Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
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PROPPANT PARTICLES FORMED FROM SLURRY
DROPLETS AND METHODS OF USE
TECHNICAL FIELD
This invention relates to hydraulic fracturing of subterranean formations in
the earth. More
particularly, sintered ceramic proppant particles formed from vibration-
induced dripping from a
nozzle of a slurry of finely-divided ceramic material are provided, along with
methods of use of the
particles.
BACKGROUND
Hydraulic fracturing is a process of pumping liquids down a well and into a
subterranean
formation at high rate and pressure, such that a fracture is formed in the
rock around the well. After
pumping a liquid volume sufficient to widen the fracture adequately, solid
particles, called
"proppant," are added to the liquid. After pumping is completed, the well is
opened for production of
hydrocarbons. The production rate of fluid from the well is usually
significantly increased after the
fracturing treatment. Vast improvements in the hydraulic fracturing process
have been developed
since the process was originally patented in 1949 (U.S. Pat. Nos. 2,596,843
and 2,596,844).
The material first used for proppant in hydraulic fracturing of wells was
silica sand. As wells
became deeper, sand was found to have inadequate strength. In deep wells,
stress of the earth causes
the sand to crush and become much less effective in increasing the production
rate of a well.
Synthetic proppant materials were developed to provide higher strength
proppants. The
original synthetic sintered proppant was sintered bauxite. In later years, a
variety of ceramic raw
materials have been used to make sintered ceramic proppants, including bauxite
containing lesser
amounts of alumina and clay minerals, such as kaolin. Generally, it has been
found that the strength
of ceramic particles increases with the amount of aluminum oxide (alumina) in
the particle, all other
factors remaining constant.
A general procedure for making synthetic proppant particles is to obtain the
ceramic raw
material, grind it to a fine powder, form it into pellets (called "green"
pellets), and sinter the green
pellets in a kiln. The final product is ceramic pellets in the size range
suitable for proppants, from
about 70 mesh to 12 mesh (0.008 inch to 0.067 inch in diameter). Different
sizes of pellets are used
depending on well conditions.
A variety of processes for forming the pellets of a proppant have been
proposed. In early
work, U.S. Pat. No. 4,427,068 describes a process for forming sintered ceramic
pellets by adding dry
powders of clay and alumina, bauxite, or mixtures to a high intensity mixer
(hereinafter referred to as
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"dry mixing method"). Powdered fine grain ceramic starting ingredients
(ceramic raw materials) are
stirred to form a dry homogenous mixture. Then, sufficient water is added to
cause agglomeration of
the fine starting dust particles to form small composite spherical pellets
from the powder. Continued
mixing time is allowed in order to grow small pellets to the desired size. A
broad range of sizes is
produced during the pellet-forming stage. A preferred mixing device is
obtained from Eirich
Machines, Inc., and is known as the Eirich mixer. The resulting pellets are
dried and sintered into the
final proppant particles. Much of the ceramic proppant made in industry in
past years has been made
with this process of forming pellets.
U.S. Pat. No. 4,440,866 discloses an alternative process for producing pellets
that are sintered
to produce high strength pellets. A continuous spray/granulation of an aqueous
aluminous ore
suspension with binder is used to form granules that are subsequently sintered
(hereinafter referred to
as "spray fluidized bed method"). All steps of this process may be carried out
in a continuous manner.
An aqueous suspension containing the ceramic raw material is continuously
atomized and fed into a
layer of already partially dried small starting dust particles (often called
seeds) that are fluidized in a
stream of hot drying air. The aqueous ceramic raw material suspension is
continuously sprayed and
dried onto the seed particles until the desired finished green particle
diameter is achieved. Particles
produced in this process have a size range that is less broad than those
typically produced by the dry
mixing method of U.S. Pat. No. 4,427,068 but are still of sufficient variation
as to require further
processing. Particles are continuously recovered from the fluidized layer and
particles of the desired
size are separated from oversized and undersized product fractions. Material
is continuously recycled
in the stream of drying air. This spray fluidized bed process has also been
used to produce large
amounts of ceramic proppants in industry.
The pellet-forming methods described above have intrinsic limitations. The dry
mixing
process produces an extremely wide range of green pellet sizes due to the
random nature of the
agitation of the rotor and pan. The spray fluidized bed process produces a
somewhat tighter green
pellet size distribution but still a much wider distribution than desired.
