Note: Descriptions are shown in the official language in which they were submitted.
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POROSITY AND PERMEABILITY MEASUREMENT
OF UNDERGROUND FORMATIONS CONTAINING CRUDE OIL,
USING EPR RESPONSE DATA
'T'E HNTC' .~T, FIELD OF THE INVENTION
This invention relates to locating subterranean
formations of crude oil, and more particularly to
determining porosity and permeability parameters of such
formations.
BACKGROUND OF THE INVENTION
Technological advances in crude oil exploration are
permitting crude oil to be captured from locations
previously considered to be impractical or unprofitable.
For example, nuclear magnetic resonance (NMR) technology
has been used for well logging applications to measure
hydrogenous materials located a short distance into the
earth's structure about the bore hole. NMR can
simultaneously sense the hydrogen in water and in oil and
other materials that may be present within the sensitive
measurement region, and thereby indicate the presence and
amount of those materials.
Sometimes the water and oil constituents contributing
to the total NMR response signal can be resolved to the
allow concentration of each to be determined. In other
cases, separate measurements of the oil and water may not
be feasible with NMR alone.
When the hydrogenous material is contained within an
underground rock formation, NMR techniques may be used to
determine pore size distribution and the porosity and the
permeability of the rock. With this information, a
decision can be made whether a particular rock formation
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contains a sufficient amount of recoverable fluid such that
drilling is profitable. However, NMR porosity and
permeability estimates do not typically attempt to
differentiate between the effect of varying proportions of
oil and water in the fluid.
SL~ARY OF THE INVENTT_ON
The invention uses a magnetic resonance technology,
specifically electron paramagnetic resonance (EPR), also
known as electron spin resonance (ESR), to detect and
measure the concentration of crude oil and certain other
hydrocarbon solids and liquids contained within underground
formations. Such detection and measurement may be obtained
from the surface of the earth to appreciable depths below
the surface. They may also be obtained from locations
adj acent to the walls of natural openings in the earth' s
surface (such as caves, open faults, cliffs, sink holes,
and hillsides) or in man made earth penetrations (such as
tunnels, wells, trenches or boreholes).
The use of EPR data is particularly advantageous in
that EPR response signals emanate only from unpaired
electrons, such as those due to broken bonds in high
molecular weight (MW) hydrocarbon compounds, in
paramagnetic and ferromagnetic materials, and in a few
metals. In naturally occurring materials, broken bonds and
paramagnetic ions are commonly found in, but not limited
to, many crude oils, asphalts, and coals. The presence of
these materials in the earth, or elsewhere, may be detected
and measured by the invention.
The invention provides rapid detection and measurement
as compared to other magnetic resonance methods, such as
nuclear magnetic resonance (NMR). The time required to
polarize and measure such electrons is commonly on the
order of a few microseconds or less.
The invention also includes the use of EPR in
combination with nuclear magnetic resonance (NMR) tc
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provide additional advantages, particularly in well logging
applications.
BRIEF DESCRIPTION OF THE DRAWINGS
FIGURE 1 illustrates an NMR/ESR detector in accordance
with the invention.
FIGURES 2A - 2K illustrate various embodiments of
antenna of FIGURE 1.
FIGURES 3A - 3G illustrate various embodiments of the
magnet of FIGURE 1.
FIGURE 4 illustrates the magnet and antenna of FIGURE
1, and a second antenna, such that the generation of the B:
field and the detection of response signals are performed
by two different antennas.
FIGURES 5A - 5D illustrate EPR signals from four
different crude oil fields, respectively.
LED DESCRIPTION OF THE INVENTION
The invention described herein is directed to
obtaining and interpreting EPR (electron paramagnetic
resonance) data from crude oil contained in formations and
structures beneath the earth's surface. As explained
below, the ESR data can be used in conjunction with NMR
(nuclear magnetic resonance) data to determine porosity and
permeability features. EPR is also known as electronic
spin paramagnetic resonance (ESR).
