U.S. patent application number 14/853519 was filed with the patent office on 2016-01-07 for determination of oil saturation in reservoir rock using paramagnetic nanoparticles and magnetic field.
This patent application is currently assigned to BOARD OF REGENTS, THE UNIVERSITY OF TEXAS SYSTEM. The applicant listed for this patent is Steven L. Bryant, Chun Huh, Keith P. Johnston, Thomas E. Milner. Invention is credited to Steven L. Bryant, Chun Huh, Keith P. Johnston, Thomas E. Milner.
Application Number | 20160002523 14/853519 |
Document ID | / |
Family ID | 44060317 |
Filed Date | 2016-01-07 |
United States Patent
Application |
20160002523 |
Kind Code |
A1 |
Huh; Chun ; et al. |
January 7, 2016 |
DETERMINATION OF OIL SATURATION IN RESERVOIR ROCK USING
PARAMAGNETIC NANOPARTICLES AND MAGNETIC FIELD
Abstract
Methods for detection of the presence and distribution of oil in
subsurface formation are described herein. The present invention
involves injection of an aqueous dispersion of the nanoparticles
into the potentially oil containing subsurface formation, followed
by a remote detection of the oscillation responses of the
nanoparticles in the oil/water interfaces in the reservoir rock by
applying magnetic field.
Inventors: |
Huh; Chun; (Austin, TX)
; Bryant; Steven L.; (Austin, TX) ; Milner; Thomas
E.; (Austin, TX) ; Johnston; Keith P.;
(Austin, TX) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Huh; Chun
Bryant; Steven L.
Milner; Thomas E.
Johnston; Keith P. |
Austin
Austin
Austin
Austin |
TX
TX
TX
TX |
US
US
US
US |
|
|
Assignee: |
BOARD OF REGENTS, THE UNIVERSITY OF
TEXAS SYSTEM
Austin
TX
|
Family ID: |
44060317 |
Appl. No.: |
14/853519 |
Filed: |
September 14, 2015 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
13508611 |
Aug 6, 2012 |
9133709 |
|
|
PCT/US2010/057080 |
Nov 17, 2010 |
|
|
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14853519 |
|
|
|
|
61262037 |
Nov 17, 2009 |
|
|
|
Current U.S.
Class: |
507/224 ;
507/228 |
Current CPC
Class: |
C09K 2208/10 20130101;
G01V 3/082 20130101; Y02A 90/344 20180101; E21B 47/11 20200501;
E21B 49/00 20130101; C09K 8/805 20130101; E21B 49/008 20130101;
C09K 8/588 20130101 |
International
Class: |
C09K 8/588 20060101
C09K008/588; C09K 8/80 20060101 C09K008/80; E21B 49/00 20060101
E21B049/00 |
Claims
1. A composition comprising: one or more coated paramagnetic
nanoparticles, wherein the paramagnetic nanoparticles are coated
with a polymer, a surfactant or any combinations thereof adapted
for a downhole administration; and a fluid comprising the one or
more coated paramagnetic nanoparticles, wherein the fluid is
selected from the group consisting of water, hard water, brine, and
any combinations thereof, wherein the composition is operable for
detecting a presence, measuring a distribution or both of an oil or
a hydrocarbon in a subsurface formation.
2. The composition of claim 1, wherein the coated paramagnetic
nanoparticles comprise a metal oxide.
3. The composition of claim 2, wherein a metal in the metal oxide
comprises at least one of iron, magnesium, molybdenum, lithium,
cobalt, nickel or tantalum.
4. (canceled)
5. The composition of claim 1, wherein the nanoparticles are coated
by adsorption of a thin polymer gel film or a coating material
around the paramagnetic nanoparticles, wherein the thin polymer gel
film is wrapped around the paramagnetic nanoparticles to prevent a
detachment of the coating during a transport of the nanoparticle in
the subsurface formation.
6. The composition of claim 5, wherein the coating is configured to
promote a high salinity tolerance to the nanoparticles for
monovalent and divalent salts.
7. The composition of claim 5, wherein the detachment of the
coating is prevented by a chemical bond of the polymer gel film or
the coating material to itself or to another agent on the
nanoparticle surface.
8. The composition of claim 7, wherein the chemical bond of the
polymer gel film or the coating material is achieved by contacting
the paramagnetic nanoparticles suspended in an aqueous solution
with the polymer, a cross-linker, a catalyst, a first stabilizer,
and a second stabilizer.
9. (canceled)
10. The composition of claim 8, wherein the polymers are selected
from the group consisting of polyacrylic acid (PAA), block
copolymer of poly(acrylic acid).sub.m-b-poly(butyl acrylate).sub.n,
random copolymer of poly(acrylic acid).sub.m-r-poly(butyl
acrylate).sub.n, poly(4-styrene sulfonic acid-co-maleic acid),
polyethylene glycol, styrene sulfonic acids, acrylic and
methacrylic acid polymers and copolymers, polylactic acid
copolymers (PLA) and polylactic glycolic acid (PLGA), vinyl
sulfonic acid, vinyl benzyl trimethyl ammonium chloride,
acrylamidopropyl trimethyl ammonium chloride, polyethylene oxide,
polypropylene oxide, and combinations or modifications thereof,
wherein m and n are the number of monomers.
11. The composition of claim 8, wherein the cross-linker comprises
1,6-hexanediamine.
12. The composition of claim 8, wherein the catalyst is selected
from the group consisting of carbodiimides, N-hydroxysuccinimide
esters, imidoesters, maleimides, haloacetyls, pyridyl disulfides,
and aryl azides.
13. The composition of claim 8, wherein the catalyst is
1-ethyl-3-(3-dimethylaminopropyl) carbodiimide.
14. (canceled)
15. The composition of claim 8, wherein the second stabilizer
increases an adsorption of the one or more paramagnetic
nanoparticles at an oil-water interface to provide an enhanced
imaging of the oil and decreases an adsorption at the subsurface
formation or a rock surface to promote the transfer of the one or
more nanoparticles in the subsurface formation or a reservoir.
16. (canceled)
17. The composition of claim 8, wherein the polymer is a
poly(acrylic acid).sub.m-b-poly(butyl acrylate).sub.n block
copolymer or a poly(acrylic acid).sub.m-r-poly(butyl
acrylate).sub.n random copolymer, where m and n are the numbers of
(acrylic acid) and (butyl acrylate) monomers, respectively, wherein
m and n can be adjusted for improved salt tolerance and interfacial
activity.
18. The composition of claim 8, wherein the polymer is a
poly(4-styrenesulfonic acid-co-maleic acid) copolymer.
19.-52. (canceled)
53. A composition comprising: (a) a plurality of coated
paramagnetic nanoparticles, wherein (i) each of the coated
paramagnetic nanoparticles has a coating that is a polymer, a
surfactant, or a combination thereof, and (ii) the coating is
suitable for a subterranean reservoir; and (b) a fluid in which the
plurality of coated paramagnetic nanoparticles are intermixed,
wherein (i) the fluid is selected from the group consisting of
water, hard water, brine, and combinations thereof, and (ii) the
composition is suitable for detecting a presence of a hydrocarbon
in subterranean reservoir, measuring a distribution of the
hydrocarbon in the subterranean reservoir, or both.
54. The composition of claim 53, wherein the coated paramagnetic
nanoparticles comprise a metal oxide, wherein the metal oxide is
selected from the group consisting of oxides of iron, magnesium,
molybdenum, lithium, cobalt, nickel, tantalum, and combinations
thereof.
55.-57. (canceled)
58. The composition of claim 53, wherein (a) the coated
paramagnetic nanoparticles are coated by adsorption of a thin
polymer gel film around the paramagnetic nanoparticles, and (b) the
thin polymer gel film is wrapped around the paramagnetic
nanoparticles to operably prevent a detachment of the coating
during a transport of the paramagnetic nanoparticle in the
subterranean reservoir, wherein the coating is configured to
promote a high salinity tolerance to the paramagnetic nanoparticles
for monovalent and divalent salts.
59.-61. (canceled)
62. The composition of claim 60, wherein the polymers are selected
from the group consisting of polyacrylic acid (PAA), block
copolymer of poly(acrylic acid).sub.m-b-poly(butyl acrylate).sub.n,
random copolymer of poly(acrylic acid).sub.m-r-poly(butyl
acrylate).sub.n, poly(4-styrene sulfonic acid-co-maleic acid),
polyethylene glycol, styrene sulfonic acids, sulfonic acids,
polystyrene, acrylic and methacrylic acid polymers and copolymers,
polylactic acid copolymers (PLA) and polylactic glycolic acid
(PLGA), styrene sulfonic acid, vinyl sulfonic acid, vinyl benzyl
trimethyl ammonium chloride, acrylamidopropyl trimethyl ammonium
chloride, polyethylene oxide, polypropylene oxide, and combinations
or modifications thereof, wherein m and n are the number of
monomers.
63.-67. (canceled)
68. The composition of claim 53, wherein (a) the coating is a
polymer; (b) the polymer is selected from the group consisting of a
Poly(acrylic acid).sub.m-b-Poly(butyl acrylate).sub.n block
copolymer, and a Poly(acrylic acid).sub.m-r-Poly(butyl
acrylate).sub.n random copolymer, where m and n are the numbers of
(acrylic acid) and (butyl acrylate) monomers, respectively.
69. The composition of claim 53, wherein the coating is a polymer,
and the polymer is a Poly(4-styrenesulfonic acid-co-maleic acid)
polymer.
70.-83. (canceled)
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This patent application is a divisional patent application
of U.S. Ser. No. 13/508,611 filed on Aug. 6, 2012, which is a
National Stage of International Application No. PCT/US2010/057080,
filed Nov. 17, 2010, and claims the benefit of U.S. Provisional
Application No. 61/262,037, filed Nov. 17, 2009. The contents of
each of which are hereby incorporated by reference in its
entirety.
TECHNICAL FIELD
[0002] The present invention relates in general to the field of oil
recovery, and more particularly, to using paramagnetic
nanoparticles for detecting the presence and determining the
saturation of oil in subsurface formations.
BACKGROUND INFORMATION
[0003] Without limiting the scope of the invention, its background
is described in connection with imaging techniques used in oil
recovery.
[0004] Accurate, non-invasive determination of oil saturation
distribution in laboratory cores, near-wellbore zones, and deep in
the reservoir, will greatly improve understanding of oil
displacement mechanisms for various enhanced oil recovery (EOR)
processes, and also help identify the location of bypassed oils so
that they can be subsequently recovered. Currently, the oil
saturation distribution can be determined: (i) for laboratory
cores, using MRI or CT-scan imaging; (ii) for near-wellbore zones,
by NMR and other logging methods; and (iii) for zones deeper in the
reservoir, e.g., by injection of partitioning tracers. The
difficulty with the NMR logging is that its probing depth is very
shallow, i.e., in centimeters. Moreover, interpretation requires
knowledge of rock surface properties (wettability, relaxivity) that
can be difficult to estimate independently. With the "echo"
injection/production of partitioning tracers, a reliable
determination of oil saturation from the tracer material balance is
difficult, because it is difficult to have the detailed knowledge
of the porosity-permeability distribution in the study zone.
[0005] U.S. Pat. No. 4,769,602 issued to Vinegar and Tutunjian
(1988) provides a method of imaging of materials to determine
petrophysical properties and measuring fluid saturations using
Nuclear Magnetic Resonance (NMR) Imaging. According to the '602
patent, an earthen core sample containing multiple fluids during a
coreflood experiment is located within a NMR Imaging Apparatus, so
that the sample and fluids therein may be imaged. In coreflood
experiments conducted for reservoir engineering applications, the
three fluid phases may typically be water or a brine phase, an oil
or oleic phase, and a gas phase.
[0006] U.S. Pat. No. 7,170,294 issued to Kasevich (2007) discloses
the application of electromagnetic tomography for efficient
recovery of oil and gas as well as the removal of unwanted liquids
from subsurface formations. The Kasevich patent involves the
deployment of both surface and a single borehole magnetic dipole
structures used for both transmitting and receiving low frequency
electromagnetic energy. Several concentric surface antenna arrays
with electronic switching between each circular array and the
downhole solenoid will have the ability to image the spread and
movement of oil and gas during thermal treatment and provide three
dimensional temperature measurement. The oil movement to recovery
wells may be provided by radio frequency heating or steam flood as
in enhanced oil recovery. This information allows for developing
very efficient oil and fluid recovery techniques by actually
observing topographic images developed according to this
invention.
[0007] U.S. Patent Application No. 20090167302 (Edwards and Ladva,
2009) discloses the use of time-lapsed NMR diffusivity measurements
in an observation well. The observation well is cased in the zone
of interest with non-magnetic and non-conductive casing that is
invisible to the NMR tool. Secondly, because NMR measurements have
a dead zone in front of the antenna depending on the spatial
variation of the fixed magnet strength, for example about 2.7
inches, a distance between the casing and the formation is reduced
to less than the dead zone length by drilling the observation well
at small deviation of about 5.degree. and running the casing
without centralizers. Both the casing and the pad-type NMR tool
will follow the low side of the borehole, ensuring the measurement
volume of the NMR tool is inside the formation and beyond the
annulus. With the appropriate observation well completion,
time-lapse diffusivity measurements with pad-type NMR tools can
address several shortcomings in the current practice of monitoring
EOR processes that rely upon changes in density and hydrogen index
(HI). Various uses of NMR imaging in wells cased with non-metallic
casing are also disclosed.
SUMMARY
[0008] Embodiments of the present invention describe a synthesis
and use of custom paramagnetic nanoparticles that adsorb
preferentially to the oil/water interface. Embodiments of the
present invention involve injecting an aqueous dispersion of the
nanoparticles into the potentially oil containing subsurface
formation, and remotely detecting the presence and distribution of
oil in the reservoir.
[0009] Embodiments of the present invention use oscillations of
paramagnetic nanoparticles in a magnetic field for the accurate
determination of oil saturation. Embodiments of the present
invention include compositions and methods of detecting oil/water
menisci in reservoir rock to indicate the presence of oil. By
injecting paramagnetic nanoparticles that adsorb preferentially on
the oil/water interface (meniscus), and by detecting the acoustic
wave generated by their oscillation, their presence in the
reservoir rock is deduced. The interpretation of this measurement
is sensitive to the wettability but not the relaxivity of the rock
grain surfaces. Independent methods are available for relating
meniscus density (number per unit volume) to oil saturation and
wettability.
[0010] When paramagnetic nanoparticles are adsorbed at the
oil/water interface or dispersed in one of the fluid phases in
reservoir rock pores and then exposed to an external magnetic
field, the resultant particle movements displace the interface.
Interfacial tension acts as a restoring force, leading to
interfacial fluctuation and a pressure (sound) wave. The underlying
physical concept of the present invention is described with the
application of the theory of ferrofluids to track the motion of an
oil/water interface in a cylindrical pore as typically observed in
reservoir rock. Results of the theoretical studies obtained herein
are consistent with the laboratory studies performed with an
aqueous suspension of iron oxide nanoparticles, in which the
interface motion is measured by the optical coherence tomography
(OCT). The relative densities of the fluid phases (air/aqueous and
dodecane/aqueous as in embodiments of the present invention)
strongly affect the displacement of the interface. Application of a
magnetic field introduces pressure-like terms into the equation of
fluid phase motion. The problem is then restated in terms of
interface motion, extending a numerical interface-tracking model
based on the level-set method to account for capillarity and
magnetic pressures simultaneously. The model of the present
invention can be used to illustrate the motion of an interface
between immiscible fluids at the pore scale when magnetic forces
are imposed on the paramagnetic nanoparticles dispersed in one
fluid phase.