These processes require
extensive screening and recycling during the manufacturing process. Under the
best manufacturing
conditions about 30% of green particles must be recycled through the pellet-
forming process. Both
the dry mixing and spray fluidized bed processes also produce a random
distribution of pore sizes in
pellets, including a small percentage of very large pores that significantly
degrade pellet strength.
Strength of the sintered pellets is a primary consideration, because if the
pellets break under high
stress in a fracture, the flow capacity of the fracture is decreased and the
hydraulic fracturing
treatment is less effective. The sphericity and surface smoothness of
particles produced by these
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processes are also important, with high sphericity and a very smooth surface
traditionally being most
desirable. All of these characteristics are strongly affected by the pellet-
forming method.
U.S. Pub. No. 2006/0016598 discloses a list of pellet-forming techniques that
may be used
for ceramic proppant formation, including agglomeration, spray granulation,
wet granulation,
extruding and pelletizing, vibration induced dripping according to U.S. Pat.
No. 5,500,162, spray
nozzle-formed droplets and selective agglomeration. U.S. Pat. No. 5,500,162
discloses producing
microspheres by vibration-provoked dripping of a chemical solution through a
nozzle plate, wherein
the falling drops form an envelope surrounded from all sides by flowing
reaction gas. The liquid
chemical solution has no or low (i.e., 20% or less) solid particles at the
time it enters the nozzle plate,
exits the nozzle plate, and passes through the first free fall section. The
reaction gas is required to
cause the precipitation (gelling) of small solid particles (typically sub-
micron) in the liquid drops as
they fall through the second free fall zone, and thereafter fall into a
reaction liquid to further gel. The
reaction gas is necessary to cause the liquid to partially gel prior to
entering the reaction liquid, and
the droplets are decelerated into the liquid through a foam or the reaction
liquid is directed onto the
falling drops tangentially in the same direction in which the droplets are
falling. These two features of
falling through reaction gas and decelerating the droplets into foam are
required to insure the droplets
are partially gelled during a sol-gel reaction and therefore not deformed, for
example flattened, when
they strike the reaction liquid. The reaction gas is sucked away inside or
outside the envelope. The
method according to the invention can be used to produce, for example,
aluminum oxide spheres up
to the diameter of 5 mm.
Vibration-induced dripping, herein called "drip casting," was originally
developed to produce
nuclear fuel pellets. Since then it has been adapted to produce a very wide
variety of metal and
ceramic "microspheres," such as grinding media and catalyst supports.
Primarily, it has been used in
the food and pharmaceuticals industries. The drip casting process is described
on the website and in
sales literature of Brace GmbH. Examples of microspheres formed by drip
casting of different
materials are also provided. U.S. Pat. No. 6,197,073 discloses a process for
producing aluminum
oxide beads from an acid aluminum oxide sol or acid aluminum oxide suspension
by flowing the
suspension through a vibrating nozzle plate to form droplets and pre-
solidifying the droplets with
gaseous ammonia and then coagulating the droplets in an ammonia solution. The
mechanical strength
of ceramic particles formed by sintering the drip cast particles was not a
factor in any of the materials
used in these references.
It is known that to produce ceramic proppant particles having maximum strength
for a given
ceramic material, the particles must contain minimum porosity, and the pores
present must be kept as
small as possible, since the strength of a given proppant particle is limited
by its largest pore. What is
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needed is a method of forming green ceramic particles that can be fired to
have reduced pore size and
therefore maximum strength for use as a proppant. Preferably, the particles
should be spherical, have
a smooth surface and have uniform size. A method for forming the green
particles without recycling
of the undesired size fraction of green ceramic pellets is also needed.
BRIEF SUMMARY OF THE INVENTION
A proppant particle is disclosed herein. The proppant particle can include a
sintered ceramic
material, a size of about 80 mesh to about 10 mesh, and an average largest
pore size of less than about
20 microns. Impinging a plurality of the proppant particle under a gas-
entrained velocity of about 260
m/s onto a flat mild steel target can result in an erosivity of the target of
about Ito about 100 mg of
target material lost due to the impinging per kg of the plurality of the
proppant particle impinging the
target. Also, a plurality of the proppant particle can lose less than 15% of
its conductivity at 20,000
psi after being subjected to 5 cycles of cyclic loading under stresses from
about 12,000 psi to about
20,000 psi, when the proppant particle has a specific gravity of about 3.5.