FIGURE 1 illustrates an EPR detector 100 in accordance
with the invention. As explained below, FIGURE 1 is an
illustrative embodiment, and many variations of this
embodiment are within the scope of the invention.
Essentially, detector 100 generates the magnetic fields
for obtaining an EPR response signal, and receives and
analyzes the EPR response signal to determine the crude oil
content of an underground formation.
The EPR analysis performed by detector 100 can be
supplemented with an NMR analysis, by also using the same
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detector 100 to generate the magnetic fields appropriate
for obtaining, receiving and analyzing an NMR response
signal. Although the following description of FIGURE 1 is
in terms of EPR detection, detector 100 may also be used
for NMR detection. As explained below, the use of both EPR
and NMR response signals, permits not only crude oil
content to be determined, but also characteristics of the
underground formation, such as pore size.
A magnet 101 produces a magnetic field of intensity Bo
(in gauss) in a sensitive region. As explained below, EPR
signals may be detected from materials in the sensitive
region.
A transmitter 102 provides power at frequency fo,
through duplexer 103 (or circulator or coupler) to antenna
104. The result is an electromagnetic field of intensity
B1 (in gauss) in the sensitive region. For maximum detection
sensitivity, the plane of the B1 field is perpendicular to
that of the Bo field. The sensitivity of detector 100
generally varies as a function of sin6 where 8 is the angle
between the B1 and Bo field vectors.
In addition to transmitting electromagnetic field
waves, antenna 104 receives an EPR response signal from the
material in the sensitive zone. The incoming signal is
delivered via duplexer 103 and filter 105 to a radio
frequency (RF) amplifier/detector 106.
As explained below in connection with FIGURE 4, as an
alternative to using the same antenna 104 for both
transmission and reception, a second (receiving) antenna
may be used for reception of the EPR response signal. This
receiving antenna would be located in view of the sensitive
zone, and connected through filter 105 to RF
amplifier/detector 106. The receiving antenna could be
oriented and located to reject direct pickup of the
transmitter signal from the transmitting antenna 104, while
obtaining maximum pickup of the cross polarized component
of the EPR response signal from the sensitive zone. If a
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separate receiving antenna is used, then duplexer 103 is
not required and transmitter 102 may be connected directly
to the transmitting antenna 104.
To provide the EPR response signal with a unique
5 identification signature, such as for detection in a
"cluttered" or "noisy" background, detector 100 may
incorporate a modulation feature. A variety of different
modulation techniques may be used either singly or in
combination. Coils 107 may be used for this purpose,
energized with ac current.
One modulation technique involves modulation of the
intensity of the magnetic field, Bo. As an example, Bo may
be slowly swept through resonance, and the peak amplitude
of the detected signal detected and recorded. The presence
of a signal at a specific range of the sweep is detected.
Combining the slow sweep with low frequency field
modulation (i.e. typically under 100 MHZ) using coils 107,
allows synchronous detection of the EPR signal at the AC
modulation frequency as well as improves the stability and
useable detection sensitivity.
A fixed Bo field for electron magnetic resonance on the
transmitter frequency, fo, may be modulated by a high
frequency current of frequency, fl, in coils 107. As a
result, any EPR response from material in the sensitive
region will contain spectral components of fo as well as of
fo f fl. If fl is greater than the line width of the normal
EPR signal, then filter 105 may be set to pass only the
upper (f~ + fl) or lower (fo -fl) sideband and to reject the
strong direct transmitter signal at frequency fo. The
sideband signal amplitude will be proportional to the
unpaired electrons in the sensitive region. Quadrature
detection means may be used to recover both upper and lower
sidebands simultaneously while rejecting fo for more
sensitive detection. A frequency controller 109 uses
detected data to maintain the frequency of transmitter 102
on the EPR frequency.