[0011] A first step for an implementation of embodiments of the
present invention is the application of a surface coating to
nanoparticles such that once they contact oil in the reservoir
rock, they are adsorbed at the oil/water interface. The steps
involved include: (a) injection of an aqueous dispersion of
paramagnetic nanoparticles into a reservoir rock that contains some
oil in its pores; (b) application of a magnetic field oscillation
so that the oil/water menisci at the rock pores oscillate, and
thereby generate an acoustic response (a pressure wave); (c)
measurement of the acoustic response with a sensitive geophone; and
(d) deduction of the oil meniscus density in the rock, thereby
obtaining the oil saturation distribution. Because the number
density of menisci is related to the degree of disconnection of the
oil phase, embodiments may also provide quantitative insights into
the fraction of oil trapped as a residual phase especially if
combined with another measurement such as resistivity.
[0012] The techniques of the present invention as described in
various embodiments combine magnetic oscillation (enhanced with
paramagnetic nanoparticles) with acoustic response measurements for
the determination of the fluid saturations in the reservoir rock,
with greater probing depth than MRI or NMR logging methods.
Additionally, because the paramagnetic nanoparticles adsorbed at
the oil/water interface will have significant influence on the
molecular spins, embodiments of the present invention can provide
(i) enhanced imaging of multi-phase fluids during the MRI scan of
the laboratory core, in the manner of nanoparticle-enhanced medical
imaging of particular human organs; and (ii) improved determination
of fluid saturation distributions by NMR logging.
[0013] Embodiments of the present invention disclose a composition
for detecting a presence, measuring a distribution or both of an
oil or a hydrocarbon in a subsurface formation comprising one or
more coated paramagnetic nanoparticles, wherein the paramagnetic
nanoparticles are coated with a polymer, surfactant, or any
combinations thereof adapted for downhole administration and a
fluid comprising the one or more coated paramagnetic nanoparticles,
wherein the fluid comprises water, hard water, brine or any
combinations thereof. In an aspect of the present invention, the
coated paramagnetic nanoparticles are metal oxides, comprising at
least 1, 2, 3, 4, 5, 6, 7 oxides of iron, magnesium, molybdenum,
lithium, cobalt, nickel or tantalum. The coated paramagnetic
nanoparticles may be dispersed or suspended in the fluid.
[0014] Embodiments of the present invention include a method of
coating the nanoparticles by adsorbing a thin polymer gel film or a
coating material around the paramagnetic nanoparticles, wherein the
thin polymer gel film or the coating material wraps around the
paramagnetic nanoparticles to prevent a detachment of the coating
during a transport of the nanoparticle in the subsurface formation.
The detachment of the coating is prevented by chemically binding
the polymer gel film or the coating material to itself or to
another agent on the nanoparticle surface. The coating imparts a
high salinity tolerance to the nanoparticles for monovalent and
divalent salts.
[0015] In aspects of the present invention the binding of the
polymer gel film or the coating material is achieved by contacting
the paramagnetic nanoparticles suspended in an aqueous solution
with the polymer (comprising monomers, a homopolymer, a copolymer
or combinations and modifications thereof), a cross-linker, a
catalyst, a first stabilizer, and a second stabilizer. Non-limiting
examples of the polymers include those selected from the group
consisting of polyacrylic acid (PAA), block copolymer of
poly(acrylic acid)m-b-poly(butyl acrylate)n, random copolymer of
poly(acrylic acid)m-r-poly(butyl acrylate)n, poly(4-styrene
sulfonic acid-co-maleic acid), polyethylene glycol, styrene
sulfonic acids, acrylic and methacrylic acid polymers and
copolymers, polylactic acid copolymers (PLA) and polylactic
glycolic acid (PLGA), vinyl sulfonic acid, vinyl benzyl trimethyl
ammonium chloride, acrylamidopropyl trimethyl ammonium chloride,
polyethylene oxide, polypropylene oxide, and combinations or
modifications thereof, wherein m and n are the number of monomers.
The cross-linker is an agent reacting with the polymer or the
coating material to bind it to the particle surface. An example of
a cross-linker is an alkane diamine like 1,6-hexanediamine A
catalyst is used to promote the cross linking reaction, and is
selected from the group consisting of carbodiimides,
N-hydroxysuccinimide esters, imidoesters, maleimides, haloacetyls,
pyridyl disulfides, and aryl azides. A non-limiting example of a
catalyst is 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide.
[0016] In a specific aspect the first stabilizer and the second
stabilizer comprise low-molecular weight substances or polymeric
materials. The first stabilizer is employed during a synthesis of
the one or more paramagnetic nanoparticles and is selected from the
group consisting of polyacrylic acid (PAA), block copolymers of
poly(acrylic acid).sub.m-b-poly(butyl acrylate).sub.n, random
copolymers of poly(acrylic acid).sub.m-r-poly(butyl
acrylate).sub.n, poly(4-styrene sulfonic acid-co-maleic acid),
polyethylene glycol, styrene sulfonic acids, acrylic and
methacrylic acid polymers and copolymers, polylactic acid
copolymers (PLA) and polylactic glycolic acid (PLGA), vinyl
sulfonic acid, vinyl benzyl trimethyl ammonium chloride,
acrylamidopropyl trimethyl ammonium chloride, polyethylene oxide,
polypropylene oxide, and combinations or modifications thereof,
wherein m and n are the number of monomers. The second stabilizer
increases an adsorption of the one or more paramagnetic
nanoparticles at an oil-water interface to provide an enhanced
imaging of the oil and decreases an adsorption at the subsurface
formation or a rock surface to promote the transfer of the one or
more nanoparticles in the subsurface formation or a reservoir, and
is selected from the group consisting of polyacrylic acid (PAA),
block copolymers of poly(acrylic acid).sub.m-b-poly(butyl
acrylate).sub.n, random copolymers of poly(acrylic
acid).sub.m-r-poly(butyl acrylate).sub.n, poly(4-styrene sulfonic
acid-co-maleic acid), polyethylene glycol, styrene sulfonic acids,
acrylic and methacrylic acid polymers and copolymers, polylactic
acid copolymers (PLA) and polylactic glycolic acid (PLGA), vinyl
sulfonic acid, vinyl benzyl trimethyl ammonium chloride,
acrylamidopropyl trimethyl ammonium chloride, polyethylene oxide,
polypropylene oxide, and combinations or modifications thereof,
wherein m and n are the number of monomers.
[0017] In other specific aspects the polymer is a poly(acrylic
acid)m-b-poly(butyl acrylate)n block copolymer or a poly(acrylic
acid)m-r-poly(butyl acrylate)n random copolymer, where m and n are
the numbers of (acrylic acid) and (butyl acrylate) monomers,
respectively, wherein m and n can be adjusted for improved salt
tolerance and interfacial activity, or a poly(4-styrenesulfonic
acid-co-maleic acid) copolymer.
[0018] In aspects of the present invention, the coated paramagnetic
nanoparticles have a diameter less than 100 nm. The coated
paramagnetic nanoparticles may have diameters of 1 nm, 5 nm, 10 nm,
25 nm, 40 nm, 50 nm, 60 nm, 75 nm, 90 nm, and 100 nm. The skilled
artisan would understand these diameters to include 1 nm, 2 nm, 3
nm, 4 nm, 5 nm, 10 nm, 15 nm, 20 nm, 40 nm, 60 nm, 80 nm, 100 nm
and incremental variations thereof, for example, 1.2 nm, 2.7 nm,
3.5 nm, 10.4 nm, 54.3 nm, 78.9 nm, and so forth.
[0019] The coated paramagnetic nanoparticles may comprise
nanospheres, nanorods, nanoclusters, nanotubes, nanofibers or any
combinations thereof. In an aspect of the present invention, the
coated paramagnetic nanoparticles preferentially adsorb at an
oil/water interface and oscillate in the presence of an externally
applied magnetic field. The coated nanoparticles generate an
acoustic wave on oscillation, wherein a frequency spectrum, a
magnitude or a combination thereof of the acoustic wave is directly
related to an oil meniscus density and saturation in the subsurface
formation.
[0020] Embodiments of the present invention provide a method of
determining a presence, measuring a distribution and saturation or
both of an oil or a hydrocarbon or CO.sub.2 in a reservoir rock or
subsurface formation comprising the steps of: (i) injecting a
dispersion of one or more coated paramagnetic nanoparticles into
the reservoir rock or subsurface formation to adsorb the coated
paramagnetic nanoparticles at an oil/water, gas/water or
CO.sub.2/water interface, wherein the paramagnetic nanoparticles
are coated with a polymer or a surfactant or any combinations
thereof and are dispersed in a fluid selected from the group
consisting of water, hard water, brine, and combinations thereof;
(ii) applying an external magnetic field to oscillate the coated
nanoparticles adsorbed at the oil/water, gas/water or
CO.sub.2/water interface; (iii) measuring an acoustic response
generated by the oscillation of the coated nanoparticles adsorbed
at the oil/water, gas/water or CO.sub.2/water interface, wherein
the acoustic response is measured by a geophone, a surface acoustic
wave sensor, a frequency analyzer or any combinations thereof; and
(iv) determining an oil or gas or CO.sub.2 meniscus density and
presence in the reservoir rock or subsurface formation rock,
thereby obtaining the distribution and saturation from the
frequency spectrum, the magnitude or a combination thereof of the
acoustic response. Embodiments of the present invention further
comprise a step of determining a fraction of the oil or gas or
CO.sub.2 present in the rock by a measurement of a resistivity,
wherein the resistivity is measured using one or more resistivity
logging tools.
[0021] In embodiments of the present invention, the coated
paramagnetic nanoparticles comprise a metal oxide, wherein the
metal in the metal oxides comprises at least one of iron,
magnesium, molybdenum, lithium, cobalt, nickel or tantalum. The
coated paramagnetic nanoparticles may be dispersed or suspended in
the fluid and are coated by adsorbing a thin polymer gel film
around the paramagnetic nanoparticles, wherein the thin polymer gel
film wraps around the paramagnetic nanoparticles to prevent a
detachment of the coating during transport of the nanoparticles in
the subsurface formation and promotes a high salinity tolerance to
the nanoparticles for monovalent and divalent salts.
[0022] The adsorption of the thin polymer gel film or the coating
material is achieved by contacting the paramagnetic nanoparticles
suspended in an aqueous solution with the polymer, a cross-linker,
a catalyst, a first stabilizer, and a second stabilizer. The
polymers comprise monomers, a homopolymer, a copolymer or
combinations and modifications thereof and are selected from the
group consisting of polyacrylic acid (PAA), block copolymers of
poly(acrylic acid).sub.m-b-poly(butyl acrylate).sub.n, random
copolymers of poly(acrylic acid).sub.m-r-poly(butyl
acrylate).sub.n, poly(4-styrene sulfonic acid-co-maleic acid),
polyethylene glycol, styrene sulfonic acids, acrylic and
methacrylic acid polymers and copolymers, polylactic acid
copolymers (PLA) and polylactic glycolic acid (PLGA), vinyl
sulfonic acid, vinyl benzyl trimethyl ammonium chloride,
acrylamidopropyl trimethyl ammonium chloride, polyethylene oxide,
polypropylene oxide, and combinations or modifications thereof,
wherein m and n are the number of monomers. The first stabilizer
and the second stabilizer used herein comprise low molecular weight
substances or polymeric materials and are selected from the group
consisting of polyacrylic acid (PAA), block copolymer of
poly(acrylic acid).sub.m-b-poly(butyl acrylate).sub.n, random
copolymer of poly(acrylic acid).sub.m-r-poly(butyl acrylate).sub.n,
poly(4-styrene sulfonic acid-co-maleic acid), polyethylene glycol,
styrene sulfonic acids, acrylic and methacrylic acid polymers and
copolymers, polylactic acid copolymers (PLA) and polylactic
glycolic acid (PLGA), vinyl sulfonic acid, vinyl benzyl trimethyl
ammonium chloride, acrylamidopropyl trimethyl ammonium chloride,
polyethylene oxide, polypropylene oxide, and combinations or
modifications thereof, wherein m and n are the number of
monomers.
[0023] In a specific aspect the polymer is a poly(acrylic
acid).sub.114-b-poly(butyl acrylate).sub.26 copolymer or a
poly(4-styrenesulfonic acid-co-maleic acid) copolymer. In other
specific aspects, the coated paramagnetic nanoparticles have a
diameter less than 100 nm. Typically, the diameters of the coated
paramagnetic nanoparticle may be 1 nm, 5 nm, 10 nm, 25 nm, 40 nm,
50 nm, 60 nm, 75 nm, 90 nm, and 100 nm. In one or more aspects, the
coated paramagnetic nanoparticles comprise nanospheres, nanorods,
nanoclusters, nanotubes, nanofibers, or any combinations thereof.
In one or more aspects, the paramagnetic nanoparticles are coated
with the polymer, the surfactant, or combinations thereof. In one
or more aspects, the method is used prior to or during an oil
recovery operation.
[0024] Embodiments of the present invention disclose a system for
determining a presence, measuring a distribution and saturation, or
both of an oil or a hydrocarbon or CO.sub.2 in a reservoir rock or
subsurface formation comprising an injection system for delivering
an aqueous dispersion of one or more coated paramagnetic
nanoparticles into the reservoir rock or subsurface formation,
wherein the paramagnetic nanoparticles are coated with a polymer or
a surfactant, or any combinations thereof and are dispersed in a
fluid comprising water, hard water, brine or any combinations
thereof, an acoustic transducer connected to the injection system
or a neighboring well, a power supply source, a current amplifier
with one or more output channels connected to the power supply
source, one or more solenoid coils that may be wrapped around a
metallic core, wherein the solenoid coil is connected to a first
output channel of the current amplifier coil and generates a
magnetic field of a prescribed wave form when the power supply
source and the current amplifier are turned on, a function
generator connected to a second output channel of the current
amplifier, and a geophone or a sonic wave frequency analyzer
connected to the acoustic transducer, wherein the geophone or the
sonic wave frequency analyzer measures a frequency spectrum, a
magnitude or a combination thereof of an acoustic wave generated by
an oscillation of the one or more coated paramagnetic
nanoparticles. In one or more aspects, the pulsed magnetic field
generated by the one or more solenoid coils exerts a force on the
coated paramagnetic nanoparticles. In one or more aspects, the one
or more solenoid coils are replaced with a spinning permanent
magnet or an array of spinning permanent magnets to produce the
magnetic field. In one or more aspects, the system as described
hereinabove is used prior to or during an oil recovery operation.
The nanoparticles are coated by adsorbing a coating material such
as a thin polymer gel film around the paramagnetic nanoparticles by
contacting the paramagnetic nanoparticles suspended in an aqueous
solution with the polymer, a cross-linker, a catalyst, a first
stabilizer, and a second stabilizer, wherein the coating imparts a
high salinity tolerance to the nanoparticles for monovalent and
divalent salts. The polymers are selected from the group consisting
of polyacrylic acid (PAA), block copolymer of poly(acrylic
acid).sub.m-b-poly(butyl acrylate).sub.n, random copolymer of
poly(acrylic acid).sub.m-r-poly(butyl acrylate).sub.n,
poly(4-styrene sulfonic acid-co-maleic acid), polyethylene glycol,
styrene sulfonic acids, acrylic and methacrylic acid polymers and
copolymers, polylactic acid copolymers (PLA) and polylactic
glycolic acid (PLGA), vinyl sulfonic acid, vinyl benzyl trimethyl
ammonium chloride, acrylamidopropyl trimethyl ammonium chloride,
polyethylene oxide, polypropylene oxide, and combinations or
modifications thereof, wherein m and n are the number of monomers.
More specifically, the polymer is a poly(acrylic
acid).sub.114-b-poly(butyl acrylate).sub.26 copolymer or a
poly(4-styrenesulfonic acid-co-maleic acid) copolymer.
