of the rotating frame reference.
When the magnetic field gradient has components in all
three spatial dimensions, a small elemental volume, dV,
of a sample is identified by a common resonance
frequency. Assuming that this volume element is located
at position r, and that the local spin density at
position r is p(r), then there will be p(r) dV spins in
that volume element.
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The intensity ofthe spin echo is determined by three
factors:
1. the likelihood of finding a magnetic moment at
position r when the first field gradient pulse is being
applied,
2. the conditional likelihood that a magnetic moment
located at r has propagated a distance Ar during the time
interval t' between the onsets of the first and the
second field gradient pulses, P(rlArrt'),
3. the phase shift AO.that each precessing spin
experiences due to its movement along the direction of
the magnetic field gradient.
Since the likelihood of finding a magnetic moment at
position r is given by the local spin density p(r),
the intensity of the spin echo can be calculated:
S(8 ,G,P)= ff p(r) P(rks.r,P)exp(i AO dr &V
= fip(r) P(rlAr ,P)exp(i)45GAr) dr dAr
[14]
Factors 1 and 2 can be combined and are commonly
referred to as the self-correlation function P(Ar,r) .
P(Ar,t')= p(r)13(rlAr,t') dr
[15]
Using Equation 11, the NMR signal amplitude may be
expressed as:
S(t,G,t')= 113(rlAr ,t1) exp(i7tGAr) dAr
[16]
The product (270-1yGt is an element of the wave vector,
k, and has units of reciprocal space. It determines the
spatial resolution of an PFG NMR experiment. The concept
of a generalized scattering vector allows applying the
formalisms derived for scattering experiments to NMR.
Using k, Equation 15 can be rewritten as:
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Ak,t) = t)exp(2,nikAr) dAr
[17]
According to Equation 16, the spin echo intensity may
be changed by varying either the time (t') or the
scattering vector (k) in a PFG NMR experiment. The spin
density can be calculated from the measured intensity of
the spin echo if the time between the field gradient
pulses (diffusion time) is long enough for all spins to
have moved to their equilibrium positions. In that case,
the likelihood that a particle has moved from position rl
to position r2 is equal to the likelihood of finding a
particle at r2, which, in turn, is equal to the spin
density at position r2, p(r2). Using Equation 16, and
with the annotation that Ar=r2-r1 it follows:
Ak,too) = ffp(ri) p(r2)exp(2.7ri k(r2 - ri)) dridr2
sp(ri)exp(¨ 27d kri) dr, p(r2) exp(27/i kr2) dr2
[18]
The integral
S(k,t.)= fp(r)exp(27zik0 dr
[19]
is in the form of a Fourier transform of the spin
density, which means that for the case of long diffusion
times, the observed NMR signal is equal to
S(k,c)=/(k)/*(k) =I/(k)12
[20]
where I(k) represents the Fourier transform, and I*(k)
the conjugated complex Fourier transform of the spin
density, p(r).
In a two dimensional context, two different imaging
techniques are commonly utilized, Fourier Imaging (Fl)
and Projection Reconstruction (PR), sometimes known as
the back projection imaging or inverse radon technique.
In PR technique, the object to be studied is first
subjected to a magnetic field. A one-dimensional field
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gradient is applied at several angles, and the NMR
spectrum is recorded for each gradient angle.
A first spectrum is recorded with the gradient at
zero degrees to the +Y axis. A second spectrum is
recorded with the gradient now at a one degree angle to
the +Y axis. The process is repeated for the 3600 between
00 and 3590. The recorded data can be converted into an
image by a 2D Fourier transformation in cylindrical
coordinates. Once the background intensity is
suppressed, an image can be seen. See, S.R. Deans, S,
Roderick, The Radon Transfer and Some of its
Applications, Wiley, New York, 1983.
In a conventional 90 -FID imaging sequence, the PR
technique can be applied utilizing the pulse sequence set
forth in Fig. 9A. Varying the angle (I) of the gradient is
accomplished by the application of linear combinations of
two gradients. Here the Y and X gradients are applied in
the following proportions to achieve the required
frequency encoding gradient Gf.
Gy = Gf Sin (I)
Gx = Gf Cos (1)
For the PR technique to be a viable imaging
technique, it also must be capable of selecting thin
slices. This is accomplished by means of the gradient Gz,
a one dimensional, linear magnetic gradient field,
applied orthogonal to the x- and y components of the Bo
field during the same period as the RF pulse. A 900 RF
pulse applied in conjunction with the Gz magnetic field
gradient will rotate spins located in a slice or plane
through the object. That can be accomplished with a,
combination of "hard" and "soft" RF pulses. A "soft" 900
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sin pulse contains a small band of frequencies about the
desired center frequency. The frequency content of a
square 900 pulse ("hard" pulse) is preferably shaped as
an apodized sinc pulse, the amplitude of the sinc
function being the largest at the frequency of the RE'
pulse. This frequency will be rotated by 90 while other
smaller and greater frequencies will be rotated by lesser
angles. The application of a "hard" 90 RE' pulse with a
magnetic field gradient in the x direction will rotate a
broad spectrum of spins in a plane perpendicular to the
x axis by 900. In contrast to this, a "soft" RE' pulse
will serve as a slice-selective read-out gradient since
only spins precessing with a Larmor frequency in the
vicinity of the center frequency of the sinc pulse will
rotate the magnetic moments. The frequency encoding
gradient in Fig. 9B is composed of a Gx and Gy gradient
in this example. The FIDs are Fourier transformed to
produce the frequency domain spectrum, which is then
backprojected to produce the image. A thorough
discussion of the 2-D PR techniques may be found in
Callaghan, P. Principles of Nuclear Magnetic Resonance
Microscopy, Oxford Press (1991), pp. 124-28.
While the above example utilizes Gx and Gy for
frequency encoding and Gz for slice gradient, the slice,
phase and frequency encoding gradients may be selected as
indicated in the following table based on the specific.
sequence being utilized in the NMR/MRI sequence.
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GRADIENT
Slice Slice Gs Phase G(1) Frequency
Plane Gf
X Y Gz Gx or Gy Gy or Gx
X Z G Gx or Gz Gz or Gx
Y Z Gx G or Gz GZ or G
Table 1
By way of example, if the XY slice plane is chosen Gs
is Gz and if Gx is selected for phase encoding, Gy will
be used for frequency encoding.