A pack of proppant particles is also disclosed herein. The pack of proppant
particles can
include a plurality of proppant particles, each proppant particle of the pack
can include a sintered
ceramic material, a size of about 80 mesh to about 10 mesh, and an average
largest pore size of less
than about 20 microns. The pack of proppant particles having a particle size
of 20-40 mesh can have a
long term permeability greater than 130 darcies at a stress of 10,000 psi and
a temperature of 250 F,
as measured in accord with ISO 13503-5, when the proppant particles have a
specific gravity of about
2.7. Impinging the proppant particles under a gas-entrained velocity of about
260 m/s onto a flat mild
steel target can result in an erosivity of the target of about 1 to about 100
mg of target material lost
due to the impinging per kg of the plurality of the proppant particle
impinging the target. Also, the
pack can lose less than 15% of its conductivity at 20,000 psi after being
subjected to 5 cycles of
cyclic loading under stresses from about 12,000 psi to about 20,000 psi, when
the proppant particles
have a specific gravity of about 3.5.
A method of hydraulic fracturing is also disclosed herein. The method can
include injecting a
hydraulic fluid into a subterranean formation at a rate and pressure
sufficient to open a fracture
therein and injecting a fluid containing a proppant particle into the
fracture. The proppant particle can
include a sintered ceramic material, a size of about 80 mesh to about 10 mesh,
and an average largest
pore size of less than about 20 microns. Impinging a plurality of the proppant
particle under a gas-
entrained velocity of about 260 m/s onto a flat mild steel target can result
in an erosivity of the target
of about 1 to about 100 mg of target material lost due to the impinging per kg
of the plurality of the
proppant particle impinging the target. Also, a plurality of the proppant
particle can lose less than
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15% of its conductivity at 20,000 psi after being subjected to 5 cycles of
cyclic loading under stresses
from about 12,000 psi to about 20,000 psi, when the proppant particle has a
specific gravity of about
3.5.
BRIEF DESCRIPTION OF THE DRAWINGS
The present invention may best be understood by referring to the following
description and
accompanying drawings that are used to illustrate embodiments of the
invention. In the drawings:
FIG. 1 is a sketch showing the principles of the pellet-forming apparatus for
proppant
particles disclosed herein.
FIG. 2 is a sketch showing a single nozzle forming droplets from a slurry
stream.
FIG. 3 is a sketch showing a multi-nozzle plate forming droplets from a slurry
stream.
FIG. 4A shows a Scanning Electron Microscope photograph at 100× of
sintered pellets
of alumina formed by the apparatus of FIG. 1.
FIG. 4B shows a Scanning Electron Microscope photograph at 100× of
sintered pellets
of alumina formed by prior art methods.
FIG. 4C shows a Scanning Electron Microscope photograph at 100× of
sintered pellets
of bauxite formed by the apparatus of FIG. 1.
FIG. 4D shows a Scanning Electron Microscope photograph at 100× of
sintered pellets
of bauxite folined by prior art methods.
FIG. 4E shows a Scanning Electron Microscope photograph at 100× of
sintered pellets
of kaolin formed by the apparatus of FIG. 1.
FIG. 4F shows a Scanning Electron Microscope photograph at 100× of
sintered pellets
of kaolin formed by prior art methods.
FIG. 5 is a graph of long term permeability as a function of stress of alumina
pellets formed
by the pellet-forming apparatus disclosed herein and by the prior art dry
mixing process using an
Eirich mixer.
FIG. 6 is a frequency plot of pore size for proppant particles of kaolin made
by the method
disclosed herein and by the prior art spray fluidized bed method.
FIG. 7 is a graph of long term permeability as a function of stress of
proppant formed from
kaolin and other materials and having different alumina contents formed by the
pellet-forming
apparatus disclosed herein and by the prior art dry mixing process using an
Eirich mixer.
FIG. 8 is a graph of long term permeability as a function of stress of
proppant formed from
bauxite and other materials and having different alumina contents formed by
the pellet-forming
apparatus disclosed herein and by the prior art dry mixing process using an
Eirich mixer.