[0025] In an embodiment the instant invention discloses a
composition comprising: (a) a plurality of coated paramagnetic
nanoparticles, wherein (i) each of the coated paramagnetic
nanoparticles has a coating that is a polymer, a surfactant, or a
combination thereof; and (ii) the coating is operable to allow the
coated paramagnetic nanoparticles to be injected into a downhole
formation; and (b) a fluid in which the plurality of coated
paramagnetic nanoparticles are intermixed, wherein (i) the fluid is
selected from the group consisting of water, hard water, brine, and
combinations thereof; and (ii) the composition is operable for
detecting a presence of a hydrocarbon in a subsurface formation,
measuring a distribution of the hydrocarbon in the subsurface
formation, or both.
[0026] Another embodiment of the instant invention provides a
method of determining a presence, measuring a distribution and
saturation or both of a hydrocarbon in a subsurface formation
comprising the steps of: (a) injecting a fluid comprising coated
paramagnetic nanoparticles into a subsurface formation to adsorb
the coated paramagnetic nanoparticles at an interface, wherein (i)
the fluid is selected from the group consisting of water, hard
water, brine, and combinations thereof; and (ii) the interface is
selected from the group consisting of an oil/water interface, a
gas/water interface, and a CO.sub.2/water interface; (b) applying
an external magnetic field to oscillate the coated paramagnetic
nanoparticles adsorbed at the interface; (c) measuring an acoustic
response parameter generated by the oscillation of the coated
paramagnetic nanoparticles adsorbed at the interface, wherein the
acoustic response is measured by a device selected from the group
consisting of a geophone, a surface acoustic wave sensor, a
frequency analyzer, and a combination thereof; and (d) determining
the presence and an oil, a gas or a CO.sub.2 meniscus density in
the subsurface formation from the measure acoustic response
parameter.
[0027] In yet another embodiment the instant invention discloses a
system for determining a presence, measuring a distribution and
saturation or both of a hydrocarbon or CO.sub.2 in a subsurface
formation comprising: (a) an injection system for delivering a
fluid comprising coated paramagnetic nanoparticles into the
subsurface formation, wherein the fluid is selected from the group
consisting of water, hard water, brine, and a combination thereof,
(b) an acoustic transducer operably connected to the injection
system; (c) a power supply source; (d) a current amplifier with a
plurality of output channels connected to the power supply source;
(e) one or more solenoid coils that are wrapped around a metallic
core, wherein the solenoid coils are connected to a first output
channel of the current amplifier coil and are operable to generate
a pulsed magnetic field of a prescribed wave form when the power
supply source and the current amplifier are turned on; (f) a
function generator connected to a second output channel of the
current amplifier; and (g) a geophone or a sonic wave frequency
analyzer connected to the acoustic transducer, wherein the geophone
or the sonic wave frequency analyzer measures a frequency spectrum,
a magnitude or a combination thereof of an acoustic wave generated
by an oscillation of the one or more polymer coated paramagnetic
nanoparticles.
DESCRIPTION OF THE DRAWINGS
[0028] For a more complete understanding of the features and
advantages of the present invention, reference is now made to the
detailed description of the invention along with the accompanying
figures and in which:
[0029] FIG. 1A shows paramagnetic nanoparticles in accordance with
embodiments of the present invention readily adhering to the
oil/water interface when injected into a reservoir rock.
[0030] FIG. 1B shows a schematic of nanoparticles with a
paramagnetic core and coated with adsorbed dispersant molecules
with no external magnetic field applied. Magnetic core radius is
typically about 80% of the particle radius.
[0031] FIG. 1C shows the nanoparticles of FIG. 1B oriented in
presence of an external magnetic field.
[0032] FIG. 2A shows the nanoparticles attached to the water-oil
(aqueous-nonaqueous) interface. Depending on the contact angle,
.theta., that the nanoparticles assume with the interface, the
curvature of the interface may vary.
[0033] FIG. 2B is a schematic of a nanoparticle with a metal oxide
core and a polymer shell which renders a desired contact angle and
a dispersion stability in water.
[0034] FIG. 3A is an example magnetization curve for spherical
magnetite (Fe.sub.3O.sub.4) particles of different radii assuming
bulk magnetization M.sub.d=4.4610.sup.5 Am.sup.-1, volume fraction
.phi.=0.01 in ferrofluid (mass fraction approximately 0.05) and
temperature T=300 K. Particle radius refers to the magnetic core
radius.
[0035] FIG. 3B is an example susceptibility .chi. curve for the
spherical magnetite (Fe.sub.3O.sub.4) particles of different radii
of FIG. 3A.
[0036] FIG. 4A is a schematic showing pressures acting on an
interface between fluid 1 (magnetized, wetting) and fluid 2
(non-wetting, non-magnetic). Note that p.sub.c=p.sub.2-p.sub.1
(thermodynamic pressures), and p.sub.1*=p.sub.1+p.sub.s+p.sub.m is
a composite pressure for the magnetized fluid, and
p.sub.n=.mu..sub.0*M.sub.n.sup.2/2 is a magnetic normal
pressure.
[0037] FIG. 4B is similar to FIG. 4A except that the non-wetting
fluid is now magnetized and the wetting fluid is not. Thus,
p.sub.2*=p.sub.2+p.sub.s+p.sub.m is now the composite pressure, and
the magnetic normal pressure acts from the non-wetting fluid.
[0038] FIGS. 5A and 5B show a magnetic pressure estimate at an
interface between the magnetized water and air relative to
capillary pressure for a capillary tube of radius 1 mm. Capillary
pressure value is 144 Pa. Because air is much less dense than
water, the p.sub.m and p.sub.s terms cancel each other regardless
of particle magnetic susceptibility. The total magnetic pressure
(black) is therefore determined by the p.sub.n term: (FIG. 5A)
nanoparticles of susceptibility 0.2, (FIG. 5B) nanoparticles of
susceptibility 20.
[0039] FIGS. 6A and 6B show a similar situation as FIGS. 5A and 5B
except that the magnetized air is replaced by dodecane. Capillary
pressure value is 64 Pa. The density of dodecane is comparable to
that of water, and thus the magnitudes of p.sub.m and p.sub.s terms
differ. Moreover, the magnitudes of all the magnetic terms depend
on particle susceptibility. Consequently, the total magnetic
pressure can be positive or negative: (FIG. 6A) nanoparticles of
susceptibility 0.2, (FIG. 6B) nanoparticles of susceptibility
20.
[0040] FIG. 7 is a plot showing an extreme value of the magnetic
pressures at an interface between two fluids (normalized by
capillary pressure for the tube of radius 1 mm) with nanoparticles
of different susceptibility suspended in water. If induced by an
oscillatory magnetic field, the magnetic pressure will vary between
this extreme value and zero.
[0041] FIG. 8 is a schematic showing a pressure wave generated by
the oscillation of an oil-water meniscus.
[0042] FIG. 9 is a plot showing rock grains (shown in gray)
delineating a small converging-diverging capillary. The initial
equilibrium interface (length scale is normalized by the radius of
grains, corresponding numerical capillary pressure used is 0.1) is
shown. The interface is then exposed to a constant magnetic field
and the wetting phase is assumed magnetized. With the fluids and
particles of FIG. 6A, and with a constant magnetic field that
yields p.sub.m+p.sub.s=0.02 and p.sub.n=0, the interface retreats
as shown. For a different choice of fluids and particles (FIG. 5A),
if a constant magnetic field is imposed that yields
p.sub.n=0.02({right arrow over (n)}{right arrow over
(e)}.sub.x).sup.2, the meniscus again retreats. The difference is
that the magnetic normal pressure is not constant along the
interface but depends on its orientation with respect to the
imposed magnetic field.
[0043] FIG. 10 is a plot showing the rock grains and same initial
location of meniscus as in FIG. 9. In this case, the nonwetting
fluid is magnetizable. Consequently, imposing the same magnetic
field as in FIG. 9 augments the capillary pressure. Thus, the
meniscus advances into the throat. Taking the same choices of
parameters as in FIG. 9, the figure also shows curves corresponding
to a negligible magnetic normal force, and a situation where the
magnetostrictive and fluid-magnetic pressures cancel.
[0044] FIGS. 11A and 11B show the x-coordinate displacement of the
center of mass of the fluid-fluid meniscus in a
converging-diverging capillary in time when exposed to an
oscillating magnetic field and when the wetting fluid is
magnetized. The total pressure value is shown as the difference
from capillary pressure. The interface is symmetric and the
magnetic field is in x-direction as well, so there is no movement
in transverse direction: (FIG. 11A) only magnetic normal pressure
component present (position dependent), (FIG. 11B) only volumetric
magnetic pressure components present (constant along the interface
for a fixed time).
[0045] FIG. 12 is a graph showing the magnetization capacity of
superparamagnetic nanoparticles in accordance with embodiments of
the present invention.
[0046] FIG. 13 is a schematic showing a magnetomotive acoustic
system.
[0047] FIG. 14 is a transmission electron microscopy (TEM) image of
iron oxide nanorods. The concentration of particles is 1% (per
weight), and the visible concentration depends on how the sample
dries while taking the TEM image.
[0048] FIG. 15 is a statistical distribution of nanorod lengths as
measured by the dynamic light scattering (DLS) apparatus.
[0049] FIG. 16 shows a system for exciting an aqueous dispersion of
paramagnetic nanoparticles with a time-varying magnetic field. The
drive delivered a sinusoidal field with frequencies between 1 and
30 Hz. The field is focused on the sample by the tip (ca. 1 mm
diameter) of the solenoid. The motion of the interface between
aqueous phase and nonaqueous phase (air or dodecane in the studies
reported here) is detected by phase-sensitive optical coherence
tomography (PS-OCT) with resolution below 100 pm.
[0050] FIG. 17 shows a dodecane-water study in a large diameter (4
mm) well. The water contains 5 wt % iron oxide nanorods. Measured
waveforms on the right show displacement (y-axis; one radial pixel
approximately equals 100 nm) vs. time (x-axis; 10,000 A-scan number
equals 1 second). The dodecane/water interface oscillates at 2 Hz
with a peak-to-valley displacement of about 5000 nm (lower right).
The air/dodecane interface response is small (peak-to-valley
displacement about 100 nm, upper right), noisy and secondary: its
motion is driven only by the motion of the underlying
dodecane/water interface.
[0051] FIG. 18 is a similar study as shown in FIG. 17 with air
instead of dodecane, showing a peak-to-valley displacement of only
500 nm, about ten times smaller than the dodecane/water interface
displacement.
[0052] FIG. 19 shows dodecane in water emulsions stabilized by iron
oxide nanoparticles coated with cross-linked PAA molecules. To form
the emulsions, 0.05 wt % nanoparticle dispersions were used at pH 7
and pH 9 without added salt and with 1 wt % salinity. The
photographs were taken 20 minutes after the emulsions
formation.
[0053] FIG. 20 shows volume fraction based distributions of
poly(acrylic acid)114-b-poly(butyl acrylate)B coated iron oxide
nanoclusters.
[0054] FIGS. 21A-21D show emulsion images of poly(acrylic
acid)114-b-poly(butyl acrylate)26 at pH 8 with: no salt (FIG. 21A),
1 wt % salt (FIG. 21B), 2 wt % salt (FIG. 21C), and 3 wt % salt
(FIG. 21D).
[0055] FIGS. 21E-21H show microscopic emulsion droplet images of
Poly(acrylic acid)114-b-Poly(butyl acrylate)26 at pH 8 with: no
salt (FIG. 21E), 1 wt % salt (FIG. 21F), 2 wt % salt (FIG. 21G),
and 3 wt % salt (FIG. 21H).
[0056] FIG. 22 is a photograph taken after 1 day of emulsions
formed with equal volume fractions of dodecane and aqueous
dispersion of 0.2 wt % random copolymer-coated iron oxide particles
with different ratio of PAA-r-PBA at pH 8 without salt and with
different salt levels.
[0057] FIGS. 23A-23F show optical micrographs (taken immediately
upon formation) of emulsion droplets formed at conditions in FIGS.
21A-21D: PAA-r-PBA (ratio 3:1), no salt (FIG. 23A), PAA-r-PBA
(ratio 3:1), 3 wt % NaCl (FIG. 23B), PAA-r-PBA (ratio 3:2), no salt
(FIG. 23C), PAA-r-PBA (ratio 3:2), 3 wt % NaCl (FIG. 23D),
PAA-r-PBA (ratio 4:1), no salt (FIG. 23E), and PAA-r-PBA (ratio
4:1), 3 wt % NaCl (FIG. 23F).
[0058] FIGS. 24A and 24B are transmission electron microscopy (TEM)
images for Poly(4-styrenesulfonic acid-co-maleic acid) coated iron
oxide nanoparticles with different ratio between 4-styrenesulfonic
acid and maleic acid: 3:1 ratio (FIG. 24A) and 1:1 ratio (FIG.
24B).
[0059] FIG. 25 shows a stability of 0.2 wt % Poly(4-styrenesulfonic
acid-co-maleic acid) coated iron oxide nanoparticle dispersions at
different pH and salinity values.
[0060] FIGS. 26A and 26B are dodecane in water emulsions stabilized
by poly(4-styrenesulfonic acid-co-maleic acid) coated iron oxide
nanoparticles at different pH and salinity values. The particle
concentration in the dispersions was 0.2 wt %, and the volume ratio
of dodecane and water: 1:1 ratio (FIG. 26A) and 3:1 ratio (FIG.
26B).
[0061] FIGS. 27A and 27B show the stability of 0.2 wt %
poly(4-styrenesulfonic acid-co-maleic acid)+DTAB-coated iron oxide
nanoparticle dispersions at different pH and salinity values: pH
6.0 (FIG. 27A) and pH 8.0 (FIG. 27B).
[0062] FIGS. 28A and 28B show dodecane in water emulsions
stabilized by Poly(4-styrenesulfonic acid-co-maleic
acid)+DTAB-coated iron oxide nanoparticles at pH 8.0 and different
salinity values: 0% salt (FIG. 28A) and 8% salt (FIG. 28B).
[0063] FIG. 29 is a schematic showing a geometry of a sandpack
holder and the rock cores in contact with the sandpack. By
measuring the acoustic responses at different locations along the
side of the upper rock core or by measuring the vertical
displacement response at the top surface of the upper core, the
acoustic response from a small volume of nanoparticle-containing
fluids imbedded in a rock sample is simulated.
[0064] FIGS. 30A and 30B show a photograph (FIG. 30A) and a
schematic diagram of a study setup (FIG. 30B).
[0065] FIGS. 31A and 31B show a displacement as measured by PS-OCT
of an air/water interface (FIG. 31A) and an air/emulsion interface
(FIG. 31B).
[0066] FIGS. 32A-32D show rock displacement signals from a sandpack
sample wetted with: 1.0 wt % nanoparticle dispersion ("solution")
(FIG. 32A), 0.5 wt % solution (FIG. 32B), emulsion (FIG. 32C), and
DI water (FIG. 32D).
[0067] FIGS. 33A-33C show phase differences between a doubled
applied magnetic field and a rock displacement signal from a
sandpack sample wetted with: 1.0 wt % solution (FIG. 33A), emulsion
(FIG. 33B), and 0.5 wt % solution (FIG. 33C).
[0068] FIG. 34 shows a magnetic field strength measured at three
different positions from the solenoid.
[0069] FIGS. 35A-35C show a rock displacement signal from a
sandpack sample wetted with: 1.0 wt % solution (FIG. 35A), emulsion
(FIG. 35B), and 0.5 wt % solution (FIG. 35C) in response to a
magnetic pulse.
[0070] FIGS. 36A and 36B show a photograph (FIG. 36A) and a
schematic diagram of an experimental setup (FIG. 36B) for a rock
displacement measurement by PS-OCT.