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Another modulation method uses transmitter 102 to
produce pulsed RF signals of the EPR frequency, fo. The
pulses are short compared to a relaxation time, T2, which is
explained below. For example, the pulse duration might be
the reciprocal of the spectral line width. For EPR, such
conditions typically require pulses having a duration
within a range of 2 to 10 nanoseconds. The field
modulation coils 107 and field modulator 108 are not
required for the pulse mode.
The EPR response signal is received by
amplifier/detector 106. A data processor 110 stores and
executes programming appropriate to perform various
calculations, which are explained below. As explained
below, processor 110 analyzes the EPR response signal, and
may also analyze an NMR response signal. It is assumed
that processor 110 has appropriate processing memory and
program memory for executing the programming. A user
interface 111 may provide a display and/or printout of the
results of the calculations.
FIGURES 2A - 2K illustrate a variety of embodiments of
antenna 104. In the following discussion, each different
antenna 104 is identified as antenna 104[2X], with the 2X
corresponding to the associated figure number 2A -2K.
FIGURE 2A illustrates a loop antenna 104(2A). The
loop 201 is tuned to the ESR frequency by a capacitor 202.
The loop 201 may be round, square, rectangular or any shape
and may be open or closed as shown. It may be of a single
turn or multiple turns and may be fed by an impedance
matching coupler or by a section of open transmission line
to form a high "Q' resonant cavity with the loop
unshielded.
FIGURE 2B illustrates a capacitive loaded loop antenna
104(2B), which is made up of wire or metal strip segments
203 separated by capacitors 204, which tune out part of the
reactance. This allows a larger area to be made resonant at
a higher EPR frequency than would be possible without
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capacitors 204. Loop antenna 104(2B) is coupled to detector
100 through an impedance matching network which may also
act with antenna 104(2B) as a high "Q" resonator.
FIGURE 2C illustrates a resonant half-wavelength
dipole antenna 104(2C), which is coupled to detector 100
through a matched transmission line. Antenna 104(2C) may
be located in close proximity and parallel to the plane of
a metal plate to improve the directivity and increase the
Q.
FIGURE 2D illustrates a crossed dipole antenna
104(2D). The two dipoles 205 and 206 are perpendicular to
each other and electronically phased at 90 degrees to each
other to produce a circularly polarized wave or at 0 or 180
degrees to produce a linear polarization. The crossed
dipole antenna 104(2D) may also be located in close
proximity to the plane of a metal plate 207 to improve the
directivity and increase the Q.
FIGURE 2E illustrates a microstrip "patch" antenna
104(2E), which has a metal conducting layer 209 separated
by a thin low-loss dielectric 210, from a metal backing
plate 211. Layer 209 is approximately one-half wavelength
electrically square and may be fed by an impedance matched
coaxial transmission line from a tap point and the backing
plate 211 to produce a vertical H-plane wave, a horizontal
H-plane wave, or circular polarized wave, as selected by
the position of the tap point. Layer 209 may be round or
elliptical or rectangular. Patch antenna 104(2E) has a
high Q and a directivity that are controlled by its
physical size, the thickness of insulation layer 210, the
dielectric constant of insulator layer 210, and the size of
backing plate 211. Multiple patch antennas 104(2E) may be
used in an array and appropriately phased to produce
greater directivity, a larger near field sensitive region,
and a far field of reduced beamwidth. The layer structure
of antenna 104(2E) may be curved to fit around a portion of
a round pipe or rod.
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FIGURE 2F illustrates a rectangular patch antenna
104(2F) and FIGURE 2G illustrates a rectangular patch
antenna 104(2G) on a curved backing. The metal conducting
layer 212 is resonant at the frequency fo being
substantially one-half wavelength long, but substantially
less than one-half wavelength wide. These antennas may be
used to generate a linear polarized wave, but not a
circularly polarized wave.