This technique could be utilized where the sensor is
rotated to change the angle of the gradient to permit the
use of back projection techniques in a downhole context.
b. Fourier Imaging Methods
Fourier Imaging (Fl) techniques may also be used to
image 2-D space. When sampling the FID in the presence
of a gradient, signal points are obtained along a single
line in k space, which is along the direction of that
gradient. In the Fl technique, it is generally ascribed
to the x-axis. The application of the phase gradient Gcl)
imparts a phase modulation to the signal dependent on the
position of the volume element along the y-axis.
Starting with Eq. 15, above, the signal may be expressed
as:
a/2 co co
S(kx,ky)= jp(x, y, z)exp {i27-c (kr x+ ky dy dz
¨a/ 2_¨co ¨00 [21]
where a is the slice thickness. Since it merely
represents the averaging of the spin density across the
slice, the outside integral may be ignored and it may be
expressed as
03 CO
S(kx,ky). fp(x,y,z)exp{i274xx+kyAdxdy
-co -co [ 22 ]
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and the inverse Fourier transform is then,:
1 '
p(x, y) = our)2 j I.
iS(kx,ky) exp[¨ i2n-(kr x + kl' Adkx dk
[23]
The 2-dimensional spin density is determined by
sampling k space along the x axis under a fixed read
gradient Gz for successively increased values of ky.
An example of a two dimensional Fl pulse sequence and
signal is set forth in Fig. 10A, together with the data
acquisition sequence for that scheme. In Fig. 10A, 'a
slice selective RF sinc pulse is applied, together with
the slice selective gradient Gz. A 180' y pulse is then
applied to rephase the spins and the slice selective
gradient is again applied. The phase gradient Gy is then
applied in equal steps across its minimum to maximum
value. The frequency or read gradient (sometimes
referred to as Gz or Gf) is then turned on and a signal
is recorded in the form of the Free Induction
Decay (FID). The sequence of pulses is typically
repeated 128 to 256 times to collect all the data
required to produce an image. The effect is to map out
the pixels in kx and ky space (the first quadrant).
Application of a negative slice gradient, together with
the varying phase gradient would permit one to map the
second k space quadrant. Since the phase encoding
gradient is applied with a negative value as well, the
third quadrant may be mapped. Lastly, by applying a
negative read gradient and a negative phase encoding
gradient, the fourth quadrant may be mapped.
See, Fig. 10B. When the amplitude is a negative y, the
third quadrant is then mapped.
Present day imaging techniques as applied within the
medical field utilize 3D techniques and Fourier Transform
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applications to provide three-dimensional images of
objects. See for example, J. Hornak, The Basics of MRI,
www.cis.rit.edu/htbooks/mri. These techniques typically
utilize yet another type of magnetic gradient field, the
frequency encoding gradient Gf, often called the read
gradient, to provide additional information. It is used
to impart a specific angle to a transverse magnetization
vector. The final transverse magnetization direction is
dependent on the initial location of the transverse
magnetization vector and subsequently applied gradients.
Figs. 11A - 11D illustrate the effect of the application
of the phase encoding and frequency encoding gradients on
spin. The following illustration has been simplified to
ignore diffusion effects and non-homogeneities in the Bo
and gradients G(1) and Gf.
Viewing from the z-axis, and looking down onto
the x-y plane, nine different spin packets (si,j), where
i=1,2,3 and j = 1,2,3) are selected for a specific slice
(following application of an slice selection gradient Gs
and slice selection RF pulse) and are subject to a
uniform magnetization field Bo. Fig. 11A. Since all of
the spin packets have the same chemical shift, ideally,
they all precess at the same Larmor frequency with
respect to each other and the reference packet.
Fig. 11A. If a magnetic gradient field (phase gradient
G(1)) is applied along the X axis, the nine spin packets
will precess at three different rates as function of the
direction of the applied G(1) gradient, as there will be
three different Larmor frequencies, as set forth in
Equation 8 above. Fig. 11B. The precessional rates
in Fig. 11B are indicated by the length of the rotational
arrow. Thus, spin packets sl,j have a common
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precessional rate, as do s2,j and 53,j. As G(1) continues
to be applied, the nine spin packets will continue to
precess at the three different Larmor frequencies.
When the G(1) is terminated (Fig. 110), the external Bo
magnetic field is essentially homogeneous. The packets
will precess at the same Larmor frequency, but having
three different phase angles (1), when compared to a
reference phase vector, within its own frame of
reference. Fig. 110. In Fig. 11D, a frequency encoding
gradient Gf is applied along the y axis. In this
instance, the nine spin packets precess at three
different Laramor frequencies, with the rate of
precession indicated by the length of the rotational
arrow. As will be noted, the thee spin packets si,1
subject to the strongest gradient all precess at the same
rate. The spin packets initially start with their
respective phase encoding with respect to a reference
spin, but now rotate at a different frequency than the
reference packet, which is subject only to Bo. The phase
angle for each spin packet in row 1 proceeds to change
with respect to the reference spin. Each spin packet si,2
likewise starts from its initial phase encoding
in Fig. 11B and now precess at a common rate
corresponding to its Larmor frequency which differs from
the frequency in row 1. At the same time, the
magnetization vector for each spin packet s1,2 remains
different. Lastly each spin packet 5i,3 starts with its
initial frequency encoding from Fig. 11 and all spin
packets precess at a faster rate corresponding to its
Larmor frequency when compared to spin packets si,1 and
5i,2 or the reference spin. The nine spin packets in
Figs. 11A - 11D each now have a unique magnetization
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vector and retain this unique vector when the Gf field is
turned off, and they all precess at the same rate in the
presence of the homogeneous Bo field. The ability to
measure magnetization vectors and spin phases for each of
the nine spin packets is essential to the use of Fourier
Imaging (Fl) imaging techniques.
Referencing Fig. 12, the simplest 3-D Fl imaging
sequence is comprised of an apodized 900 sinc RF slice
selective pulse, a slice selective Gs magnet gradient
pulse, a phase encoding gradient pulse 4, a frequency
encoding gradient pulse Gf and a subsequent signal, the
magnetic gradient pulse sequences representing the
amplitude of the gradient pulse and its duration.