[0071] FIGS. 37A and 37B show the displacement: of a rock core with
0.5 wt % nanoparticle solution (FIG. 37A), and of a rock core with
0.5 wt % nanoparticle solution and oil (FIG. 37B) under a
sinusoidal magnetic field.
[0072] FIGS. 38A and 38B show displacements: of a rock core with
0.5 wt % nanoparticle solution (FIG. 38A), and of a rock core with
0.5 wt % nanoparticle solution and oil (FIG. 38B) under a pulsed
magnetic field.
DETAILED DESCRIPTION
[0073] While the making and using of various embodiments of the
present invention are discussed in detail below, it should be
appreciated that the present invention provides many applicable
inventive concepts that can be embodied in a wide variety of
specific contexts. The specific embodiments discussed herein are
merely illustrative of specific ways to make and use the invention
and do not delimit the scope of the invention.
[0074] To facilitate the understanding of this invention, a number
of terms are defined below. Terms defined herein have meanings as
commonly understood by a person of ordinary skill in the areas
relevant to the present invention. Terms such as "a", "an" and
"the" are not intended to refer to only a singular entity, but
include the general class of which a specific example may be used
for illustration. The terminology herein is used to describe
specific embodiments of the invention, but their usage does not
delimit the invention, except as outlined in the claims.
[0075] The term "nanoparticles" as used herein refers to the size
distribution of the particles constituting the corresponding
material that includes particles of nanometer scale in size.
Typically, "nanoparticles" have an average diameter of 1 .mu.m or
less, preferably from 10 to 500 nm, and more preferably from 10 to
100 nm. While the term "diameter" is used herein to describe
suitable particle sizes, it should be understood that nanoparticle
materials suitable for use in the present invention need not be
substantially spherical in shape.
[0076] The term "paramagnetic" as used herein refers to a substance
that is generally nonmagnetic under normal circumstances. However,
when placed under a magnetic field, the substance possesses
magnetization in direct proportion to the strength of the
field.
[0077] The term "downhole" as used herein refers to a direction
farther from the earth's surface measured along the path of the
wellbore. "Downhole" composition refers to compositions ready to be
fed down an oil well, in other words the composition comprises all
components that it will contain as it is fed down the oil well and
that it is at the desired temperature and pressure at which it will
be fed down the oil well.
[0078] The term "polymer" refers to thermoplastic, synthetic,
organic polymeric material, and includes, but is not limited to,
homopolymers, copolymers, terpolymers and the like, and
combinations of any two or more thereof. A "monomer" is an atom or
a small molecule that may bind chemically to other "monomers" to
form a polymer. The term "homopolymer" is used to indicate a
polymer in which all of the monomer units are identical. A
"heteropolymer or copolymer" is a polymer derived from two (or
more) monomeric species.
[0079] The term "acoustic wave" as used herein refers to a wave
that is transmitted through a solid, liquid, and/or gaseous
material as a result of the mechanical vibrations of the particles
forming the material. The normal mode of wave propagation is
longitudinal (i.e., the averaged direction of motion of the
particles is parallel to the direction of wave propagation), the
wave therefore consists of compressions and rarefactions of the
material.
[0080] The term "oscillation" as used herein refers to a
reciprocating or a to and fro movement rhythmically about a mean
position, or a dithering or a perturbation in a random or
semi-random manner but so that the time-averaged position is a
selected or desired position.
[0081] Described herein is a method for accurate determination of
oil saturation in subsurface formations using electromagnetic
imaging with paramagnetic nanoparticles. Embodiments of the present
invention detect the oil/water menisci in reservoir rock, which
indicates presence of oil. By injecting paramagnetic nanoparticles
that adsorb preferentially on the oil/water interface (meniscus),
and by detecting the acoustic wave generated by their oscillation,
their presence in the reservoir rock is deduced.
[0082] The penetration depth for the detection of oil distribution
in the reservoir rock is currently very limited. Embodiments of the
present invention increase the probing depth for the measurement of
oil distribution more than the currently used MRI or NMR methods.
Embodiments of the present invention remotely detect the spatial
distribution of oil saturation in the reservoir rock pores. In
addition to improved detection by injecting an image-enhancing
agent into the subsurface rock formation, the properties of the oil
reservoirs can be measured more accurately and reliably.
Embodiments of the present invention may be also employed to detect
the presence and distribution of (i) gas or (ii) CO.sub.2 that had
been sequestered earlier in the subsurface formations.
[0083] Embodiments of the present invention have many first of its
kind features that are absent in the prior art. The injection of
paramagnetic nanoparticles into the subsurface formation for the
purpose of enhanced imaging of the distribution of oil in the
reservoir is novel and no such attempts have been made before.
Also, embodiments of the present invention permit a chemical
coating on a surface of nanoparticles to be designed in a way such
that the nanoparticles do not adsorb on the rock pore walls, but
preferentially adsorb on the oil/water interfaces. Detection of the
oscillation responses of the nanoparticles on the oil/water
interfaces in the reservoir rock by applying magnetic field has not
been made or described before.
[0084] Accurate, non-invasive determination of oil saturation
distribution in the reservoir will greatly improve understanding of
oil displacement mechanisms for various enhanced oil recovery (EOR)
processes, and also helps to identify the location of bypassed oils
so that they can be subsequently recovered. With current methods of
oil saturation determination, such as the NMR logging and the
injection of partitioning tracers, it is difficult to obtain
reliable information for a large volume of the reservoir. For
example, the probing depth of NMR logging is very shallow, i.e., in
centimeters. With the "echo" injection/production of partitioning
tracers, a reliable determination of oil saturation from the tracer
material balance is difficult, because detailed knowledge of the
porosity-permeability distribution in the study zone that is
required for proper interpretation of the tracer flow is usually
not available. Recognizing that the detection of the oil/water
menisci in reservoir rock means presence of oil, and borrowing from
the idea of enhancing magnetic resonance imaging (MRI) with use of
paramagnetic nanoparticles, embodiments of the present invention
detail the use of such particles for accurate determination of oil
saturation in reservoir rock.
[0085] Super-paramagnetic nanoparticles are currently being used to
enhance MRI of targeted human body parts (Oh et al. 2006). The
coating of the particles is designed to attach to specific human
tissue. In subsurface pore spaces, the coexistence of multiple
fluid phases implies presence of, for instance, water-oil
interfaces. If one of the phases contains paramagnetic particles,
the interface (also in contact with the solid) can show an elastic
response (and even resonance) when exposed to an oscillating
external magnetic field. The present inventors tested and validated
this concept of detecting the acoustic response, which may lead to
the development of a novel method of determining the hydrocarbon
saturation distribution in subsurface formations. This is akin to
measurements of seismic response to an imposed electromagnetic
field earlier proposed as a hydrocarbon detection technique. The
latter relies on the dielectric difference between the oil and
water phase (Pride, 1994; Thompson and Gist, 1999), whereas
embodiments of the present invention relies on the presence of
paramagnetic nanoparticles, which may be introduced by injection
from wellbores.
[0086] Referring to FIG. 1A, a consideration for a method of oil
saturation determination 100 in accordance with embodiments of the
present invention is that when nanoparticles 102 are injected into
a reservoir rock 104 and contact oil 108, they readily adhere to
the oil/water interface 110, but do not adhere to the pore wall.
Making a colloidal particle readily adhere to an interface between
oil and water of given compositions has been an active research
subject because emulsions/foams stabilized with colloidal particles
("Pickering" emulsions) are widely used, though not in the oil
industry (Binks 2002; Binks and Lumdson 2000). During the last 10
years or so, making nanoparticles stay at the immiscible
fluid/liquid interface, and their characterization, has been
studied extensively (Dickson et al. 2004; Binks and Horozov 2006;
Arney et al. 2006; Adkins et al. 2008).
[0087] A factor that allows use of functional nanoparticles for
applications in oil exploration and production is their small size,
so that they can be transported with ease in the reservoir rock,
unlike the colloidal particles that are generally filtered within a
short distance from injection. The transport of dilute aqueous
dispersions of nanoparticles in porous media is an area of active
research by the present inventors (Rodriguez et al. 2009) and
others (Li et al. 2007).
[0088] Adhesion of a nanoparticle 200 at an interface generally
requires the coating of the nanoparticle surface with a polymer or
surfactant, so that the contact angle (.theta.) made by the
oil/water interface on the nanoparticle surface is close to
.theta.=90.degree. (208), as shown in FIG. 2A. If
.theta.>90.degree., and the interface is densely populated by
the nanoparticles, the interface is curved toward the water phase
and a water-in-oil (or water-in-CO.sub.2) emulsion is formed. If
.theta.<90.degree., the interface is curved toward the oil phase
(Binks 2002; Kralchevsky et al. 2005). The free energy of adhesion
for a nanoparticle at the interface is given by:
.DELTA.G.sub.ad=.pi.a.sup.2.gamma..sub.ow(1-|cos .theta.|).sup.2
(A)
where a is particle radius; and .gamma..sub.ow is the interfacial
tension.
[0089] The above adhesion energy is quite large (Binks 2002; Binks
and Horozov 2006), which is the cause for the unusually long-term
stability of solid-stabilized emulsions, compared to the
surfactant-stabilized emulsions. This also brings out an advantage
of using nanoparticles in embodiments of the present invention,
i.e., even when the nanoparticles in the bulk water phase are
flushed out after the initial injection, those adsorbed at the
oil/water interface remain there without being desorbed.
[0090] A variety of methods of coating nanoparticles or creating a
shell 204 to a nanoparticle core 202 (FIG. 2B), have been reported
in the literature (Bourgeat-Lami and Duguet 2006). For example, to
create a stable super-critical CO.sub.2-in-water emulsion, the
inventors prepared silica particles of varying surface wettability
by reacting the strongly hydrophilic silica with
dichlorodimethylsilane to reduce the surface density of silanol
groups (Dickson et al. 2004). To create a stable water-in-CO.sub.2
emulsion, the inventors were able to form, around a hydrophilic
colloidal or fumed silica core, a shell of cross-linked
trifunctional agent,
(heptadecafluoro-1,1,2,2-tetrahydrodecyl)triethoxysilane, to render
the particles CO.sub.2-philicity (Adkins et al. 2008). Dey and
O'Connor (2004) employed the atom transfer radical polymerization
(ATRP) method to create a polystyrene coating around a magnetic
nanoparticle. Saleh et al. (2005) created highly charged surface by
sulfonation of the ATRP-prepared polystyrene coating to silica
core.
[0091] A probe used in embodiments of the present invention is a
suspension of nanosize (<100 nm) particles typically coated with
a molecular layer of a dispersant and suspended in a liquid carrier
(see FIG. 1B). Unlike in magneto- or electrohydrodynamics, the body
force acting on the fluid is due to magnetic polarization of the
particles only. Further, the present inventors considered
paramagnetic particles which align themselves parallel to the
applied magnetic field and do not retain magnetic moment after the
field is removed (so called soft magnetic materials, see FIG. 1C)
in contrast to permanent magnets (so called hard magnetic
materials).
[0092] Ferrofluids applications range from a large number of
engineering devices to tracers of blood flow in medical
diagnostics: major breakthroughs happened in the 1970s and 1980s
(Rosensweig, 1997). Subsurface applications were explored more
recently (Moridis et al. 1998, Oldenburg et al. 2000), in
particular to guide the ferrofluid through a porous formation by
exposing it to a strong magnetic field.
[0093] The particle size (two orders of magnitude less than the
colloidal particles) enables suitably surface-coated nanoparticles
to flow through the reservoir rocks without retention in pore
throats, even at very large particle concentrations (Rodriguez et
al. 2009). Particle coating is a matter of design to ensure the
dispersability of the nanoparticles and also to avoid adsorption on
(charged) rock surfaces. Further, a coating can be designed to make
particles prefer either the aqueous or non-aqueous phase, or the
non-aqueous/aqueous interfaces. In the latter case, particles
require high energy to adsorb at the interfaces and once adsorbed,
they will not detach easily (FIG. 2A) and will consequently form a
monolayer at the interface (for comprehensive review, see Bresme
and Oettel, 2007). The application of nanoparticles at the
interface in stabilizing emulsions, and a study parallel to the
present invention is available in Zhang et al. (2009).
[0094] A foundation of a theoretical treatment of an application of
embodiments of the present invention comprises adding magnetic
forces to the Navier-Stokes equation and developing stress tensors
accordingly. Rosensweig (1997) expounds this theory, and Lavrova et
al. (2006) provide a recent numerical treatment of a free surface
application. They classified the equation sets required for
numerical simulation of the interface motion and studied the
interactions among Maxwell, Young-Laplace and Navier-Stokes
equations for some of classical problems in ferrohydrodynamics and
applied their numerical scheme to them. Bashtovoi et al. (2002)
studied the equilibrium of a magnetic fluid column inside a
cylindrical capillary in the presence of a uniform external
magnetic field. They found that the total pressure drop in the
fluid decreases in magnetic fields longitudinal and transverse to
the axis of the capillary tube. Polevikov and Tobiska (2004)
extended this and studied the instability of a layer of magnetic
fluid in a plane capillary in the presence of a uniform external
magnetic field. They found two different types of instability with
increasing magnetic field.
[0095] Embodiments of the present invention are interested in
subsurface applications of ferrofluids, with particular attention
to hydrocarbon/water interfaces. Having the magnetizable fluid
guided through the subsurface in mind, Oldenburg et al. (2000)
added the magnetic force to the pressure gradient and gravitational
body force terms in Darcy's Law and calculated the resulting
transport of the ferrofluid. Calculating the magnetic field
strength H in a general medium with variable magnetic permeability
(such as any porous medium), the resulting magnetization of the
ferrofluid M, and the gradient of the field strength (required for
the magnetic force term) are non-trivial tasks. On the related
subject of the oscillation of the fluid/fluid interfaces held in
rock pores in response to an imposed seismic vibration, a detailed
literature review is given by Huh (2006). Hilpert (2007) and others
examined the resonance exhibited by oil blob interfaces when
exposed to an oscillating external body force. As shown below,
however, the forcing resulting from a magnetic field has somewhat
different (and more involved) physics.
[0096] The present disclosure includes a basic exposition of the
theory applying for the aqueous dispersion of paramagnetic
nanoparticles, and derives the relevant equations for the
particular application of modeling the interfacial movements in
response to the imposed magnetic field. Specific examples of the
interfacial displacements, obtained from analytical solutions, are
then given to provide insight on the interpretation of the
laboratory measurements. The numerical modeling of interfacial
oscillations in complex pore geometry is also described with some
simple example results. The phase-sensitive optical coherence
tomography (PS-OCT) set-up that directly measures the displacement
of a fluid/fluid interface in response to the imposed magnetic
field is also described.
[0097] From the modeling standpoint, the present inventors
recognize three steps: oil-water interface modeling, exposing the
interface to magnetic field (assuming paramagnetic particles were
injected), and measuring the sound wave in response to the
interface movement (oscillation). The first two steps are described
herein.
[0098] If nanosize paramagnetic particles are suspended in a fluid,
they will not show magnetic properties until an external magnetic
field is applied (FIG. 1C). When the field is applied, the tendency
of the dipole moments to align with the field is partially overcome
by thermal agitation. As the field strength is increased, the
particles become more and more aligned, and at some point the
magnetization achieves the saturation value (i.e., all particles
are aligned as depicted in FIG. 1C).