FIGURE 2H illustrates a phased dipole array antenna
104(2H), comprising a configuration of phased, vertical
dipoles 220 mounted around the periphery of a metal tube or
rod 221. The 220 dipoles are spaced from rod 221 by a
distance selected to meet physical size, impedance, and Q
constraints. Antenna 104(2H) is intended for use in bore
holes to determine properties of the formation outside the
bore hole. The dipoles 220 are electrically phased at 90
degrees relative to each other by feed line network 222 to
produce a circular pattern about rod 221 with the H-field
encircling the rod 221. Rod 221 could be magnetized axially
to produce H-field lines parallel to the rod. This causes
a sensitive zone to encircle rod 221 at a distance where
the B-field intensity is adequate for EPR or NMR at the
transmitter frequency. Additional encircling arrays of
dipoles 220 may be used around rod 221 to extend the axial
length of a sensitive region in the formation that is
coaxial with and along the axial direction of rod 221.
FIGURE 2I illustrates a phased patch array antenna
104(2I), which is similar in concept to the antenna of
FIGURE 2H, except that patch type antennas 223 are used in
the phased encircling array. Antenna 104(2I) is
particularly advantageous because it may be mounted to
directly fit the contour of the rod 224 (or magnet) due to
a metal backing plate. The encircling patches 223 are
electrically phased at 90 degrees by a feed line network to
produce a circular sensitive zone that is coaxial with the
magnet. By selection of the feed point the H-field from the
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patch array may be made vertical, horizontal or circular to
allow a match to the requirements of different magnetic
field directions and configurations. Patch arrays may be
stacked vertically along the rod to extend the length of
the sensitive region.
FIGURE 2J illustrates a horn antenna 104(2J), which
provides a directive pattern and field concentration that
can extend the useful range between the ESR sensor and the
sensitive region of the material. The H component of the B:
field may be vertical or horizontal, as required to make
the B1 field perpendicular to the Bo field.
FIGURE 2K illustrates a solenoid coil or helical
antenna 104(2K). The helical configuration is approximately
one wavelength in diameter. The sensitive region extends
along the axis from one end of the coil. The directivity
increases with number of turns. A backing plate
(reflection) is used at the feed end.
FIGURES 3A - 3G illustrate a variety of embodiments of
magnet 101. Each of these magnets 101 provides the Bo field
required to establish resonance at the selected EPR
frequency. In the following discussion, each different
magnet 101 is identified as magnet 101[3X], with the 3X
corresponding to the associated figure number 3A -3G.
FIGURE 3A is a loop type electromagnet 101(3A), which
carries an electrical current and produces a magnetic field
that is oriented perpendicular to the plane of the loop.
The current may be a DC current to provide a static
magnetic field, in particular, a static magnetic field that
adds to the earth's magnetic field intensity in the area of
the loop and in the spatial volume extending both above and
below and around the loop area. The current may be an AC
current of a selected frequency to modulate the magnetic
field intensity as described above. The loop may have a
round, square, rectangular, triangular, or non-uniform
shape . Its size is comparable to the maximum distance to
the desired locations of the sensitive region outside the
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area of the loop. The loop may be operated on the surface
of the earth, for example, for detection of EPR signals
from materials below the surface of the earth.
Electromagnet 101(3A) could be oriented to provide a
5 polarized Bo field in the desired spatial region. Two loop
antennas 101(3A) may be used side by side in the same plane
to produce a magnetic field component, parallel to the
plane and both above and below the loops, in the space
between the loops. Antenna 104 would be oriented to
10 provide the properly polarized B1 field in this region.
FIGURE 3B illustrates a rod magnet 101(3B), which
provides a field along the axis and a near coaxial Bo field
along its length. The Bo field intensity decreases as a
function of distance away from the diameter of rod antenna
101(3B), but is constant at all angles in a plane
perpendicular to the axis. At a given radial distance, the
magnetic field varies symmetrically above and below the
center of magnet 101(3B). The magnetic field is generally
oriented parallel to the axis but deviates substantially
near the end of the rod magnet 101(3B). The antenna 104
used with magnet 101(3B) should produce a B1 field that is
oriented parallel to a plane that is perpendicular to the
Bo field lines. That is, B1 is generally perpendicular to
the axis of magnet 101 (3B) . The most sensitive region is
where the Bo and B1 lines are perpendicular and where B
causes an EPR response (and/or NMR response, if used) at
the desired frequency(s). Rod magnet 101(3B) may be a
permanent magnet or a solenoid type of electromagnet.