The slice selection gradient Gs turned off upon
completion of the RF pulse and the phase encoding
gradient is turned on. Once the slice selection gradient
is turned off, the phase encoding gradient G(1) is turned
on. The phase encoding gradient is then turned off and
the frequency encoding gradient Gf is turned on and a
signal is recorded. The signal is in the form of a FID
signal. The sequence is typically repeated numerous
times to collect data necessary for imaging purposes.
Each time the sequence is repeated, the magnitude of the
phase gradient is changed in equal steps between its
maximum value G+11)rn and its minimum value G...01.
The sequence may then be repeated for multiple slices to
create a 3-D image of the object.
2.Imaging Sequences
a. Multislice Imaging
The basic Multislice Imaging sequence is set forth in
Fig. 12. However, it is not practical to attempt to use
this sequence in either the medical or borehole
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environments, where a 90 flip angle is used. The reason
is the time required to acquire the necessary information
for a data image. An alternative method would be to
decrease the pulse angle, e.g., to 10 , thereby
decreasing the time required for the sequence.
However, in a non-homogeneous field, the spectral width
of the object being studied must be less that the
spectral width of the pulse, otherwise no FID can be
observed. Assuming that the entire FID-based sequence of
Fig. 12 can be repeated every 1 seconds and
that 256 differing values of the phase gradient are
applied, it would take over 4 minutes to acquire the data
for a single, small field of view image, where the field
of view (FOV) is defined according to the following
relationship:
FOV = fs /y Gf [24]
The use of smaller pulse angle will substantially
reduce the signal recovery time between scans. One other
technique that may be used is to reduce the FOV volume
being investigated. Where fs is the sampling rate and
Gf is the frequency gradient. Any imaging utilizing this
technique would be impractical with a constant logging
speed tool. The Multislice Imaging technique maybe
improved by utilizing RF pulses having differing
frequencies (or center frequencies in the instance of
sinc pulses) see Fig. 13. Thus, so long as the respective
gradient fields and RF pulses do not overlap, the time
required to acquire image data may be substantially
reduced when compared with the time for the sequence of
Fig. 12. Commercial NMR tools having multi-frequency
capability, such as the MRIL-PRIME, may be utilized to
perform multi-slice imaging. The time required for this
technique may not present a problem when used in
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conjunction with a formation tester having a long test
program (and the tool string is already stationary).
b. Spin Echo Sequence
One of the more commonly utilized MRI imaging pulse
sequences is the "Spin-Echo" sequence. The basic Spin-
Echo pulse calls for the application of a 900 RF pulse,
following polarization of the sample. The 90 pulse
flips the nuclei into the transverse (x-y) plane.
Following termination of the RF signal, the nuclei begin
to dephase and a FID signal is detected. At t=t, a 180
RF pulse is applied which flips the spinning nuclei 180 ,
for example, about the X axis and partially rephases the
nuclei and produces an echo signal. The pulse sequence
and resultant signals are depicted in Fig. 14.
The sequence begins with the 90 pulse and simultaneous
application of the Gs slice selection gradient. A phase
encoding gradient is applied between the 90 and 180
pulses. As with the Multislice imaging technique, the
phase encoding gradient is varied in multiple steps
between G(In and G_01. In order to minimize the TE (echo
time) a frequency encoding gradient is also applied
between the 90 and 180 pulses. This gradient is along
the same direction as the frequency encoding gradient and
dephases the spins so that they will rephase by the
center of the echo. The slice selection gradient is
applied in conjunction with the 180 selection pulse.
Following the 180 pulse, the frequency gradient is
applied during the time that the echo is recorded.
The entire process is repeated every TR (Time Repeat)
seconds until all the phase encoding steps have been
recorded. Again the time required to perform 256
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variations in the phase gradient pulse magnitude tends to
be time prohibitive, where TR Pe, Tl.
c. Inversion Recovery Imaging
An inversion recovery sequence utilizing spin echo
sequence to detect magnetization may also be used to
provide imaging information. In this technique the RF
pulses are 1800 - 90 - 180 . The sequence utilizes a 90
FID signal with the exception that a 90 FID is
substituted for the spin echo part of the sequence.
The sequence is illustrated in Fig.15. A slice selective
180 pulse is applied in conjunction with the slice
selective gradient. The effect of the 180 pulse is to
achieve maximum disruption from the equilibrium position
induced by BO. When applied in conjunction with the
slice selection gradient is operates to suppress unwanted
spins. After time TI (Time Inversion), for example, the
pulse echo sequence set forth in Fig. 13 is applied.
The phase encoding gradient field is again stepped
through equal steps between Go and G...0 by assigning a
different value each sequence. In this instance, the
phase encoding gradient is not applied after the first
180 pulse as the spins have not been placed in the
transverse plane. The frequency encoding gradient is
applied after the second 180 pulse during signal
acquisition. The FID signal following the 90 pulse is
ignored. The dephasing gradient is applied between
the 90 and 180 pulses to assure that they rephase by
the center of the echo. The entire process is repeated
every TR seconds with a differing phase encoding gradient
value. Again, this is a time consuming process that
requires stepping through each of the phase encoding
gradient values.
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d. Gradient Recalled Echo Imaging
Yet another technique that may be applied in the
context of MRI imaging is the gradient recalled echo
technique. This technique addresses one problem
associated with the previous techniques - the fact that
it requires the magnetization to recover its equilibrium
position .along the z axis. If the Tl time is
significant, it will lengthen an already time-consuming
imaging process. If the magnetization is rotated toward
the transverse plane by an angle 0 less than 90 , it will
recover equilibrium state, but at the loss of signal
strength. It will be appreciated that the loss of signal
strength will be proportional to sin0. This loss of
signal may be compensated for by averaging multiple
signals for the same area and averaging them together to
make up for the loss of signal. The pulse sequence
associated with Gradient Recalled Imaging is set forth in
Fig. 16. An RF pulse is applied to produce a movement
from the gradient equilibrium toward the transverse
magnetization plane on the order of 10 - 90 , together
with a slice selection gradient Gs pulse. Following
termination of the gradient selection pulse, a phase
encoding gradient is applied, again it is varied in equal
steps over the range G...01 to Gm, a differing value for
each sequence. Simultaneous with the application of the
phase encoding gradient, a frequency gradient is applied.
The frequency gradient is initially applied with a
negative value. The frequency gradient is then turned on
with a positive value and signal acquisition begins.