[0099] The classical Langevin theory gives the relationship between
the magnetization of the ferrofluid, the applied magnetic field (of
magnitude H), and the magnetization of the bulk solid material from
which the nanoparticles are made, via the Langevin function, L:
M .phi. M d = coth ( .alpha. ) - 1 .alpha. = L ( .alpha. ) ( 1 )
##EQU00001##
where
.alpha. = m H kT ##EQU00002##
is a ratio of magnetic and thermal energies for a single particle,
k=1.380710.sup.-23 JK.sup.-1 is Boltzmann's constant and T is
temperature. For small .alpha. (soft magnetic materials) the
relationship is approximately linear,
L ( .alpha. ) .apprxeq. .alpha. 3 . ##EQU00003##
This equation is not only important in ferrofluids, but is also
used to determine the particle size of a magnetic solid dispersed
in a support material (e.g., iron in a piece of rock). An example
magnetization curve is shown in FIG. 3A. The review paper by Gupta
and Gupta (2005) provides more details on magnetization properties
of nanoparticles.
[0100] The relationship between the magnetic induction field {right
arrow over (B)}, magnetic field strength {right arrow over (H)},
and magnetization is given by {right arrow over
(B)}=.mu..sub.0({right arrow over (M)}+{right arrow over (H)}),
i.e., the resulting magnetic induction is a sum of the induction
due to the impressed magnetic field strength and that of the
magnetized material itself (the proportionality constant
.mu..sub.0=4.pi.10.sup.-7 Hm.sup.-1 is the permeability of the
vacuum). For soft magnetic materials and the magnetic fields of
moderate strength, {right arrow over (M)} and {right arrow over
(H)} are co-linear, {right arrow over (M)}=.chi.{right arrow over
(H)}. The proportionality constant .chi. is dimensionless and is
called magnetic susceptibility; see FIG. 3B for an example
calculation of how susceptibility changes with the particle size.
In this case:
{right arrow over (B)}=.mu..sub.0({right arrow over (M)}+{right
arrow over (H)})=.mu..sub.0(.chi.{right arrow over (M)}+{right
arrow over (H)})=.mu.{right arrow over (H)} (2)
[0101] In applications described herein, there is no free electric
charge flow, thus the Maxwell equations reduce to the second Gauss
Law:
.gradient.{right arrow over (B)}=0 (3)
and the form of Ampere's law when there is no electric current
flow:
.gradient..times.{right arrow over (H)}=0 (4)
[0102] In other words, the magnetic induction field is divergence
free (akin to the velocity of an incompressible fluid), and the
magnetic field is vorticity free. At the boundary of two materials
with different magnetic properties, this results in the continuity
of the normal component of magnetic induction, and of the
tangential component of magnetic field:
{right arrow over (n)}({right arrow over (B)}.sub.1-{right arrow
over (B)}.sub.2)=0 (5)
{right arrow over (n)}.times.({right arrow over (H)}.sub.1-{right
arrow over (H)}.sub.2)=0 (6)
[0103] Equation of Ferrofluid Motion: Embodiments of the present
invention consider oscillations of the fluid-fluid interface around
an equilibrium position (average fluid velocity=zero) rather than
solutions to the equations of motion of bulk fluids with nonzero
average velocity. Though a focus is on the balance between
capillary and magnetic forces, it is convenient to cast this
problem as the boundary (interface) conditions of the equations of
bulk multi-phase fluid motion.
[0104] Because the particles are paramagnetic and are dispersed in
the bulk fluid, a magnetic force acts on an element of magnetizable
fluid like a combination of thermodynamic pressure (normal to the
surface of the fluid volume in question) and a volumetric force
analogous to that of gravity. While the calculation of the force
can be rather complex, it can nevertheless be formulated as a
gradient of a magnetic stress tensor.
[0105] Equation of Motion for Non-Magnetized Fluid: The
Navier-Stokes equation for two phase flow of incompressible fluids
of constant viscosity:
.rho. D .upsilon. .fwdarw. Dt = - .gradient. p + .eta. .gradient. 2
.upsilon. .fwdarw. + .rho. g .fwdarw. ( 7 ) ##EQU00004##
where the notation is standard: .rho., .eta. are density and
viscosity (both discontinuous at the fluid-fluid interface), p is
thermodynamic pressure, {right arrow over (v)},
D .upsilon. .fwdarw. D t ##EQU00005##
velocity and its material derivative and {right arrow over (g)}
gravitational acceleration. The terms of the right hand side
constitute a force density {right arrow over (f)}, which is the sum
of the pressure, viscous and gravity forces. The effect m of the
pressure and viscous forces on a volume of fluid can be viewed as
force acting normal to the surface of the volume. Introducing the
stress tensor notation, the pressure and viscous tensor is given by
the formula:
T=-.gradient.pI+.eta.(.gradient.{right arrow over
(v)}+.gradient.{right arrow over (v)}.sup.T) (8)
[0106] The total force on a volume V of fluid (whose surface is S)
is given by {right arrow over (F)}=.intg..sub.s{right arrow over
(n)}TdS=.intg..sub.v .gradient.TdV and the force density is then
{right arrow over (f)}=.gradient.T.
Fluid-Fluid Boundary Conditions for Non-Magnetized Fluids: Boundary
conditions for the interface between the (immiscible) fluids are
modeled using the Young-Laplace equation. According to the
Young-Laplace equation, the interface at equilibrium supports a
pressure difference (so called capillary pressure p.sub.c). It does
so by adopting a curved surface whose curvature .kappa.
satisfies:
p.sub.c=p.sub.nw-p.sub.w=.sigma..kappa. (9)
[0107] Equation of Motion for Magnetized Fluid: Similar to pressure
and viscous stress tensors, one can derive a magnetic stress
tensor. The derivation is rather lengthy (Rosensweig, 1997) and the
magnetic stress tensor in its most general form is given as:
T m ' = - p ( .rho. , T ) I - { .intg. 0 H .mu. 0 ( .differential.
( .upsilon. M ) .differential. .upsilon. ) H , T H + 1 2 .mu. 0 H 2
} I + B .fwdarw. H .fwdarw. T m ( 10 ) ##EQU00006##
[0108] Here
.upsilon. = 1 .rho. ##EQU00007##
is specific volume. Because our application is to ferrofluids, it
is convenient to include the thermodynamic pressure p in this
tensor. This motivates the definition of composite pressure:
p * = p ( .rho. , T ) + .mu. 0 .intg. 0 H .upsilon. (
.differential. M .differential. .upsilon. ) H , T H p s + .mu. 0
.intg. 0 H M H p m . ( 11 ) ##EQU00008##
p.sub.s and p.sub.m are called magnetostrictive and fluid-magnetic
pressure, respectively. Further, magnetic force (that excludes the
thermodynamic pressure component) is given as:
f .fwdarw. m = .gradient. T m = - .gradient. [ .mu. 0 .intg. 0 H
.upsilon. ( .differential. M .differential. .upsilon. ) H , T H +
.mu. 0 .intg. 0 H M H ] + .mu. 0 M .gradient. H ##EQU00009##
which results in the amended Navier-Stokes equation:
.rho. D .upsilon. .fwdarw. Dt = f .fwdarw. p pressure force + f
.fwdarw. m magnetic force + f .fwdarw. .upsilon. viscous force + f
.fwdarw. g gravity force ##EQU00010## .rho. D .upsilon. .fwdarw. Dt
= - .gradient. p * + .mu. 0 M .gradient. H + .eta. .gradient. 2
.upsilon. .fwdarw. + .rho. g .fwdarw. ##EQU00010.2##
[0109] It must be noted that the composite pressure has replaced
the thermodynamic pressure term from the standard Navier-Stokes
formulation. Furthermore, most applications (Oldenburg et al. 2000,
Lavrova et al. 2006) ignore the magnetostrictive pressure: this can
be safely done for single phase, incompressible ferrofluid
applications where the magnetization does not vary with fluid
density. In two-phase flow where only one phase is magnetized,
however, the present inventors show below that the magnetostrictive
term is not necessarily negligible.
[0110] Boundary Conditions for the Interface Between a Magnetized
Fluid and a Non-Magnetized Fluid: Assume the wetting (W, aqueous)
fluid is magnetizable, and the non-wetting (NW, non-aqueous) fluid
is not (see FIG. 4A), and using the magnetic stress tensor stated
above and the fact that the normal components of B and tangential
component of H are continuous across the NW-W interface, the
interface at equilibrium curves in order to satisfy a modified
Young-Laplace equation as follows:
p.sub.c-(p.sub.s+p.sub.m+p.sub.n)-.sigma..kappa.=0 (12)
The equation above contains the new pressure term, magnetic normal
pressure:
p.sub.n=.mu..sub.0(H.sub.2n-H.sub.1n).sup.2/2 (13)
that appears due to integration of the magnetic stress tensor at
the interface between non-magnetized and magnetized fluids, and
H.sub.1n is the component of the magnetic field strength in fluid 1
normal to the interface. As before,
p.sub.c=p.sub.nw-p.sub.w=p.sub.2-p.sub.1 stands for capillary
pressure. For boundary conditions, gravity forces are assumed small
(but could be added to the analysis). Further, had the non-wetting
fluid been magnetized and not the wetting fluid (see FIG. 4B), the
sign of the term (p.sub.s+p.sub.m+p.sub.n) in the modified
Young-Laplace equation, Equation (12), would change. Assuming B and
H are collinear (consistent with the use of soft magnetic
material), the pressures evaluate to:
p m = 1 2 .mu. 0 .chi. H 1 2 = 1 2 .mu. 0 .chi. ( .chi. + 1 ) 2 B 1
2 p s = - 1 2 .mu. 0 .chi. H 1 2 .rho. 1 .rho. 1 - .rho. 2 = - 1 2
.mu. 0 .chi. ( .chi. + 1 ) 2 B 1 2 .rho. 1 .rho. 1 - .rho. 2 p n =
1 2 .chi. 2 H 1 n 2 = 1 2 .chi. 2 ( .chi. + 1 ) 2 B 1 n 2 ( 14 )
##EQU00011##
[0111] All terms have nonlinear dependence on the magnetic
susceptibility .chi. of the suspended nanoparticles (note that the
nonlinear dependence of p.sub.n is .chi. times that of p.sub.m or
p.sub.s). Magnetostrictive term p.sub.s also depends on the
densities of the two fluid phases (and can be positive or
negative). The magnetic normal pressure p.sub.n, on the other hand,
depends on the component of magnetic field normal to the
fluid/fluid interface, and thus it is not constant along the
interface.
[0112] Equation (12) extends the Young-Laplace relationship to
account for magnetic forces. It is remarkable that the effect of
the magnetic field can be incorporated in terms of pressure-like
quantities p.sub.s, p.sub.m and p.sub.n. This means the existing
body of theory and simulators for capillarity-controlled
displacements can be readily extended to handle ferrofluids like
the ones disclosed herein. The magnetic pressure terms can augment
or diminish the capillary pressure, depending on the type of fluids
(e.g., their density ratio), as well as on which phase is
magnetized (wetting or not, denser or not). Further, which of the
magnetic terms becomes dominant as well as their size relative to
the capillary pressure term is controlled by multiple factors. In
general, a fluid/fluid configuration that is stable in the absence
of a magnetic field will respond in one of three ways when a
magnetic field is applied. The induced motion may be incremental
and reversible, e.g., to a new stable configuration occupying the
same pores and throats; oscillatory, e.g., interfaces vibrating in
the same throats; or irreversible, e.g., Haines jumps of the
nonwetting phase into previously unoccupied pores.
[0113] Example Calculation of Interfacial Movement: The present
inventors calculated the contributions to composite pressure in an
example application. Following Oh et al. (2006), the inventors
carried out studies in which the following sinusoidal magnetic
field is applied in a z direction:
{right arrow over (B)}(x,y,z,t)=sin(2.pi.f.sub.n)B.sub.z(z){right
arrow over (k)} (15)
where f.sub.n is modulation frequency of the applied sinusoidal
magnetic field, and B.sub.z its maximum strength. Variation of
B.sub.z in x and y directions was negligible.
[0114] To demonstrate how different fluids, pore geometry, and type
of particles influence the composite pressure, the inventors
assumed a straight capillary of radius r. The capillary contains
water (wetting phase) on the bottom and a less dense non-wetting
fluid on top. The situation is taken directly from the study set-up
described later, for which the following values are assigned:
r=10.sup.-3 m; water phase of density .rho..sub.1=1000 kgm.sup.-3;
contains paramagnetic nanoparticles of .chi.=0.2 and 20; and
non-wetting phase has density .rho..sub.2=1 kgm.sup.-3 and
interfacial tension .sigma.=0.072 Nm.sup.-1 (air), or
.rho..sub.2=750 kgm.sup.-3, and .sigma.=0.032 Nm.sup.-1 (dodecane).
A constant value of magnetic field strength B.sub.z(z)=0.05T and a
frequency of 1 Hz are assumed. To simplify the demonstration, the
projection B.sub.1n, which varies with position along a curved
interface, is approximated with a constant corresponding to its
value at angle 45.degree. with respect to the magnetic field. The
capillary pressure is set to the equilibrium value in the absence
of a magnetic field, i.e., to
2 .sigma. r . ##EQU00012##
[0115] Considering an air/water interface first, the ratio
.rho. 1 .rho. 1 - .rho. 2 ##EQU00013##
in Equation (14) in this case is very close to unity, so no matter
which particle susceptibility is considered, the p.sub.m and
p.sub.s terms almost cancel each other, as the sinusoids in FIGS.
5A and 5B illustrate. The sum of the magnetic pressures will
therefore be determined by the magnetic normal pressure p.sub.n and
thus is always positive. The total magnetic pressure is about a
factor of ten smaller than the capillary pressure for particles of
small susceptibility, as shown in FIG. 5A, but three times larger
than the capillary pressure for particle susceptibility 100 times
greater, as shown in FIG. 5B. The imposed field would thus be
expected to induce oscillation of the interface for the situation
in FIG. 5A, but would overcome capillary forces and induce fluid
displacement for large susceptibility particles (assuming no
gravity forces).
[0116] In a dodecane/water combination, on the other hand, the
p.sub.m and p.sub.s terms are of opposite sign but not of equal
magnitude. Depending on particle susceptibility, the relative sizes
of all the magnetic terms differ and can sum to a negative value or
positive value. For small susceptibility, as shown in FIG. 6A, the
total magnetic pressure is negative, while for large
susceptibility, as shown in FIG. 6B, the total magnetic pressure is
positive. Consequently, an imposed magnetic field can affect the
fluids in dramatically different ways, depending on the
susceptibility of the paramagnetic particles. In both cases, the
magnitude of the total magnetic pressure is several times greater
than the capillary pressure. Thus, small susceptibility need not
render magnetic forces negligible relative to capillary pressure.
The fluid densities are important in this respect; the normalized
magnetic pressure is an order of magnitude larger for
dodecane/water (see FIG. 6A) than for air/water (see FIG. 5A) for
particles of small susceptibility. For large susceptibility, the
normalized magnetic pressures are similar for air/water and
dodecane/water systems.
[0117] The particular fluid-fluid-solid surface combination adds
another dimension to this behavior. If water is the wetting phase,
the total magnetic pressure is subtracted from the capillary
pressure, as in Equation (12). If water is nonwetting, the magnetic
pressure is added to the capillary pressure. As seen in FIGS. 6A
and 6B, the total magnetic pressure itself may be either positive
or negative. Therefore, there are four possible scenarios when
exposing the system to a magnetic field as shown below:
TABLE-US-00001 p.sub.m+ p.sub.n+ p.sub.s positive p.sub.m+ p.sub.n+
p.sub.s negative Water-wet solid Effect of p.sub.c Effect of
p.sub.c diminished augmented Oil-wet solid Effect of p.sub.c Effect
of p.sub.c augmented diminished
Diminishing the effect of p.sub.c means that the fluid/fluid
interface will adopt a curvature smaller than it would in the
absence of the magnetic field. Augmenting p.sub.c causes the
interface to become more curved.