FIGURE 3C illustrates a U-shaped magnet 101(3C), whose
open faces are its poles. The B1 field of interest is
oriented vertically. The sensitive region is outside the
physical extent of the poles and in the vertical region
corresponding to the area of the gap. The field intensity
generally decreases as a function of distance away from the
plane of the poles. A ferromagnetic plate 31 between the N
and S poles provides a spatial region over a specific
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distance range (from the plane of the pole faces) in the
sensitive zone, over which the Bfl field is more uniform than
without plate 31. Antenna 104 is located in the gap
between the poles and oriented to produce a B1 field in the
horizontal plane, that is, perpendicular to the plane of
the poles. The angular coverage of Bo about the pole-to-pole
axis of magnet 101 (3C) is a maximum of under 90 degrees.
Over this angular range the position of the line of
constant intensity, relative to this axis, varies. Magnet
101(3C) may have a square or rectangular cross section as
shown, or it may be round.
FIGURE 3D illustrates another U-shaped magnet 101(3D),
which provides a uniform field, as a function of angle
about the axis, over 360 degrees. The poles are of uniform
magnetic intensity around the complete circumference and
polarized radically with the connecting rod (or tube),
providing additional magnetic field or a ferromagnetic
return path. The Bo field is oriented from pole-to-pole and
extends radially outward from the magnet about the gap
between the poles. The Bo field generally decreases with
radial distance. However, use of a shunt in the gap, the
shunt being a length of ferromagnetic tube of selected wall
thickness and diameter (near that of the poles), will
provide a region of reduced gradient at a selected range of
radical distances. The antenna 104 is located in the gap
between the poles and outside the ferromagnetic shunt and
produces a B1 field perpendicular to the Bo, preferably of
uniform intensity as a function of angle about the axis.
The antenna of FIGUREs 2B and 2I are particularly
useful with magnet 101(3D) and produce a sensitive region
of a "donut" or cylindrical shape at a selected distance
about magnet 101(3D). The Bo field is appropriate for EPR
(or NMR) at the selected transmitter frequency.
FIGURE 3E illustrates an enhancement for certain of
the above-described magnets to minimize the loss of
magnetic flux out of the top and bottoms of the magnets .
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The main magnet 32 could be magnet 101(48), 101(3C), or
101(3D). Auxiliary magnets 33 and 34 are polarized similar
to the ends of the main magnets to force more lines of flux
outward, radially, and increase the intensity of the B~
field.
FIGURE 3F illustrates a magnet 101(3F) that is
polarized perpendicular to the axis, and that produces a B~
field that is also polarized perpendicular to the axis. The
Bo field region of interest is perpendicular to the plane of
the poles and decreases in intensity as a function of
distance away from magnet 101(3F). The B1 field is polarized
along the plane of the axis. The sensitive zone is
perpendicular to the plane of the poles and along the axis
at a selected distance from the center line.
FIGURE 3G illustrates a magnet 101(3G), which is
similar to magnet 101(3F), except that it is round to
better f it in a bore hole . A slot on each side permits
antenna 104 to be within the selected overall diameter.