The effect of initially applying a negative gradient
value is to dephase the spins, with the positive pulse
rephasing them to produce a maximum signal amplitude at
the center of the acquisition period. The echo time TE
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is defined herein as the time between the start of the RF
pulse and the maximum signal amplitude, with the sequence
being repeated every TB. seconds. Because the sequence
does not fully tip the spins into the transverse plane,
the time required for the spins to cover and reach Bo
equilibrium following the sequence is greatly reduced.
As such, TR can be greatly reduced.
As demonstrated above, different techniques may be
utilized with a borehble apparatus capable of performing
PFG experiments, as were disclosed above. The techniques
may be utilized to create near-bore 3-D formation images.
Further, the structures disclosed above are capable of
performing known NMR/CPMG based logging experiments in
addition to the MRI imaging techniques discussed.
Thus, the structures above are capable of determining
petrophysioal properties of the formation as well as
being able to image the formation.
3. Low Imaging
Yet another application of PFG imaging techniques
within the present invention is the ability to image
connate fluid flow within the formation. In order to
image flow, a flow must be induced within the formation
and may be accomplished by means of a formation test
tool, drill stem tester, or other device to create flow
within the formation. The ability to image this flow
yields a far more accurate estimate of in situ
permeability that does not depend on the particular flow
model (laminar, spherical).
As noted above, one use of the present invention
would be in conjunction with a formation test tool.
A flow would be induced by the formation tester and the
MRI sensors used to determine the fluid characteristics
and the imaging of the fluid itself as it flows through
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the formation. Flow imaging, also referred to as
angiography, was pioneered in the medical arts field for
the imaging of blood as it flowed through a patient's
arteries and veins. It will be appreciated that the very
same techniques may be utilized to image fluids flowing
from the formation into the formation test tool. .
There are several angiography techniques that have been
applied to the medical arts, each of which is discussed
herein.
a. Time of Flight Angiography
Time of flight (TOF) angiography is also referred to
as "spin tagging" and is the most common form of
angiography utilized within the medical field. There is
no single technique for carrying out TOF angiography.
One technique utilizes a spin echo sequence where a 90
slice selective pulse is applied followed by a 180 slice
selective pulse having a differing frequency. The net
effect would be to have two differing slices. Referring
to Fig. 17A, the activation of the various pulse
sequences are depicted along a common "time line" with
the movement of fluid through a formation. In Fig. 17A,
a 90 slice selection RF pulse and a slice selection
gradient Gs are applied. The phase encoding gradient G(1)
and the frequency (or read) gradient Gf are applied after
the 90 RF pulse and the slice selection gradient.
The slice selection gradient and pulse excites the spins
within the target slice 600 within the flow path 604, in
time line A. As the energized spin packet flows along
flow path 604, the phase and frequency gradients are
applied. When the 180 RF pulse is applied, it is applied
to a packet 602 that was not subject to the initial
gradients and 90 'RF pulse. While the FID signal may be
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detected, no echo signal will be detected In order to
overcome this, the frequency of the 90 RF pulse differs
from that of the 1800 RF pulse. The effect is to make
two different slice selections, with the 180 RF pulse
slice selection following the 90 slice in the direction
of the flow. As seen in Fig. 17B, the 90 RF pulse is
applied, together with the slice selection gradient Gs.
The spin packet 600 within the 90 slice thickness is
moved to the transverse plane. This is followed by the
application of the phase encoding and read gradients.
When a 180 RF pulse of a differing selected frequency is
applied, the spin packet 600 which has begun to dephase
is within 180 slice (line B), the spin packet continues
in the direction of flow and the frequency Gf or read
gradient is applied and the echo signal is detected.
It will be appreciated that if the spin packets
energized by the 90 RF pulse are not subjected to the
180 pulse, that no echo signal will be detected.
Likewise, unless the packet 600 subjected to the 180 RF
pulse has been moved into the transverse plane by
the 90 pulse, no echo signal will be detected. Further,
if there is no flow, the 90 RF excited spin packets will
not move into the slice thickness for the 180 pulse.
Another technique permits the use of a single
frequency/same slice selection is the use of successive
interrogations of the selected slice in multiple pulse
train utilizing a stimulated echo imaging sequence
variant. As set forth in Fig. 18, a 90 RF sinc pulse is
applied in conjunction with a Gs slice selection
gradient. This is followed by the application of a G(1)
phase encoding gradient, together with a frequency/read
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gradient Gf. Following application of the read gradient,
a square 90 RF wave pulse is applied. A sequence
consisting of a 90 RF sinc pulse, 'applied in conjunction
with a Gs selection gradient is applied, followed by a Gi
read gradient during which time the signal is acquired.
By repeating the final sequence, the motion of the target
slice is successively followed in a single phase encoding
experiment. The entire sequence is then repeated with a
differing phase encoding gradient G4). The signal
intensity is then plotted against time, from which the
velocity is determined, given the tagging and slice
selection separation. In this instance, the imaging
resolution is limited by the slice thickness.
The stimulated echo method further offers the advantage
that a normal spin density image can be obtained by
utilizing the spin echo (not shown) that arises between
the second 90 RF spike pulse and the third 90 sinc
pulse. The specific timing techniques are well known and
are set forth in Merboldt, K., et al.. Journal of
Magnetic Resonance, Vol. 67, p. 336 (1986). What is
clear is that the above techniques are limited in terms
of the velocity ranges. Since a typical slice thickness
for these techniques is on the order of 100 m and the
observation time at about 100 ms, the observable
velocities are in the range of 1 mm/sec or greater.
It will be appreciated that flow rates seen in a
formation may not be within the observable range of flow
velocities.
TOF techniques may be utilized to measure flow
velocities in response to formation test tool fluid
withdrawal. Moreover, the existence of known spin echo
imaging techniques, e.g., phase alternated CPMG sequences
may be used to determine the fluid characteristics.
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B. Phase Encoding Angiography
A different technique used to establish flow rates is
known as phase encoding or phase contrast angiography.
This techniques used differ substantially from the TOF
techniques described above and utilize the application of
a bipolar gradient G* between the slice selection and
imaging sequences, and derives the flow velocity from
transverse magnetization phase shifts. A bipolar
gradient pulse is one in which the gradient is turned on
having a positive or negative amplitude, then turned on
in the opposite amplitude for the same period of time.