[0118] FIGS. 5A and 5B and FIGS. 6A and 6B show that the normalized
total magnetic pressure oscillates between zero and some extreme
value. Large values of magnetic pressure are expected to be useful
in applications. Thus, the dependence of the extreme value upon
particle susceptibility offers insight in the full range of
possibilities, as shown in FIG. 7. The extreme value grows with
particle susceptibility but exhibits saturation. Thus efforts to
increase response by deploying particles of greater susceptibility
will reach a point of diminishing returns. The inset in FIG. 7
shows that the extreme value can be a large negative number at
small susceptibility, depending on fluid densities. Thus some fluid
pairs may work well with particles of modest susceptibility and
poorly with particles of greater susceptibility. This
counterintuitive result raises interesting questions for the design
of particles for this application. Further, air has a narrow range
of extreme values (and is likely going to be examined only in a
laboratory environment), while dodecane, of interest in field
applications, has a much wider range of extreme values.
[0119] Typical sandstone pore size (radius) is about 10 micron,
i.e., 100 times smaller than the tube considered in the example
above. The previous discussion applies, but the ratio of magnetic
pressures relative to the capillary pressure is 100 times smaller.
In the field, it is therefore expected that interfaces will
oscillate when exposed to an oscillating magnetic field.
[0120] Oscillation of oil/water meniscus in a pore: The presence of
the oil/water interfaces (menisci) in reservoir rock influencing
the seismic wave propagation has been recognized by the petroleum
geophysicists for some time (Li et al. 2001). For example, Miksis
(1988) did modeling analysis to see if the fluctuation of the
oil/water menisci at rock pores is a main mechanism for the seismic
velocity attenuation. In the attempts to explain the enhanced oil
recovery by seismic vibration that has been claimed by Russian
researchers (Roberts et al. (2003)), Hilpert et al. (2000) and many
others investigated the possibility of generating resonance when a
seismic vibration is conveyed to an oil-containing reservoir zone
(see Huh (2006) for review). Because the oil/water interfacial
tension has a restoring force when displaced, the oil/water
meniscus oscillation generates a pressure wave, as schematically
shown in FIG. 8.
[0121] A detailed pore level interface description at residual oil
saturations in arbitrary geometries can readily be obtained
(Prodanovi and Bryant, 2006, 2008, 2009; Prodanovi , 2009). The
approximate modeling of the oscillation of the oil/water interface
in a rock pore, in response to the imposed magnetic field, can be
carried out by modifying the software developed by the present
inventors (Prodanovi and Bryant, 2006, 2008, 2009). A short summary
of the approach is as follows. The moving surface of interest is
embedded as the zero level set of function .phi.({right arrow over
(x)}, .tau.) defined on an entire domain and r is a time-like
parameter that tracks the motion of the interface toward an
equilibrium position. The zero level set is the set of points
{right arrow over (x)} such that .phi.({right arrow over (x)},
.tau.)=0. Such representation enables elegant calculation of
various interface properties. For instance, the normal to the
interface is simply,
n .fwdarw. = .gradient. .phi. .gradient. .phi. , ##EQU00014##
where .gradient..phi.=(.phi..sub.x,.phi..sub.y,.phi..sub.z) is the
spatial gradient of .phi., and (twice the) mean curvature .kappa.
is divergence of the normal. In level set methods, the level set
function evolves in time according to the following partial
differential equation:
.phi..sub..tau.+F|.gradient..phi.|=0,.phi.(x,0)given (27)
where F is the speed of the interface in a normal direction. More
general equation:
.phi..sub..tau.+{right arrow over
(u)}.gradient..phi.=0,.phi.(x,0)given (28)
where {right arrow over (u)} is external velocity field (if
u .fwdarw. = F n .fwdarw. = F .gradient. .phi. .gradient. .phi. ,
##EQU00015##
the previous equation will be obtained). In the most general two
phase flow application, one would propagate the fluid-fluid
interface using velocity field {right arrow over (u)} obtained by
solving the Navier-Stokes equation. If capillarity is the dominant
force, however, the interface at equilibrium will curve itself
while balancing capillary pressure and interfacial tension
(Young-Laplace equation p.sub.c=.sigma..kappa.). Thus, the
appropriate normal speed model at the core of slow, quasi-static
interface movement is:
F({right arrow over (x)},.tau.)=p.sub.c-.sigma..kappa.({right arrow
over (x)},.tau.) (29)
[0122] The inventors modeled the situation where the wetting fluid
is perfectly wetting the solid surface (contact angle zero). This
is effectively done describing the solid phase with a separate
level set function and implementing a simple penalization if the
meniscus enters the solid phase. For more details refer to
Prodanovi and Bryant (2006, 2008).
[0123] Without magnetic pressures, the interface adopts a curvature
that (at equilibrium) balances capillary pressure only. Such an
interface can be found by solving Equations (27) and (28) in the
limit of large .tau.. With one of the fluids magnetized and exposed
to an external magnetic field we need to add magnetic pressures
into the equation as per Equation (12) and thus the speed function
becomes (for wetting fluid being magnetized):
F({right arrow over
(x)},.tau.,t)=p.sub.c-(p.sub.m(t)+p.sub.s(t)+p.sub.n(t))-.sigma..kappa.({-
right arrow over (x)},.tau.) (30)
[0124] If the non-wetting fluid is magnetized and the wetting fluid
is not magnetized, the sign in front of the magnetic pressures
turns positive. t now denotes real time (of the magnetic field
oscillation, if applicable). If no damping of the interface motion
due to viscosity is assumed, for each real time t, the interface
instantaneously finds the equilibrium position (steady state
solution to Equation (27) with respect to the parameter .tau.). For
practical application, one could find the physical link between
real time and the parameter .tau. and use the equation to monitor
motion in real time.
[0125] The inventors studied the influence of various magnetic
pressure terms using constant and sinusoidally changing magnetic
fields, the latter motivated by Equation (15), in a simple
converging-diverging capillary.
[0126] Constant Magnetic Field: In the presence of a simple
permanent magnet, the magnetic field as well as magnetic induction
field within the magnetized fluid in a small capillary are constant
(to a good approximation). Thus, magnetostrictive (p.sub.s) and
fluid-magnetic pressures (p.sub.m) are constant as well. If
magnetic normal pressure is negligible (as for example in the case
of dodecane and water with low susceptibility particles, FIG. 6A),
then the total pressure difference to be balanced by the curved
interface will be a constant. The value of the constant will be
smaller or larger than the original thermodynamic capillary
pressure, depending on whether NW or W phase is magnetized.
[0127] From the perspective of the fluid/fluid interface, the
effect of the constant magnetic field is equivalent to the effect
of an increment/decrement in capillary pressure. Thus, the
interface will assume new position with a larger/smaller meniscus
curvature. Depending on the geometry of the (capillary) pore space,
the new position will be reached reversibly and nearby (in a
converging geometry) or irreversibly and far-away (interface jump
in a converging-diverging geometry when the new pressure is
smaller/higher than the critical value for a neighboring
pore/throat).
[0128] FIG. 9 illustrates this behavior. The initial location of
the meniscus is the equilibrium position for value p.sub.c=0.1,
.sigma.=0.02,
.kappa. = p c .sigma. = 5. ##EQU00016##
The nonwetting phase is on the left side of the meniscus, and the
magnetizable wetting phase on the right. Suppose a constant
magnetic field is applied in the x-direction (horizontal direction
in FIG. 9), and suppose further that magnetic normal pressure
p.sub.n is negligible. The inventors chose a strength of the field
so that the total magnetic pressure p.sub.m+p.sub.s=0.02. The
magnetic pressure diminishes the capillary pressure, because the
wetting phase contains the paramagnetic particles. Hence, the
meniscus retreats (to the left in FIG. 9) to a new equilibrium
position in a less constricted part of the pore throat. The
imposition of the constant field in this case causes a small amount
of imbibition.
[0129] Suppose now that the fluids and susceptibility are chosen as
in FIG. 5A, so that the magnetostrictive and fluid magnetic
pressures are of opposite sign and the same magnitude, and the
magnetic normal pressure is non-negligible. In this case, the total
magnetic pressure is dominated by the magnetic normal pressure and
therefore varies with location along on the interface. The
equilibrium interface position will necessarily differ from the
previous case where the total magnetic pressure is constant
everywhere. Starting from the same parameters that produced the
non-magnetized equilibrium configuration, a constant magnetic field
is again imposed in the x-direction. The strength of the field is
chosen so that the maximum value of magnetic normal pressure is
p.sub.max=0.02, i.e., the same value as the total magnetic pressure
in the previous illustration. The local value of magnetic normal
pressure is thus p.sub.n=p.sub.max({right arrow over (n)}{right
arrow over (e)}.sub.x).sup.2 where {right arrow over (n)} is the
interface normal. This magnetic pressure diminishes the effect of
the capillary pressure when the W fluid is magnetized, so the
meniscus is expected to retreat. Since the magnetic normal pressure
depends on the interface position, an equilibrium position is found
(shown in FIG. 9) different from the one found when
magnetostrictive and fluid magnetic pressure of the same magnitude
was applied.
[0130] When the non-wetting phase is magnetized (and the wetting
phase is not), the situation is reversed, as shown in FIG. 10. In
this case, imposing the magnetic field causes a small amount of
drainage. Clearly if the meniscus were near the narrowest part of
the throat, even a small amount of drainage could lead to a Haines
jump.
[0131] In an oscillating magnetic field, assuming no damping by
viscosity, p.sub.m+p.sub.s=0 and the magnetic normal pressure of
the form p.sub.n(t)=p.sub.max({right arrow over (n)}{right arrow
over (e)}.sub.x).sup.2sin.sup.2(.omega.t), the interface will
oscillate at the same frequency .omega. between the zero
magnetization and constant magnetization positions as shown in
FIGS. 9 and 10. If for the purpose of illustration, a relationship
t=.tau. is assumed and the displacement of the interface center of
mass is monitored, it is observed that the interface withdraws
somewhat and ultimately oscillates around a position in between the
previously discussed end members as depicted in FIG. 11A. Adding
the magnetostrictive and fluid-magnetic pressure (i.e., volumetric)
terms of the same order of magnitude, e.g.
p.sub.m+p.sub.s=p.sub.max sin.sup.2(.omega.t), shows the same
qualitative behavior as depicted in FIG. 11B.
[0132] Acoustic response of superparamagnetic nanoparticles to
magnetic field oscillation: Because of a wide variety of
applications, preparation of superparamagnetic nanoparticles is an
active research area (Lu et al. 2007). FIG. 12 shows the
magnetization capacity of the iron oxide nanoparticles prepared by
the present inventors.
[0133] In biomedical engineering, sending paramagnetic
nanoparticles to a target human organ, when injected into the blood
stream, is an active research subject. The placement of
paramagnetic nanoparticles at the target tissue allows enhanced
imaging of the tissue, or delivery of a drug to it. The present
inventors employed magnetic impulse and acoustic response to detect
the presence of superparamagnetic nanoparticles in a surrogate
tissue (Oh et al. 2006). FIG. 13 shows the schematics of the system
1300 for the magnetic field generation and acoustic response
recording. System 1300 comprises a water bath/tank 1302, which
contains a rock sample 1304 to be imaged. The tank 1302 is filled
with water or an aqueous dispersion 1306 comprising the coated
paramagnetic nanoparticles. An acoustic transducer 1322 is also
placed in the tank 1302 to transmit the acoustic waves to a sonic
frequency analyzer 1318. Images from the analyzer 1318 are viewed
on a display device 1320. The system 1300 also comprises a power
supply source 1312. A current amplifier 1316 with one or more
output channels is connected to the power supply source 1312, and a
function generator 1314 is connected to a second output channel
1326 of the current amplifier 1316. A solenoid coil 1310 is wrapped
around a metallic core 1308, wherein the solenoid coil 1310 is
connected to a first output channel 1324 of the current amplifier
1316, wherein the solenoid coil 1310 generates a magnetic field
from the power supply 1312 and the current amplifier 1316.
[0134] Milner and his group also employed the phase-sensitive
optical coherence tomography to measure the nano-scale
displacements of the nanoparticle-imbedded sample, in response to
the applied magnetic impulse (Telenkov et al. 2004). Such direct
measurements of interfacial oscillation, for a simple model
oil/water meniscus, will be very valuable in basic understanding of
the acoustic generation. Both of the above measurement techniques
can be employed when the magnetic field is applied in sinusoidal
wave form, instead of the pulse form. Phase shifts in acoustic
response and displacement response can be measured.
[0135] For embodiments of the present invention, the acoustic
response to the imposed magnetic wave is measured in terms of the
oil saturation in the rock sample, the sample size, lithology and
permeability of rock sample, the nanoparticle size and surface
wettability, and the compositions of oil and brine in the reservoir
rock. Such detailed measurements allow development of the
correlation between the oil saturation and magnetic impulse. Such
correlations serve as a basis not only for the development of a new
tool that "illuminates" the oil in the reservoir rock, but also for
enhancing the capabilities of the existing tools such as the MRI
for core scanning and the NMR logging.
[0136] Materials and Methods: An objective of the study described
hereinabove was to model the oscillation of the oil/water
interfaces in reservoir rock pores when a magnetic field is
imposed, so that the feasibility of detecting the acoustic response
can be evaluated. The inventors herein describe the measurement of
the displacement of a fluid/fluid interface in response to the
imposed magnetic field. The aqueous phase, which contains the
paramagnetic nanoparticles, and another immiscible fluid are
contained in a small cylindrical cell at ambient condition, forming
an essentially flat interface between them. The procedure and the
results are described below.
[0137] Materials: NanoAmor iron oxide nanorods, dispersed in water
at 35.+-.2 wt % concentration, were obtained from Nanostructured
& Amorphous Materials Inc. (Houston, Tex.). The Transmission
Electron Microscopy (TECNAI 12 Spirit Biotwin, manufactured by FEI)
images show that the nano-rods have an aspect ratio of about 5:1,
as shown in FIG. 14. The size distribution of the nano-rods was
measured with a Dynamic Light Scattering (DLS) apparatus (provided
by the Chemical Engineering Department, UT Austin). FIG. 15 and
Table 1 show the volume percentage as a function of the
hydrodynamic diameter of the rods, which is close to the rod
length. The scattering angle was set to 90.degree. and the data
were analyzed using a digital autocorrelator (Brookhaven BI-9000AT)
and a non-negative least-squares (NNLS) routine (Brookhaven
9KDLSW32). The measured count rate was approximately 150 kcps.
Measurements were made over a period of 2 minutes. The nanorods had
a reasonably narrow size distribution with peak value at 77 nm, and
also contained a small amount of aggregates of about 250 nm
diameter. The nanoparticle dispersion was diluted with de-ionized
(DI) water as needed. Reagent grade dodecane and DI water were
used.
TABLE-US-00002 TABLE 1 Local (G) and cumulative (C) distribution of
nanoparticle equivalent diameter (d) as measured by DLS. d (nm)
G(d) C(d), % 58.01 0 0 61.36 0 0 64.86 0 0 68.58 12 4 72.51 61 23
76.67 100 54 81.07 83 80 85.72 38 92 90.63 0 92 95.83 0 92 101.33 0
92 107.14 0 92 113.29 0 92 119.78 0 92 126.65 0 92 133.92 0 92
141.60 0 92 149.72 0 92 158.31 0 92 167.39 0 92 176.99 0 92 187.14
0 92 197.87 0 92 209.22 0 92 221.23 0 92 233.91 4 93 247.33 8 96
261.52 8 98 276.52 5 100 292.38 1 100 309.15 0 100 326.88 0 100
345.63 0 100
[0138] FIG. 16 shows a schematic of the system 1600, which
comprises: (i) a glass slide holder 1628, capable of holding a
glass slide 1612 with a small cylindrical well 1602 (diameter 2 to
4 mm) into which the sample liquid(s) are placed; (ii) an
electromagnetic solenoid 1620 with an iron tip 1608, which
generates the magnetic field of a prescribed schedule of strength
vs. time; and (iii) a phase sensitive optical coherence tomography
(PS-OCT) system 1606 that measures the displacement of the
fluid/fluid interface in response to the imposed magnetic field.