FIGURE 4 illustrates one example of a magnet 101 and
antenna 104 combined for stimulating and sensing EPR
response signals. The U-shaped magnet 101(3C) provides the
Bo field in the sensitive zone. Antenna 104(2C), mounted in
the gap, provides the B1 field. As illustrated, a second
antenna 104(2C), oriented perpendicular to the first
antenna may be used. The two antennas 104(2C) are shielded
from each other to the extent possible. One antenna 104(2C)
is the transmit antenna to generate the B1 field. The other
antenna 104(2C) is the receive antenna to intercept the EPR
response signals from the materials being measured. Both
antennas have a direct and unshielded path to the sensitive
region. The configuration of FIGURE 3 is an alternative to
the embodiment of FIGURE 1, where a single antenna 104(2C).
functions both to generate the B1 field and to intercept the
EPR response signals from the material in the sensitive
region.
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Qp Prar; nn of the 'invention
The method of the invention involves obtaining and
analyzing EPR response data from an underground rock
formation. The result is a determination of the crude oil
concentration in the underground formation. NMR response
data may also be obtained and analyzed to provide
additional information about characteristics of the
formation, such as its porosity and the total hydrocarbon
materials in the formation.
Equipment for obtaining NMR data is known in the art
of oil exploration. The same magnets 101 and antennas 104
as those described above for obtaining EPR response signals
may be used. However, different control electronics will
be more suitable for NMR because of the difference in
polarization times, excitation frequency, and response
signal sensitivity. For example, NMR polarization times
are typically 0.2 to 0.8 seconds for oil and 2.0 to 2.5
seconds for water, whereas polarization times for EPR are
in the order of microseconds. In the same static magnetic
field, EPR frequency is greater than that of NMR by a
factor of about 658 and the sensitivity is proportionally
greater.
For obtaining the NMR data, the material to be
evaluated is located in a static magnetic field Bo. For
transient NMR, the material is also preferably exposed to
one or more pulses of a radio frequency (RF) field, B1.
Selected nuclei in the material will absorb energy from the
B1 field, and will produce a detectable response when the RF
frequency, vo, is related to the Bo field, by the Larmor
equation:
v~ = y B~/2~ ( 1 )
where y is the gyromagnetic ratio of the particular
absorbing nuclei. Following the RF pulse (or pulses), the
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resonating nuclei precess in the field at an angular
frequency, coo, and will induce small transient signal
voltages in an adjacent sensor coil. These NMR signals are
the magnetization decay signals. This method is generally
called time domain NMR, and the peak amplitude of the
response signal is proportional to the concentration of
selected atomic specie (e. g. hydrogen) in the measured
volume of material.
When nuclei absorb energy, thermal equilibrium is
disturbed and the absorbed energy is exchanged
exponentially with the surroundings. These exchanges are
characterized by two preliminary time constants: the spin
lattice (T1) and the spin-spin or transverse (T2) relaxation
times. The first time constant, T1, is related to the time
required for nuclei in the material being measured to
become polarized in a magnetic field. T1 also sets the
minimum time that the material must be exposed to a
magnetic field prior to an NMR measurement and it
determines how rapidly NMR measurements can be beneficially
repeated on the same sample. The second time constant, T2,
determines how rapidly the NMR signal decays in a perfect
magnetic field.
In general, low-field NMR measures three useful
parameters: the equilibrium nuclear magnetization, M~, which
is proportional to the total signal amplitude and to the
fluid-filled porosity, and T1 and T2 , which are the two
relaxation time constants. These parameters can be
correlated with petrophysical properties such as pore size,
producible fluid, and permeability.
In fluid-saturated porous rock, the fluids may
interact with the rock surface to promote NMR relaxation.
As a result, the T2 values for fluids in pores can be
shorter than for bulk fluids. In the fast diffusion limit,
the T2 relaxation rate, 1/T2 , is proportional to the
surface-to-volume (S/V) ratio of a pore, such that:
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1/Tz = p (S/V) pore (2)
The factor p is the surface relaxivity, which is a
measure of the rock surface's ability to enhance the
5 relaxation rate. It falls within a reasonably narrow band
for a broad sampling of sedimentary rocks and is typically
a few micrometers per second. For example, p is
approximately 0.0005 cm/s for carbonates, and is
approximately 0.0015 cm/s for sandstone. The volume, V, is
10 the pore size. The surface area, S, varies depending on
the shape of the pore and the roughness of the surface.