Where the initial lobe is negative, the gradient is
described as a negative bipolar gradient; where the
initial lobe is positive, it is described as a positive
bipolar gradient. This bipolar gradient imposes a phase
shift on the spin packet that is dependent on the net
spin displacement occurring over the time period of
interest. The gradient G*(t) may be made sensitive to
velocity, acceleration or higher derivatives or
displacements. See, Moran, P. R., et al., Technology of
Magnetic Resonance, p.149 (1984); Nishimura,
D. G., et al., IEEE Transactions of Medical Imaging,
MI-5, p. 140 (1986). The effective phase shift
experienced at time t by a spin I following the path
ri (t') in a gradient field g (t') can be expressed as:
00= yfG(P)=ri(P)dtt
0 [25]
Where all the spins have a non-Brownian motion, e.g.,
a constant velocity, Eq. 24 may be simplified, given
constant velocity v, then rj (t1) is reduced to rj (0) +
vt'. Similarly, where the flow is undergoing a constant
acceleration, rj (-C) can be
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expressed as rj (0) + vt' + a t' 2. The resulting phase
shifts involve successively higher moments of G*(t).
The zeroth moment must be equal to zero if the final
phase shift depends only on the motion and not on the
starting position of the spins. Therefore, by choosing
the particular time dependence for G*(t), the spin echo
signal may be made sensitive to velocity or acceleration
of the flow. In most oilfield applications, the flow
velocity and not acceleration or some higher order of
displacement is of primary interest. However,
acceleration information could be used to model transient
flow characteristics of the formation that may then be
used in the study of the anisotropic permeability of the
formation. The gradient modulation may be produced by an
opposite sign pair as shown in Fig. 19, or by a pair of
identical pulses separated by a phase-inverting 180
pulse. If the mean velocity over time t for spins in a
position r is v, then the induced phase shift for that
position/voxel may be expressed as exp[ip = v(r)],
where p is the velocity encoding gradient (1)i (t) for a
non-zero first moment.
One pulse sequence for flow imaging of a constant
velocity flow is depicted in Fig. 19. A 90 RF sinc
slice selective pulse is applied together with the slice
selection gradient Gs. Thereafter, a positive bipolar Gs
gradient is applied together with the phase encoding
gradient G. The Gs slice selection gradient is applied
again with a 180 RF sinc pulse, followed by the
application of a negative amplitude read/frequency
gradient (to dephase the spins) and an immediate
application of a positive amplitude read gradient during
signal acquisition (again rephasing spins, thereby
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ensuring maximum amplitude at the center of the
acquisition period). The sequence of Fig. 19 is then
repeated but with a negative bipolar pulse. When the raw
signal from the positive and negative bipolar sequences
is subtracted and all of the stationary spin signal is
cancelled, the remaining signal is attributable solely to
the constant flow spins. Other pulse sequences and means
of achieving signal cancellation attributable to
stationary spins may be found in Callaghan, P. T.,
Principles of Nuclear Magnetic Resonance Microscopy,
pp. 429-34, Oxford Press (1991). When angiography
techniques are applied to formations in conjunction with
formation testers, and their induced flow, the MRI
device, as depicted in Figs. 3 and 4, may be used to
accurately measure the flow of the fluids within the
formation. Further, the same structures may be utilized
to perform conventional CPMG experiments to determine
formation characteristics and fluid typing.
See, e.g., Coates, G. R., et al., NMR Logging Principles
and Applications, pp. 77-90, Halliburton Energy Services
(1999).
c. Velocity and Diffusion Determination
The phase encoding techniques applied above may be
further processed to determine not only the velocity of
the flow of the connate fluids, but the self-diffusion of
the fluids themselves. This is done utilizing a
combination of k space and q space imaging. This
combined imaging technique is generally referred to as
dynamic microscopy. Recall that the concept of k space
imaging was first discussed with respect to Fourier
Imaging techniques above and represents a means for
interpreting the received NMR signal, where:
k = (27i- )-1 yGt
[26]
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where G is a component of the gradient. For
experiments with field gradient pulses of a certain
duration, 8, a reciprocal space vector q is similarly
defined by: [27]
/
/
q=(220-178G=¨ (40tõ di
A
0
where G is the effective intensity of the pulsed
field and A represents the time differential between the
centers of two antiphase pulses. in a gradient pulse
pair.
The pulse sequence for dynamic microscopy shown in
Fig. 20 is an example of a PGSE or pulsed gradient spin
echo sequence. In this sequence, a 900 RF sinc pulse is
applied in conjunction with the slice selection gradient.
A 1800 rephasing square pulse is applied, followed again
by the application of the slice gradient. A PGSE phase
gradient is then applied at varying values up to some
maximum value g for a period 8. A rephasing 180 square
pulse is again applied followed by the application of two
phase gradient sequences. This effectively eliminates
the velocity encoding and encodes the fluctuating
component of the velocity or acceleration. The effect of
the phase encoding sequences herein is to phase encode
the fluctuating component of velocity in q space while
preparing to sample k space.
Again, G has a different
value applied in equal steps to its maximum value.
The phase encoding Gy and frequency encoding Gx gradients
are then applied for varying values, the x gradient for
different positive x-values, the y values for both
negative and positive values and the signal is obtained.
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The signal obtained from the PGSE imaging pulse
sequence of Fig. 20, for a single PFG pair may be
expressed as:
S(k,q)= fp(r)exp[i2n- k = r] f13,(rIr' A.)exp I[127r q = (r ¨rldr' dr
[28]
where Ps(rle, A) is the conditional probability that for
a spin originating at time r will move to position r'
during the diffusion time between the onset of the two
field gradient pulses, A.
Equation 24 can be simplified for experiments with
pulsed field gradients by use of the echo attenuation
function, EA(q,r). Since in that experiment, the field
gradient pulses can be switched off, the intensity of the
,spin echo with field gradient pulses being applied can be
normalized to the intensity of the spin echo without any
applied field gradient pulses switched on during the
experiment. For stationary particles, EA(q,r) will have a
value of unity, while diffusion molecules will
reduce EA(q,r) to values smaller than one. This procedure
cancels all relaxation effects which otherwise would also
contribute to the attenuation of the spin echo amplitude.
The echo attenuation function as a function of q
space and position r in time A may be expressed as:
EA(q,r)=S13,.(rIr',A)exp(i2rt-q(r'¨r))dr1
[29]
which is the q Fourier transform of the local conditional
probability that a particle has moved from position r to
position r' during the time A.