The sample path optical fiber (PS-OCT) 1606 is in communication
with a gradient index (GRIN) lens 1610. The laser beam from the
optical fiber 1606 is focused through lens 1610 and passed through
a light splitter 1614 that allows for 95% transmission and 5%
reflection. PS-OCT allows measurement of displacement of a fluid
element or a solid particle in a sample with a sensitivity of tens
of picometers (Pierce et al. 2002). With a vertical scan (or a
horizontal scan, if needed) of the measurement location, the
interface location can be identified and its displacement can be
subsequently measured. PS-OCT has recently been employed to measure
the displacement of laser- and magneto-excited nanoparticles (Joo
et al. 2005; Adler et al. 2007). In the system 1600, the
displacement sensitivity of the PS-OCT 1606 is 65 pm and the depth
resolution is 10 to 15 microns. The imaging depth, the depth to
which reliable measurements in the fluid can be obtained, is 2 mm.
A laser beam used in the PS-OCT 1606 has a diameter of 30 microns.
The cylindrical well 1602 can be drilled directly into the glass
slide 1612, which enables convenient positioning of the sample for
the PS-OCT measurements. The system 1600 also comprises a power
supply source 1622. A current amplifier 1624 with one or more
output channels is connected to the power supply source 1622. A
function generator 1618 is connected to a second output channel
1626 of the current amplifier 1624. Cooling to the system is
provided by an externally connected cooler 1616.
[0139] The cylindrical well 1602 was partially filled with an
aqueous suspension of 5 wt % iron oxide nanorods. The remaining
volume in the well 1602 was filled with dodecane, as shown in FIG.
17. The PS-OCT 1606 was used to measure the displacement of both
interfaces (water/dodecane and dodecane/air) when a 1 Hz magnetic
field of approximately 0.05 T was applied. The displacement of
water-dodecane interface, measured from peak to valley, was about
5000 nm. The frequency was 2 Hz, twice the frequency of the
magnetic field. The frequency doubling is characteristic of
ferrofluids made with paramagnetic particles. No displacement of
the air/dodecane interface is expected, since neither phase is
magnetizable. The motion of the underlying dodecane/water interface
does cause measurable displacement at the air/dodecane, however.
The displacement is small (about 100 nm from peak-to-valley of the
2 Hz signal as seen in FIG. 18) and noisy: the high-frequency
fluctuations are almost half the amplitude of the 2 Hz signal.
[0140] The study was repeated without dodecane, so that the only
interface is between air and the aqueous suspension of nanorods.
The motion of the interface is clear, FIG. 18, but the maximum
displacement of the interface is 500 nm, an order of magnitude
smaller than for the dodecane/water interface.
[0141] The two studies demonstrated that the existence of
nanoparticles in one fluid phase results in measurable
displacements of the interface between that fluid and another,
non-magnetized fluid when a magnetic field is imposed. This
displacement is maximum at the interface of the magnetic fluid and
the non-magnetic fluid. Focusing the PS-OCT at depths below the
interface (results not shown here) shows that the displacement
decays with distance from the interface. Secondary displacement
(motion induced by the moving interface) also occurs above the
interface. Thus sound waves propagated through the fluids in this
study.
[0142] The studies also confirmed an important aspect. The measured
displacement of the interface between the magnetic and non-magnetic
fluids depends strongly on the densities of the fluids. Greater
displacement occurred when the non-magnetizable fluid (air or
dodecane) was denser. This observation is in accordance with the
above theoretical discussion. According to Equation (14), the sum
of magnetostrictive and fluid-magnetic pressures is inversely
proportional to the difference in the densities of the fluids and
directly proportional to the density of the non-magnetic fluid (the
density term in Equation (14) is near unity for the air/water
experiment and about 5 for the dodecane/water study). Therefore,
the denser the non-magnetic fluid, the larger the magnetic
pressures will be, and the greater the perturbation of the
interface [Equation (12)].
[0143] Studies with a ferrofluid (aqueous suspension of iron oxide
nano-rods) below a second, non-magnetizable fluid (air, dodecane)
showed measurable displacements of the fluid/fluid interface when
the system is exposed to an oscillating magnetic field. The
relative densities of the fluid phases strongly affect the
displacement, confirming theoretical prediction. A sinusoidal
magnetic field causes displacements of double frequency, also
confirming theoretical analysis. Quadratic sinusoidal terms emerge
in magnetic pressures, which are of the same order as capillary
pressure in the experiments. Theoretical modeling reveals an
insight into the nature of the displacements and the key material
properties, e.g., magnetic susceptibility, needed to design
nanoparticles to suit the practical purpose of interest.
[0144] Extension of the Navier-Stokes equation to ferrofluids
yields an important result for modeling the motion of fluid/fluid
interfaces: the magnetic field manifests itself as several
pressure-like terms. This greatly facilitates the extension of
existing models of capillarity-controlled displacements at the
grain scale to include magnetic forcing. Preliminary implementation
in an interface-tracking model agrees qualitatively with the
dynamic behavior observed in experiments.
[0145] Embodiments of the present invention further disclose a
novel nanoparticle coating technique, which makes their reservoir
application possible. The present inventors employed a copolymer
and a crosslinker that form a gel, and generates a thin layer of a
polymer network around the nanoparticle. The polymer gel film does
not detach from particle even when the coating material is removed
from the injection water, unlike the surfactants or polymers
adsorbed. By adjusting the hydrophilic and lipophilic parts of the
copolymer, the salt-tolerance of the dispersion and the oil/water
interfacial activity of the nanoparticles can be optimized.
[0146] Coating of iron oxide particles with poly(acrylic acid)
(PAA) during synthesis resulted in sub-100 nm nanoclusters with
electrostatic and steric stabilization. Cross-linking of PAA at
various cross-link densities led to a coating with a polymer
concentration of about 12% that did not desorb even for iron oxide
concentrations down to 0.014 wt %. Without cross-linking, over half
of the polymer desorbed from the particle surfaces at these dilute
conditions. The superparamagnetic nanoclusters with cross-linked
PAA were characterized using a superconducting quantum interference
device or (SQUID) magnetometer, transmission electron microscopy
(TEM), dynamic light scattering (DLS), thermo gravimetric analysis
(TGA), and zeta potential measurements. The incorporation of the
cross-linking agent, 1,6-hexanediamine, enhances the hydrophobicity
and thus the interfacial activity of the clusters at the oil-water
interface. In this general and highly flexible approach, iron oxide
nanoparticles may be formed with an adsorbed polymer stabilizer,
which is then permanently bound to the surface via cross-linking.
This cross-linking approach offers important benefits for the
formation of inexpensive coatings on nanoparticles for large scale
applications including magnetomotive imaging of subsurface
reservoirs.
[0147] In FIG. 19, the emulsion behavior is shown with and without
1 wt % NaCl. The presence of the organic functionalities via
crosslinking makes the particles less hydrophilic and clear water
phases are observed with salt added. This cross-linking approach
with the large volume of the nanoclusters relative to the primary
nanoparticles and the small mass of the cross-linked PAA coating
offers important benefits for the formation of inexpensive coatings
on nanoparticles for large scale applications including
magnetomotive imaging of subsurface reservoirs.
[0148] Examples based on the copolymer-coated nanoparticle concept
are presented herein below:
Example I
Poly(Acrylic Acid).sub.114-b-Poly(Butyl Acrylate).sub.B Block
Copolymer Coatings on Iron Oxide Nanoparticles
[0149] Iron oxide nanoparticles were synthesized from iron
chlorides in the presence of a PAA-b-PBA polymer. This block
copolymer was properly balanced to give a high absorption of
nanoparticles at the oil/water interface. The inventors used three
different ratios of copolymers with a polymer concentration of 2 wt
% for the systematic study. Higher hydrophobic ratio showed a
higher interfacial tension. The hydrodynamic diameter of the
particles was controllable as a function of the reaction
concentrations. The results presented herein were obtained with
nanoclusters with a diameter on the order of 100 nm. The aqueous
dispersions were stable up to 3 wt % salt at pH 8. Therefore, upon
intense probe sonication, micron sized oil/water (oil/water)
emulsions were formed and with significant stability. Emulsions of
water and dodecane with drop sizes down to 5 .mu.m are stabilized
with 100 nm interfacially active nanoclusters of sub-10 nm iron
oxide primary particles at an extremely low loading of 0.2 wt %.
FIG. 20 shows the volume fraction based distributions of
Poly(acrylic acid)-b-Poly(butyl acrylate) coated iron oxide
nanoclusters. FIGS. 21A-21D show emulsion images of Poly(acrylic
acid)114-b-Poly(butyl acrylate)26 at pH 8 with no salt, 1 wt %
salt, 2 wt % salt, and 3 wt % salt, respectively. FIGS. 21E-21H
show microscope images of Poly(acrylic acid)114-b-Poly(butyl
acrylate) 26 at pH 8 with no salt, 1 wt % salt, 2 wt % salt, and 3
wt % salt, respectively.
Example II
Poly(Acrylic Acid).sub.m-r-Poly(Butyl Acrylate).sub.n Coatings on
Iron Oxide Nanoparticles
[0150] The inventors synthesized stable dispersions of small, about
100 nm superparamagnetic iron oxide nanoclusters with high
magnetization, and controllable sizes, employing inexpensive random
copolymers. In order to achieve these requirements, the inventors
introduced random copolymers of Poly(acrylic acid)m-r-Poly(butyl
acrylate)n as coating materials on iron oxide nanoparticles. This
simple synthesis to apply various ratios of hydrophilic and
hydrophobic monomers to design these copolymers allows independent
tuning of the molecular weight, attachment density of hydrophobic
block, and hydrophobicity of the coatings. A systematic study was
performed to relate interfacial activity at the oil-water interface
to the copolymer structure. The Fe3O4 particles were produced by
co-precipitation of iron chloride salts in aqueous alkaline media
with .about.10 nm individual size. The clustering was kinetically
controlled without utilizing complicated synthetic approaches and
templating agents. The size of the formed magnetic clusters was
measured by using dynamic light scattering.
[0151] For the random copolymers with different ratios between
hydrophobic and hydrophilic moieties, the key properties could be
adjusted. Carboxylate complexes with the Fe atoms and chemisorbs at
the iron oxide nanoparticle surface. Above a certain pH (.about.8
for the copolymer), the nanoparticle exposes negative charge to the
solution and provides electrostatic stabilization. Also, Poly(butyl
acrylate) groups give high interfacial activities between the oil
and water. Overall, the random copolymer coating provides good salt
tolerance for the magnetic nanoparticles because of high adsorption
and large charge for electrostatic stabilization. There is still
sufficient surface charge on the particles at high solution
salinities (.about.3 wt % NaCl) at pH 8. FIG. 22 shows emulsions
formed with equal volume fractions of dodecane and aqueous
dispersion of 0.2 wt % random copolymer-coated iron oxide particles
with different ratios of PAA-r-PBA at pH 8 without salt and with
different salt levels. The photographs of emulsion formation were
taken after 1 day. Optical micrographs (FIGS. 23A-23F) of emulsions
formed are shown at conditions described in FIGS. 21A-21D. FIG. 23A
shows PAA-r-PBA (ratio 3:1) with no salt, FIG. 23B shows PAA-r-PBA
(ratio 3:1) with 3 wt % NaCl, FIG. 23C shows PAA-r-PBA (ratio 3:2)
with no salt, FIG. 23D shows PAA-r-PBA (ratio 3:2) with 3 wt %
NaCl, FIG. 23E shows PAA-r-PBA (ratio 4:1), with no salt; and FIG.
23F shows PAA-r-PBA (ratio 4:1) with 3 wt % NaCl. The optical
micrographs were taken immediately after emulsion formation.
Example III
Poly(4-Styrenesulfonic Acid-Co-Maleic Acid) Coated Nanoparticles
for High Salt Tolerance
[0152] The present inventors also studied the properties of the
Poly(4-styrenesulfonic acid-co-maleic acid) coated iron oxide
nanoclusters for exceptional salt tolerance (up to 8 wt % salt),
higher than that achievable for acrylic-based polymers. The
paramagnetic nanoparticles are coated with random copolymers
(Saleh, Phenrat et al. 2005) of maleic acid and styrene sulfonic
acid, which are suitable for achieving interfacial activities
between oil and water. Generally, a random copolymer is usually
inexpensive and relatively simple to synthesize. Overall, the
method to synthesize the Poly(4-m styrenesulfonic acid-co-maleic
acid) coated iron oxide nanoclusters has advantages over other
procedures in that it is a quick, inexpensive, and a one-step
process which is highly reproducible.
[0153] Aqueous dispersions of 0.2 wt % superparamagnetic iron oxide
nanoclusters were stabilized with Poly(4-styrenesulfonic
acid-co-maleic acid) on the particle surface, with a high loading
of 90% iron oxide. The dispersions were stable for months even with
high salt concentrations up to 8 wt % at pH 6 and pH 8 based on the
hydrodynamic diameter measurements from dynamic light scattering.
The 4-styrenesulfonic acid and maleic acid groups provide
sufficient electrostatic repulsion for high stability. The small
size of the clusters, superparamagnetic properties, and high salt
tolerance are highly beneficial for mapping of petroleum reservoirs
with magnetomotive techniques. The TEM images for
Poly(4-styrenesulfonic acid-co-maleic acid) coated iron oxide
nanoparticles with different ratio between 4-styrenesulfonic acid
and maleic acid: 3:1 ratio and 1:1 ratio are shown in FIGS. 24A and
24B, respectively. FIG. 25 shows the stability of 0.2 wt %
Poly(4-styrenesulfonic acid-co-maleic acid) coated iron oxide
nanoparticle dispersions at different pH and salinity values.
Dodecane in water emulsions stabilized by Poly(4-styrenesulfonic
acid-co-maleic acid) coated iron oxide nanoparticles at different
pH and salinity values are shown in FIGS. 26A and 26B. The particle
concentration in the dispersions was 0.2 wt %: 1:1
4-styrenesulfonic acid and maleic acid ratio (FIG. 26A) and 3:1
ratio (FIG. 26B).
Example IV
Poly(4-Styrenesulfonic Acid-Co-Maleic Acid) Coated Nanoparticles
with DTAB (Decyltrimethyl Ammonium Bromide) DTAB
[0154] In order to improve the stability and interfacial activity
of the nanoparticle dispersion, the inventors added DTAB such that
the cationic head group interacted with the carboxylate moieties.
The DTAB also lowered the hydrophilicity of the particles by
replacing COO-- with hydrophobic ion paired tail groups. The
inventors used this as a simple technique to determine the effect
on the particle partitioning between oil and water phases and at
the interface. This information is being used to design systems
with copolymers. The DTAB greatly increased the interfacial
activities and salt tolerance (up to 8 wt % NaCl) as shown in FIGS.
27A (pH 6) and 27B (pH 8). In these studies, the excess stabilizer
was removed by centrifugation and re-dispersion in de-ionized (DI)
water and the appropriate buffer. The less hydrophilic particles
partitioned more strongly to the oil-water interface, as shown in
the figure after 1 day. As the salinity increased, the particles
partitioned out of the aqueous phase at pH 6 and 8. FIGS. 28A and
28B show dodecane in water emulsions stabilized by
Poly(4-styrenesulfonic acid-co-maleic acid)+DTAB-coated iron oxide
nanoparticles at different pH and salinity values. The particle
concentration in the dispersions was 0.2 wt %. The emulsions were
formed with probe sonication and the photographs were taken 1 day
after the emulsions formation.