Permeability estimation using NMR is based on the fact
that permeability has dimensions of length squared, and
uses the pore size obtained from NMR data. By knowing S/V
15 for the pore, the permeability of a porous medium can be
estimated. For carbonate, the following estimate for
permeability, k, can be used:
k = ~4(V/S)2 (3)
where ~ is the porosity. Thus, the permeability is
proportional to (1/T2)z.
Porosity also may be measured from the NMR signal
amplitude. NMR proton magnetization amplitude is directly
proportional to the fluid-filled porosity. In the
excitation sequence (90° - t - 180° - echo - delay) for
spin-spin relaxation measurement, if a fluid is assumed to
be contained in a single pore size, the echo following the
180° rotation of the magnetization vector is given by:
M(t) - Mo exp(-t/T;) (4)
where Mo is the magnetization at equilibrium, and M(t) is
the observed magnetization as a variable delay time, t,
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between the 90° and 180° measurement pulses. For a porous
rock, the observed magnetization will depend on various T2
parameters of all pores, that is, on the various pore
sizes.
Because the NMR relaxation time is proportional to
pore size, and it is known that rocks have broad
distributions of pore sizes, NMR transverse relaxation (T2)
data can be expressed as a sum of exponential functions:
M(t) - ~ Mi exp(-t/T2i) (5)
where Mi is proportional to the number of spins with
relaxation time constant T2i . M (t ) is the sum of all NMR
magnetization decays of the fluid-saturated rock.
The preceding equation fox M(t) can be inverted into
a T2 relaxation time distribution. Thus, instead of
estimating a single relaxation time from magnetization
decay, a spectrum (distribution) of relaxation times,
M (T2i) , is estimated.
Computing a T2 spectrum from M(t) is not
straightforward. The relaxation time, T2, is a function of
the type of fluid, proton frequency, temperature, pore
surface chemistry, and pore size . For a porous rock, the
observed magnetization will depend upon the T2 (i.e., pore
size) of all pores. The variation of magnetization with
time may be obtained by summing over all T2's:
M(t) - Mo J exp(-t/T2) f (T2) dT2 (6)
, where the limits of integration, T2min and T2max represent
the smallest and largest values of T2 expected for the
particular rock. T2max may be taken to be the value for the
bulk fluid used to saturate the pores. The function, f(T2),
is the desired T2 distribution, which is related to the pore
volume distribution. The extraction of f(T2) from the
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observed magnetization, M(t), requires the solution of the
preceding equation.
In water-saturated rocks, the bulk water relaxation
rate, (1/T2B) is often negligible because the bulk water
relaxation time, T2bulk~ is about 2-3 seconds. However, for
water in pores, T2 is only from several milliseconds to a
few hundred milliseconds, and the distribution of T2 arises
from the distribution of surface-to-volume ratios of the
pores, as shown above. Because T2 depends linearly on pore
size, the T2 distribution corresponds to pore size
distribution, with the largest pores having the longest
relaxation times. It can be concluded that if Mi in the
preceding equation is plotted against T2i, it can be
rescaled according to the above equation for 1/T2 to obtain
the pore size distribution. This M versus T2i data is a
useful way to present NMR relaxation data.
The above calculations assume that the rock is filled
with a given fluid. However, in practice, the fluid is
comprised of both water and oil, which affect the NMR data
differently. For example, oil has a proton density that is
about 5-15% higher than for water. For this reason, and
others, it is not always possible to obtain accurate
porosity and permeability estimates from NMR data alone.
For this reason, detector 100 is used to acquire EPR data.
Electron paramagnetic resonance (EPR) is similar in
principal to NMR, but the response is due to unpaired
electrons or free radicals instead of nuclei. When a sample
with unpaired electrons is placed in a static magnetic
ffield of strength Bo, there is an interaction between the
electrons and the magnetic field. The two spin orientations
of an electron, which are degenerate in the absence of the
magnetic field, are split when they are placed in a
magnetic field. The degree to which they are split depends
on the strength of the applied magnetic field.