Relating Equation 25 to Equation 24, the signal
intensity measured with a PFG NMR imaging sequence may be
written as:
S(k,r)= fp(r)EA(q,r)exp[i2n-k=r]dr
[30]
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In reviewing Eq. 26, the reconstruction of the signal
in k space can be expressed as p(r) EA(q, r), which will
provide a diffusion-weighted spin density at position r.
The q Fourier transform of the local conditional
probability set forth in Eq. 25 calls for an
infinitesimal volume dr, which as a practical matter, is
averaged over some 3d voxel. Given this background, one
may measure both velocity, acceleration and self
diffusion of the molecules being studied.
Fig. 21 illustrates the conditional probability
function P. A velocity and a diffusion map for each
voxel may be obtained by computing the width and offset
of Ps in Z space. In practice, dynamic profiles are
obtained by stepping the PGSE gradient G in np steps to
some maximum value Gm, followed by performing a digital
Fourier transform in q space for each voxel. As noted in
Callaghan, P., Principles of Nuclear Magnetic Microscopy,
Oxford University Press (1991), it may then be derived
that the mean molecular velocity for the voxel is
v=27z-nDki, I Nyg AGõ,
[31]
where N is the number of time domain points digitally
sampled. The diffusion value is then expressed as :
D = (nDkFri,H,02 I ((41n(2) 2 )2,2,52Gi2nN2A)
[32]
where kFWHM represents the full-width, half maximum value
in displacement space in the Z direction. See, Fig. 22.
This is simply one technique by which one can determine
both velocity of the flow and the self -diffusion of the
molecular flow.
d. Position Exchange Spectroscopy (PDXSY).
Yet another means for determining fluid flow
characteristics is the use of position exchange
spectroscopy (POSXY) 2-D Fourier Transform techniques.
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A POSXY experiment recognizes that the amplitude of the
echo is a function of the area of two differing field
gradient pulses. Since the area of the field gradients
are related to the length scale, a 2-dimensional plot
results in a probability density of finding a particle at
position 1 at time 1 and at position 2 at
time 1 + diffusion time. This allows one to map the
change of position of particles within the diffusion
time. A POSXY experiment provides a correlation diagram
of the average position with displacement by using pure
phase encoding techniques.
4. Real Time" Imaging Techniques
The imaging techniques discussed above are applicable
where the MRI apparatus stationary (in the instance or a
formation tester or drill stem tester) or moving at a
relatively slow logging speed. Again, the logging speed
is limited by the recovery times associated with the
above techniques. It will be appreciated that MRI
logging techniques are more likely to be a commercial
success where they can be applied at or near current
logging rates, e.g., 30+ ft./min. In order to achieve
MRI faster scan (and logging) times, one must consider
what factors go into limiting scan time. Spin echoes are
usually quite brief in nature and to a great extent are
limited by T2 times. Table 2 sets forth typical Tl and
T2 times encountered in the well logging context.
Fluid Tl (ms) T2 (ms) T1/T2
Brine 1 - 500 1 - 500 1
Oil 3,000 - 4,000 300 - 1,000 1
Gas 4,000 - 5,000 30 - 60 0.2 - 0.4
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TABLE 2
Source: G. R. Coates, et al., NMR Logging, Principles &.
Applications, Halliburton Energy Services, p. 78 (1999).
The necessary molecular spatial encoding required to
form an image cannot usually be performed in the above
time periods. Accordingly, the sequences are repeated
until there is sufficient data to complete any image.
Of course, when the sequences are repeated, the signal
amplitude is reduced. Eventually the S/N ratio is so low
that the formation under investigation must eventually
undergo total remagnetization before additional signal
can be obtained. However, the remagnetization of the
molecules is limited by Tl. It will be appreciated that
many of the techniques set forth above would requires
several seconds at each location in the borehole.
Several imaging techniques have been employed in the
medical field to allow for near real time video imaging.
These are generally a combination of pulse sequences, the
manner in which k-space is sampled and methods used to
improve the S/N ratio. The scan time for a volume is
generally follows:
Scan Time = TR x Number of Phase Encodes x NEX
[33]
where TR is the repetition time between successive RF
pulses; Number of Phase Encodes which determines spatial
resolution; and NEX is the number of averages of the data
required to form a sufficiently noise free image.
One means of reducing TR is to reduce the transverse
angle 0 from 90 to a lesser angle. This technique was
already touched on in the above discussion of Gradient
Recall Echo Imaging. The smaller 0, the less time
required for remagnetization (effectively decreasing Tl)
times; however, it also decreases, the strength of the
signal received in response to the RF pulses. It will be
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appreciated that merely reducing 0 to less than 50 will
have an adverse affect on the NEX value. This reduced 0
forms the basis for FLASH techniques.
a. FLASH Techniques
FLASH (Fast Low Angle SHot) techniques were
introduced into the medical field as a means of obtaining
complete imaging scans in the tens of seconds. In FLASH
techniques, the low angle excitation is used to sweep an
entire k space in a relatively short period of time.
With repetitive reading and relatively small TR/T1 times,
the FID signal amplitude may be expressed as:
M =M cos" sin()
0 [34]
where n is the number of times RF pulses are used to move
spins to angle 0. As noted above, the low 0 value
adversely effects the S/N ratio. Fig. 23 is a sequence
diagram for a FLASH technique that utilizes a "rewinding"
phase gradient in each cycle. The RF pulse is applied
along with the Gs slice gradient, that changes sign to
refocus the spins. The phase gradient is applied in
equal steps from its -Go to its Go; simultaneously, the
read gradient is turned on with a negative sign to assure
that the echo will be centered in the if the read period
when the read gradient is turned positive. The sequence
ends with the phase gradient "rewinding" the spins by
applying it from Go to -GM. The sequence is then
repeated n times. The particular sequence shown in
Fig. 22 is sometimes called a FAST SSFP (Steady State
Free Precession) is that by applying the rewinding
gradient, the transverse coherence of the spins is
retained to create a steady state free precession.
The result is that a complete sampling of k-space for
a FLASH image can be accomplished in less than a second.
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There are a number of differing low angle techniques that
may be used to decrease the TR time necessary to complete
a scan. Other low 8 sequences include CE-FAST, FISP,
FADE, Turbo FLASH and can be used to reduce the scan
times to less than a second for small areas of
investigation. A detailed discussion of the various high
speed/low angle techniques may be found in M. Cohen,
Rapid Imaging: Techniques and Performance
Characteristics, Radiology, Lippincott, New York, N.Y.