[0155] In addition to the frequency doubling, the phase shift
between the imposed magnetic wave and the measured acoustic wave
may be employed as a finger-printing parameter to detect particles
adsorbed at oil/water, gas/water or CO.sub.2/water interfaces.
Interfacial fluctuation due to particle oscillation is elastic with
restoring force, while the bulk fluid fluctuation due to particle
oscillation is viscous and dissipative. The inventors describe
novel techniques for acoustic response measurements: (i) use of
PS-OCT for rock displacement measurements; and (ii) use of
polyvynilidene fluoride (PVDF) film sensor or fiber Bragg grating
sensor for rock stress measurements. These sensors have properties
suitable for this research: a low working frequency (0.001-100 Hz),
high sensitivity (0.0103 V/N), and a low acoustic impedance close
to water. The inventors measured rock stress responses from rock
samples and from sandpack samples imbedded between Boise sandstone
cores. The inventors measured rock displacement responses from
sandpack samples imbedded between Boise sandstone cores and from
rock samples.
Example V
Measurements of Rock Displacement Response from Sandpack Sample
Imbedded Between Boise Sandstone Cores
[0156] The nanoparticle sample comprised a 1.0 wt %
Poly(4-styrenesulfonic acid-co-maleic acid) coated iron oxide
nanoparticles (mean diameter: 120 nm, magnetization: 64 emu/g) in
de-ionized (DI) water. A 0.5 wt % nanoparticle dispersion
("solution") was prepared by adding same amount of DI water to 1.0
wt % solution. An emulsion was made from dodecane and 1.0 wt %
solution at a 50:50 volume ratio using a ultrasonic sonifier
(Branson Ultrasonics). The sandpack sample was prepared from Boise
sandstone rock pieces by crushing them. Overall individual grain
diameter is around 0.4 mm. A sandpack holder 2900 was designed to
accommodate a point source of acoustic pressure placed in between
two rock cores. It comprises two Boise sandstone rock cores
(designated as 2904) and sandpack 2906 placed between them (FIG.
29). The holder is encased in a plastic case 2902. Each side of the
rock core was coated with epoxy to prevent diffusion of
nanoparticle samples into the rock cores, and was fully saturated
with water.
[0157] Two different magnetic fields, sinusoidal (4 Hz, 4000 Gauss
peak to peak) and pulsed, were applied. Pulsed magnetic field was a
DC magnetic field with intensity of more than 2 Tesla and time
duration of 1 ms. Pulse was generated from a custom built magnetic
pulser.
[0158] The 1.0 wt % solution and the emulsion were used to test
their basic response with applied magnetic field. Displacement of
each interface, air/water and air/emulsion, was measured by the
procedure as previously described.
[0159] Measurement of rock displacement response from sandpack
sample holder: After 8 grams of sandpack was put into the gap in
the sandpack sample holder, the sandpack sample was wetted with 4
ml of 1.0 wt % nanoparticle solution. The sandpack sample holder
was located at the place where PS-OCT light was focused fixed by a
clamp. The center of the solenoid coil was placed at the side of
the sandpack sample. Immediately after application of the magnetic
field, the displacement of the top surface of the upper core was
measured over a 4 second time duration. FIGS. 30A and 30B show a
photograph and a diagram of the system 3000, which comprises: (i) a
PS-OCT holder 3006; (ii) a sandpack holder 3026 is attached to a
sandpack holder clamp 3008 that is placed close to the holder 3006;
(iii) an electromagnetic solenoid 3014, which generates the
magnetic field of a prescribed schedule of strength vs. time; and
(iv) a phase sensitive optical coherence tomography (PS-OCT)
measurement system that measures the displacement of the core
sample in response to the imposed magnetic field, comprising a
sample path optical fiber (PS-OCT) 3002 in communication with a
gradient index (GRIN) lens 3004. The laser beam from the optical
fiber 3002 is focused through lens 3004 and passes through a light
splitter 3028 that allows for 95% transmission and 5% reflection.
Sandpack holder 3026 is designed to hold the sandpack as a point
source of acoustic pressure. It comprises two Boise sandstone rock
cores (designated as 3010) and sandpack 3012 placed between them
(FIG. 29). The holder is encased in a plastic case 3030. The system
3000 also comprises a power supply source 3018. The solenoid 3014
located at the side of the nanoparticle-containing sandpack 3012
generates the magnetic field, and the rock displacement resulting
from the oscillations of the paramagnetic nanoparticles is measured
at the top surface of the upper rock core by the PS-OCT (3002,
3004, and 3028). A current amplifier 3020 with one or more output
channels is connected to the power supply source 3018. A function
generator 3016 is connected through 3024 to a second output channel
3022 of the current amplifier 3020. Three additional PS-OCT
measurements were recorded as above with two other nanoparticle
samples and DI water.
[0160] Measurement of displacement of air/nanoparticle-sample
interfaces: FIGS. 31A and 31B show a comparison of the PS-OCT
measured interfacial displacements of a 1.0 wt % solution and
emulsion, respectively. The displacement of the emulsion is two
times larger than that of the 1.0 wt % solution although
nanoparticle concentration in the emulsion was 0.5 wt % (as
dodecane and 1.0 wt % solution were mixed at 50:50 ratio).
Frequency and magnitude of applied magnetic field were 4 Hz and 780
gauss peak to peak.
[0161] Measurement of rock displacement response from the sandpack
sample: FIGS. 32A-32D illustrate recorded rock displacement signals
from the sandpack sample, measured by PS-OCT. Note that the rock
displacement from the sandpack sample wet with emulsion is about
two times larger than from the sandpack sample wet with 0.5 wt %
solution. Applied magnetic field was 10 Hz and the field strength
was measured by a magnetic Hall sensor (Magnetometer, AlphaLab
Inc., USA) at different positions of the sandpack sample 3400 as
shown in FIG. 34. Sandpack sample 3400 comprises two Boise sand
stone rock cores (designated as 3402) and sandpack 3406 placed
between them. The holder is encased in a plastic case 3404. The
magnetic field applied for testing was achieved by the use of
solenoid 3408 that generates the magnetic field: (i) at the edge of
the bottom surface of the lower rock core that is closest to the
solenoid; (ii) at the center of the bottom surface; and (iii) at
the bottom surface edge that is farthest from the solenoid.
[0162] Phase differences between measured rock displacement signal
and applied field, were calculated by the following signal process
procedure, and are displayed in FIGS. 33A-33C: (i) compute
frequency doubled applied field by squaring measured magnetic
field; (ii) display measured rock displacement signal together with
the m frequency-doubled applied field; (iii) compute FFT of the
measured displacement signal (includes all frequency components);
(iv) find phase of the frequency-doubled (20 Hz) signal component;
(v) compute FFT of the frequency doubled applied field (obtained by
squaring applied field) and obtain phase of the frequency doubled
field; and (vi) subtract phase of frequency doubled signal from the
phase of frequency doubled applied signal to give the phase delay
between the applied field wave and the measured displacement
wave.
[0163] Phase difference from the case wetted with emulsion was
distinguished from the cases wetted with 1.0 wt % and with 0.5 wt
%. It may be due to the elastic oscillation of nanoparticles
adsorbed at oil/water interfaces in emulsion.
[0164] Recorded rock displacements from sandpack samples, measured
by PS-OCT, are shown in FIGS. 35A-35C. Time constant of the signal
was calculated to show how fast signal decays. Time constant is the
time required for a physical quantity to fall to 36.8% of its
initial value. In the study described hereinabove, a sandpack
sample filled with emulsion showed bigger displacement response
compare to the sandpack sample filled with 0.5 wt % nanoparticle
solution. This indicates that an oil/water interface with
nanoparticles can generate a stronger acoustic signal than
nanoparticle dispersion and there is possibility for calculated
phase difference and time constant to be another fingerprint to
detect oil in reservoir rock.
Example VI
Measurements of Rock Displacement Response from Rock Sample
[0165] The nanoparticle sample comprised a Poly(acrylic
acid)114-b-Poly(butyl acrylate)B block copolymer coated iron oxide
nanoparticles in DI water. Boise sandstone (BS) rock core was
presented as a typical example of an oil reservoir rock. The rock
core was 6'' long and 1'' in diameter. Two samples were prepared:
(i) a rock core (L1) that had been initially flooded with 0.5 wt %
nanoparticle solution and then flushed with nanoparticle-free
water; and (ii) another rock core (L2) with oil and flooded with
0.5 wt % nanoparticle solution, and subsequently flushed with
nanoparticle-free water. Retention of nanoparticles on rock
surfaces was 53.4% in L1 and 72.3% in L2, after post flushing with
water.
[0166] BS rock core was fixed by a clamp as described previously in
Example V and rock displacement was measured by PS-OCT after
application of a magnetic field. Two different magnetic fields,
sinusoidal (4 Hz, 4000 Gauss peak to peak) and pulsed, were applied
in turns. FIGS. 36A and 36B show a photograph and a schematic
diagram of the system 3600, which comprises: (i) a PS-OCT holder
3608; (ii) a 6'' long BS rock core 3610 that is placed close to the
holder 3608 via a clamp 3630; (iii) an electromagnetic solenoid
3612, which generates the magnetic field of a prescribed schedule
of strength vs. time; and (iv) a phase sensitive optical coherence
tomography (PS-OCT) measurement system that measures the
displacement of the core sample in response to the imposed magnetic
field and comprises a sample path optical fiber (PS-OCT) 3602 in
communication with a gradient index (GRIN) lens 3604. The laser
beam from the optical fiber 3602 is focused through lens 3604 and
passes through a light splitter 3606 that allows for 95%
transmission and 5% reflection. The solenoid (3612) located at the
side of the nanoparticle-containing rock core sample (3610)
generates the magnetic field, and the rock displacement resulting
from the oscillations of the paramagnetic nanoparticles is measured
at the top surface of the rock core by the PS-OCT (3602, 3604, and
3606). The system 3600 also comprises a power supply source 3616. A
current amplifier 3620 with a plurality of output channels is
connected to the power supply source 3616. A function generator
3614 is connected through 3624 to a second output channel 3622 of
the current amplifier 3620.
[0167] FIGS. 37A and 37B show the measured rock core displacement
in response to the sinusoidal magnetic field. The figure shows that
the displacement of rock core with nanoparticle solution and oil
(L2) (FIG. 37B) was larger than that of rock core with nanoparticle
solution only (L1) (FIG. 37A). FIGS. 38A and 38B illustrate the
measured rock core displacement by PS-OCT with pulsed magnetic
field. Time constant was calculated from both rock cores, and
showed consistency with the result from the sandpack samples
described above. The study presented above shows that the
displacement of a rock core with oil and water is larger than that
of a rock core with water only. Therefore, nanoparticle adsorption
at oil/water interfaces needs to be maximized while retention on
rock surfaces minimized.
[0168] Embodiments of the present invention provide for the
detection of the oil/water menisci in reservoir rock indicating the
presence of oil. By injecting paramagnetic particles that adsorb
only on the oil/water interface (meniscus), and by detecting the
density wave generated by their oscillation, their presence in the
reservoir rock can be determined.
[0169] Somewhat similar hydrocarbon-detection methods, which
neither recognizes the presence of oil/water menisci, nor uses
paramagnetic nanoparticles, have been proposed by Thompson et al.
(1999) and others. In those methods, an electromagnetic oscillation
is applied to the reservoir zone, and the seismic response due to
the pore fluid oscillation is detected with sensitive geophones.
The supporting theory for the methods has been developed by Pride
(1994). Because these methods are proposed for oil exploration and
the governing frequencies are of seismic domain with wavelength in
kilometers, the methods' resolution for oil detection is believed
to be of similar length scale. As briefly described above, for the
detection of paramagnetic nanoparticles sent to the target human
tissue, combination of MRI and ultrasound scanning is being
employed (Oh et al. 2006; Norton and Vo-Dinh 2007). Because the MRI
and ultrasound probes are intended to image microscopically
localized areas, they employ frequencies in the mega-Hz range or
higher, and their probing depth is not deep.
[0170] In addition to the above magnetic-acoustic combination
method, just as the medical applications of the functionalized
magnetic nanoparticles (Ito et al. 2005), the basic concept of the
magnetic nanoparticle adsorption at the oil/water meniscus could be
utilized to enhance the capabilities of the MRI scanning of rock
core samples (Chen et al. 2006; Sheppard et al. 2003) and the NMR
logging (Dunn et al. 2002). The spectrometric measurements of the
effects of the paramagnetic nanoparticle adsorption on the NMR
relaxation time (T1, T2) could help better determine the oil
saturation in the reservoir rock. This could be done in the manner
to quantify the effects of rock surface wettability on the
relaxation time (Zhang et al. 2000).
[0171] It is contemplated that any embodiment discussed in this
specification can be implemented with respect to any method, kit,
reagent, or composition of the invention, and vice versa.
Furthermore, compositions of the invention can be used to achieve
methods of the invention.
[0172] It will be understood that particular embodiments described
herein are shown by way of illustration and not as limitations of
the invention. The principal features of this invention can be
employed in various embodiments without departing from the scope of
the invention. Those skilled in the art will recognize, or be able
to ascertain using no more than routine experimentation, numerous
equivalents to the specific procedures described herein. Such
equivalents are considered to be within the scope of this invention
and are covered by the claims.
[0173] All publications and patent applications mentioned in the
specification are indicative of the level of skill of those skilled
in the art to which this invention pertains. All publications and
patent applications are herein incorporated by reference to the
same extent as if each individual publication or patent application
was specifically and individually indicated to be incorporated by
reference.
[0174] The use of the word "a" or "an" when used in conjunction
with the term "comprising" in the claims and/or the specification
may mean "one," but it is also consistent with the meaning of "one
or more," "at least one," and "one or more than one." The use of
the term "or" in the claims is used to mean "and/or" unless
explicitly indicated to refer to alternatives only or the
alternatives are mutually exclusive, although the disclosure
supports a definition that refers to only alternatives and
"and/or." Throughout this application, the term "about" is used to
indicate that a value includes the inherent variation of error for
the device, the method being employed to determine the value, or
the variation that exists among the study subjects.
[0175] As used in this specification and claim(s), the words
"comprising" (and any form of comprising, such as "comprise" and
"comprises"), "having" (and any form of having, such as "have" and
"has"), "including" (and any form of including, such as "includes"
and "include"), or "containing" (and any form of containing, such
as "contains" and "contain") are inclusive or open-ended and do not
exclude additional, unrecited elements or method steps.
[0176] The term "or combinations thereof" as used herein refers to
all permutations and combinations of the listed items preceding the
term. For example, "A, B, C, or combinations thereof' is intended
to include at least one of: A, B, C, AB, AC, BC, or ABC, and if
order is important in a particular context, also BA, CA, CB, CBA,
BCA, ACB, BAC, or CAB. Continuing with this example, expressly
included are combinations that contain repeats of one or more item
or term, such as BB, AAA, AB, BBC, AAABCCCC, CBBAAA, CABABB, and so
forth. The skilled artisan will understand that typically there is
no limit on the number of items or terms in any combination, unless
otherwise apparent from the context.
[0177] All of the compositions and/or methods disclosed and claimed
herein can be made and executed without undue experimentation in
light of the present disclosure. While the compositions and methods
of this invention have been described in terms of preferred
embodiments, it will be apparent to those of skill in the art that
variations may be applied to the compositions and/or methods and in
the steps or in the sequence of steps of the method described
herein without departing from the concept, spirit and scope of the
invention. All such similar substitutes and modifications apparent
to those skilled in the art are deemed to be within the spirit,
scope and concept of the invention as defined by the appended
claims.
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* * * * *
References