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18
To effect transitions between these energy levels, a
resonance condition must be fulfilled. Expressed
mathematically:
(6)
~c = g~oBo
where g is a spectroscopic splitting factor and (3o is the
Bohr magneton of the electron. Typically, for free radicals
(unpaired electrons), measurements in the laboratory are
made at X-band. For resonance, the Bo field is around 3300
gauss and the EPR frequency is centered about 9.25 GHz
(nominal).
EPR occurs at a nominal frequency of 2.8 MHZ per gauss
of the static magnetic field, which is about 658 times as
great as for NMR in the same magnetic field. Consequently
most laboratory EPR work is carried out at microwave
frequencies (GHz). For better (deeper) penetration of the
formation, EPR for borehole and other earth measurements
uses relatively low frequencies and modest magnetic fields.
These range from 28 to 2800 MHZ and 10 to 1000 gauss,
respectively.
FIGURES 5A -5D illustrate EPR signals from crude oil
obtained from four different oil fields. The static
magnetic field strength (in gauss) is plotted against the
amplitude of the EPR response signal. EPR signals are not
produced by water or gas, but are produced by many, if not
all, crude oils. By using EPR to sense the oil in fluid-
rock, the amount of oil can be directly measured. The
amplitude of the EPR signal is proportional to the amount
of the oil inside the rock. For a known volume of the
sensitive region, a concentration of crude oil per unit
volume can be determined. Although not all crude oils have
the same signal amplitude for a given concentration,
calibration factors for the type of oil can be readily
determined and applied. In addition, EPR spectra can
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provide information about some oil constituents. In FIGURE
5D, there is an additional resonance peak, which is
possibly due to contributions from two or more radical
species with different heteroatom compositions.
Using a combination of EPR and NMR measurements, the
components of water and oil in the NMR signal can be
separated. Specifically, by subtracting the concentration
of crude oil from the concentration of total hydrogen-
bearing material, the concentration of water is known.
Based on a number of facts, the components of water
and oil in a rock sample can each be accurately measured
from a combination of EPR and NMR measurements. These
facts include: an EPR response signal is produced by crude
oils but not by water, the proton density in oil is about
5 - 15% higher than water on a volumetric basis, and the
surface relaxivity for oil is about one-third that of
water. The relationship between pore size and the T2
relaxation rate, as expressed above, can be rewritten as:
I /T2 = fwater pwater (S/V) pore + foil poil (S/v) pore
where pwater and poil are the surface relaxivities, and fwate_
and f~:.y are the fraction weights, for water and oil
respectively. As indicated, the relaxation rate is a sum
of two terms: one representing the effect of crude oil and
one representing the effect of water.
When oil and water coexist in a pore, the relaxation
rate (1/T2) of fluid in contact with rock surfaces is
enhanced by those surfaces. The fraction of oil in a water-
oil mixture can be used to increase the accuracy of the
calculation of 1/T2. This, in turn, increases the accuracy
of estimates of pore size distribution and permeability of
the rock formation about boreholes or in fluid-saturated
cores.
For example, for 50% oil and 50% water mixtures, if in
a carbonate, pwater is 0.0005 cm/s, poii is (1/3) 0.0005 cm/s,
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and T2 is 0.5 seconds, then from the above equation, the
calculated pore diameter is 10 microns. However, if only
NMR measurements were used, the calculated pore diameter
would be 15 microns. The permeabilities for 10 and 15
5 micron pore sizes are 0.04 and 0.09 microns squared,
respectively, resulting in a nearly 2:1 difference.
Other Embodiments
Although the present invention has been described in
10 detail, it should be understood that various changes,
substitutions, and alterations can be made hereto without
departing from the spirit and scope of the invention as
defined by the appended claims.