(1992).
b. K-Space Rapid Sampling Techniques
In an effort to decrease the k-space sampling time,
partial k-space sampling techniques may be used'.
MRI sequences measure the complex matrix, I(kx, ky).
In the absence of noise and other artifacts, the image
matrix in k-space may be expressed as follows:
[35]
Under these conditions, only half of the matrix need
be measured and the other half can be inferred. As a
practical matter, noise, field non-homogeneities, and
sample effects introduce a phase variation across the
matrix introduces error into the sampling. Corrections
can be made by sampling into the second half of the
matrix and assuming the phase variation to be linear, and
applying it to the inferred data. Two common techniques
used for partial k-space sampling are the Fractional
Echo, and Fractional NEX Imaging. The Fractional Echo
imaging technique is typically utilized in conjunction
with a spin-echo sampling sequence. The Fractional Echo
technique focuses on shortening the minimum echo time TE
and may be used with techniques such as FLASH for rapid
acquisition. Filling the k space data matrix column by
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column, the remaining data is extrapolated in the matrix
using the technique as follows:
k11 12 ki314 kll k * *
12
kn kn kn kv k * *
n kn
k31 k32 k33 k34 k31 k * *
32
k k * *
_ k41 k42 k43 k44_ _ 41 42 [36]
where * is the calculated complex conjugate value - kji*.
Fractional NEX Imaging or Half NEX techniques may also be
used to sample k-space and reduce the time required.
In reviewing the k-space image, the matrix I(Kx, Ky) can
be expressed as follows:
k -k k k k14
k21
k12k13," n u Pt
kn kn kn k24- k21k k k24
21 22 23
=
* * * *
km kn kn km
k41 k42 k 43 k44 * * * *
- - - [37]
where * is the calculated complex conjugate value - kji*.
Thus, in the example, only k11 - k24 need actually be
sampled, requiring only half of the time.
c. SPRITE Techniques
Yet a different means for creating essentially real
time images for fluid evaluation is the use of the SPRITE
(Single Point Ramped Imaging with Tl Enhancement).
Fig. 23A is a depiction of a SPRITE sequence. SPRITE is
a pure phase encoding Fourier Transform method that
employs broadband RF pulses to excite magnetization and a
ramped gradient in the primary phase encode direction (in
this instance Gx). The steps in this Gx gradient
typically last only a few milliseconds. K-space is
sampled on a point by point basis. It will be
appreciated that k-space sampling techniques discussed
above may be used to decrease the sampling time.
Fig. 23B is a depiction of this modified k-sampling
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technique in which slice selection is used to spin lock
the transverse magnetization for subsequent readout.
Thus, only half of the k-space is sampled.
These rapid imaging techniques are capable of
providing real time angiography information relating to
the flow of fluid within the formation as well as
borehole imaging. It will be further appreciated that
these techniques may be used in addition to known NMR
techniques within the well borehole.
5. Background Gradient Suppression
The above discussion relating to positional
measurement and self diffusion are within homogeneous
systems wherein Tl T2. However, such is not always the
case in the formation. However, in heterogeneous systems
that have components with differing magnetic
characteristics, a distribution of spatially dependent
background gradients for the differing components may
result in attenuation of the echo signal and the
introduction of systematic error in the measurement of
diffusion. Specifically, the background field
inhomogeneities can cause a decrease in the observed T2
times through the effects of translational diffusion of
the spins. In severe cases, it could result in erroneous
modeling of the formation or prevent the use of NMR
techniques altogether
Several PFG sequences have been proposed to address
these background gradients. Specifically, the use of an
alternating bipolar gradient pulse to minimize the
effects of the cross term (GaGo) created by the applied
gradient Ga and the background gradient Go. Several of
the techniques for suppressing background gradients were
discussed in Cotts, R.M., et al., Pulsed Field Gradient
Stimultated Echo Methods for Improved NMR Diffusion
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Measurements in Heterogeneous Systems, Journal of
Magnetic Resonance vol. 83, pp. 252-66 (1989). The paper
therein discusses the "nine", "thirteen" and "seventeen"
interval Hahn sequences, also known as Carr Purcell PFG
sequence, utilizing bipolar gradients. It describes the
spin echo factors in terms of the total effective
gradient g(t).
k = y G(t)dt
0 [38]
and
=7.1.0)dt
4 [39]
In attempting to minimize the cross terms
attributable to the background gradient, each of the
sequences discussed in the paper has two solutions:
Condition I.: (kp - kr) = 0
Condition II: (kp + kr) = 0
In Figs. 24A and B, an illustrative thirteen interval
sequence is set forth. In Fig. 24A, the true laboratory
gradient is set forth for Condition I. It will be noted
that the effective gradient is the same during the
preparation period as during the read period of the
sequence. Fig. 24B represents the applied polarities of
the system. As in the true gradient illustration, the
effective gradient is similar during the preparation and
read phases of the sequence. As noted therein
(See Eqs. [3] - [12]), the echo amplitudes for the
various sequences each includes a cross term GaGo.
By selection of the interval following the various pulse
sequences and the selection of the length of the gradient
pulse, one can minimize the effect of the cross term.
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With respect to a thirteen interval sequence, the echo
amplitude may be expressed as:
In[inI(Gotc) 4 3 3
= y 2
D[82 (4A+6 ¨2 8)Ga2 +2 vc5(81 ¨82 )Ga Go + ¨ Go
in1 (0, t, ) 3 = 3
[40]
for Condition I. As might be seen, the selection
of 81 = 82 effectively eliminates the cross term GaGo.
However, the thirteen interval sequence fails to
eliminate the cross term:
[mit (Gil, tc)1
2 6-2
4 3
In _________________ = ¨ 72D52 (4A+6 ¨ 8)G,2, +8 3
+s;) GaGo+ ¨ Go
[41]
However, the effect of this cross term may be
minimized by the selection of the length of the gradient
pulse.
While the 9 interval pulse sequence set forth in the
paper does similarly eliminate or minimize the cross
term, use of the 13 interval sequence assists in
attenuation of the signal which is important for
measurement of low diffusivities as may be seen where
measuring gas and one experiences long Tl times, despite
the existence of relatively short T2 times (See, Table 1,
supra). A modification of a Carr Purcell PFG sequence
such as the thirteen interval sequence may be utilized to
not only suppress background gradients as may be seen
downhole, but to provide additional information relating
to the correlation of displacement and imaging.
In Han, I. et al., Two-Dimensional PFG NMR Encoding
Correlations of Position, Velocity and Acceleration in
Fluid Transport, Journal of Magnetic Resonance vol. 146,
pp. 169-180 (2000), techniques for encoding additional
information that may be used to characterize the
position, velocity and acceleration of flow are
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described. In imaging with phase encoding, these
techniques can be extended to probe motion in more than
one direction. Therein, it is suggested that the
introduction of bipolar gradients stepped independent of
the other may be used for the purposes of encoding
information relative to the position and velocity of the
particles in the flow. It will be appreciated that by
being able to track motion in more than one direction,
one may be able to determine the source of the fluid
flow. When applied to a formation test tool, one may
determine anisotropic permeability characteristics from
the directional flow.
These concepts are generally referred to as POSXY
(position exchange spectroscopy) and VESXY (velocity
exchange spectroscopy).
The POSXY technique encodes average position on the
principal diagonal and position change corresponding to
velocity on the secondary diagonal. In one technique, The
gradients are stepped independently and are bipolar along
the secondary diagonal such that kl = -k2 resulting in a
wave vector in q space. See Fig. 25a. Along the
principal diagonal the two gradient pulses are unipolar
so that k = (k1 + k2)/2 is represented corresponding to
the average position between two time points t = 0 and
t = A. A 2D Fourier transformation permits one to
correlate the displacement of the spin packets with the
average position r parallel to the applied gradient
direction. This can then be used to determine an average
velocity of the spin packet by dividing the displacement
by the elapsed time A. In VEXSY, the pulse sequence
utilizes two independent bipolar gradient pulse pairs,
each covering an equal "area" or intensity
wherein 1(1 = -k2 and k3 = -k4. As noted therein, the
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application of a second set of gradient pulses k3 and k4
may be used to derive higher order derivatives, as
acceleration of the flow. See Fig. 25B The first anti-
phase pulse pairs are used to encode initial and final
velocities resulting in average velocity along the
principal diagonal fluctuating components of velocity or
acceleration on the secondary diagonal.
The present invention may utilize the POSXY and VESXY
techniques disclosed in the Han article in combination
with the thirteen interval sequence. An exemplary
proposed sequence of this type is depicted in Fig. 26.
The sequence is similar to the conventional sequence
depicted in Fig. 25a, with the exception of the nature of
the applied pulsed field gradients. The first gradient
pulse which encodes kJ., is stepped from between a range
G1 and -G1 for a period of 8a, whereas the second one
encoding k2 is stepped between a range G2 and -G2 for a
period of 8b. As noted in the Han article, the
requirement is that the intensity of the gradient paid be
such that k1 = -k2. Accordingly, the range for each of
the pulses need not be the same so long as the intensity
of the pulse is equal but negative. Pulsed gradients
producing 1c3 and k4 are shown as having similar
magnitudes and durations. While depicted as such in
Fig. 26, it should be noted that while kJ_ = -k2, k3 and
k4 need not be of the same intensity. The only
requirement is that k3 = -k4. The received signal
intensity is then plotted two-dimensionally as a function
of the area of the gradient pairs, kJ_ and k2, and k3 and
k4, which permits one to determine the correlation
=
spectrum of particle displacement, velocity with
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compensation of background gradients. Similarly, the
VESXY experiment of Fig. 25b may be extended to
background gradient compensation to yield a correlation
spectrum of velocity and acceleration corresponding to
the correlation of average velocity and diffusion
broadening. Fig. 26 does not depict the selection of the
polarization of the gradient pulses. The pulses may be
selected such that kJ_ is stepped by changing - G1 to G1
(a "-" pulse), while k2 is stepped by changing G2 to -G2
(a "+" pulse). It is contemplated within the present
invention that one could vary the sequence in which the
gradient pulse pairs are applied. For example the pulse
sequence could be + - +
or - + + -, or any sequence of
positive and negative pulses so long as the gradient
pulse produce pairs of equal but negative intensity with
respect to each other. In summary when combined with the
application of independent bipolar gradient pulses
subsequent application of a 2-D Fourier transformation
correlation centered around 180 RF pulses to replace
original gradient pulses in PDXSY and VEXSY, by spectra
of fluid displacement, velocity, and acceleation in the
formation as it flows into the snorkel of the formation
tester can be obtained. Here the background gradient
compensated PDXSY experiment is a 2D version of
the 13 interval sequence.
Further modifications may be made to the 13 interval
sequence. For compensation of magnetization dephasing in
quadratic fields, each gradient pulse of the original
sequence is replaced by an antiphase pairs of antiphase
gradient pulses involving two 180 RF pulses,
where k1 = -k2 = -k3 = k4 and k5 = -k6 = -k7 = kg.
Fig. 27. In a similar fashion the VESXY experiment of
Fig. 25b for correlation of velocity and acceleration may
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be modified to account for compensation of linear,
quadratic, and other non-linear background field
profiles.
Conclusion
The present invention discloses various RF antenna -
permanent magnet - EM coil structures that may be used to
carry out pulsed field gradient experiments, including
eccentered (near borehole wall) structures and borehole
centered devices. The present invention discloses a
means for directly determining permeability as a function
of fluid flow images, including directional flow to
determine anisotropic permeability. The present
invention further discloses the application of various
MRI imaging techniques that may be used to image the
formation about the borehole for the disclosed
structures. The present invention discloses means for
creating azimuthally sensitive MRI images of the
formation about the borehole. The present invention
further discloses a means for inducing flow from the
formation using a formation test tool and imaging the ,
formation fluid characteristics and determining self-
diffusion of the fluid. These MRI imaging techniques may
be used in conjunction with known NMR logging techniques
to determine porosity, permeability and determining the
character of the fluids within the formation.
The present invention further discloses MRI imaging
techniques that may be used in conjunction with test
tools that induce flow from the formation into the
borehole, thereby measuring formation flow rates and
obtaining a more accurate determination of permeability
of the formation.
While the present invention has been described in
terms of various embodiments, modifications in the
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apparatus and techniques described herein without
departing from the concept of the present invention.
It should be understood that the embodiments and
techniques described in the foregoing are illustrative
and are not intended to operate as a limitation on the
scope of the invention.
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