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FIG. 9 is a graph of erosivity as a function of proppant velocity for bauxite
proppant formed
by conventional methods and alumina proppant formed by the drip cast method of
FIGS. 1-3.
FIG. 10 is a graph showing the long term conductivity of conventional bauxite
proppant and
drip cast alumina, each of 20/40 mesh sizing, after subjecting each to 50
hours of 20,000 psi closure
stress, followed by 5 cycles of cyclic loading under stresses from about
12,000 psi to about 20,000
psi, and finally re-measuring each under 20,000 psi closure stress to
determine a decrease in
conductivity due to cycling.
FIG. 11 is a graph showing the long term conductivity of conventional bauxite
proppant and
drip cast alumina, each of 20/40 mesh sizing, after subjecting each to 50
hours of 14,000 psi closure
stress, followed by 5 cycles of cyclic loading under stresses from about 6,000
psi to about 14,000 psi,
and finally re-measuring each under 14,000 psi closure stress to determine a
decrease in conductivity
due to cycling.
FIG. 12 is a graph showing the long term conductivity of conventional bauxite
proppant and
drip cast alumina, each of 30/50 mesh sizing, after subjecting each to 50
hours of 20,000 psi closure
stress, followed by 5 cycles of cyclic loading under stresses from about
12,000 psi to about 20,000
psi, and finally re-measuring each under 20,000 psi closure stress to
determine a decrease in
conductivity due to cycling.
FIG. 13 is a graph showing the beta factors of conventional bauxite proppant
and drip cast
alumina, each of 20/40 mesh sizing, after subjecting each to 50 hours of
20,000 psi closure stress,
followed by 5 cycles of cyclic loading under stresses from about 12,000 psi to
about 20,000 psi, and
finally re-measuring each under 20,000 psi closure stress to determine an
increase in beta factors due
to cycling.
FIG. 14 is a graph showing the beta factors of conventional bauxite proppant
and drip cast
alumina, each of 30/50 mesh sizing, after subjecting each to 50 hours of
20,000 psi closure stress,
followed by 5 cycles of cyclic loading under stresses from about 12,000 psi to
about 20,000 psi, and
finally re-measuring each under 20,000 psi closure stress to determine an
increase in beta factors due
to cycling.
DETAILED DESCRIPTION
Referring to FIG. 1, pellet-forming apparatus 10 having a single nozzle is
shown to illustrate
the principles of the method disclosed herein, which is commonly called "drip
casting." Nozzle 12
receives slurry 15 from feed tank 14, which contains the ceramic raw materials
suspended in water.
Pressure applied to feed tank 14 by pressure supply system 16 causes slurry to
flow through nozzle 12
at a selected rate, preferably in laminar flow. Below nozzle 12 is coagulation
vessel 17, which
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receives the droplets. Vibrator unit 18 is connected to nozzle 12 and is used
to supply pressure pulses
to the nozzle or directly in the slurry flowing to the nozzle. The resulting
vibration of the slurry flow
through the nozzle causes the stream exiting the nozzle 12 to break into
droplets of uniform size. As
droplets fall toward coagulation vessel 17, surface tension effects tend to
form the droplets into
spheres. Spherical particles are formed without the necessity of a sol-gel
reaction, reaction gas free
fall zone, foamed layer of reaction liquid or reaction liquid directed onto
the droplets prior to entering
the reaction liquid bath.
FIG. 2 shows details of slurry 15 exiting nozzle 12 and breaking into drops.
Surface tension
of the slurry drives the drops toward minimum surface area, which is acquired
in a spherical shape, as
they fall toward coagulation vessel 17. The distance of fall is preferably
selected to be great enough to
allow the droplets to become spherical before entering a liquid in vessel 17.
Slurry 15 from feed tank 14 contains a finely ground (0.01-50 microns in size)
mineral or
processed powder capable of producing a strong ceramic material after
sintering, a proper amount of
dispersant necessary for keeping the solid particles in the slurry well
separated, water, and a reactant
that will react with a component in liquid 19 in coagulation vessel 17 to form
a semi-solid or
insoluble compound. The solids content of the slurries may range from about
25% to about 75%. The
viscosity of the slurries will normally be from 1 to 1,000 centiPoise, but may
be higher. Lower
viscosity of the slurry aids in improving droplet formation and formation of
spherical particles and is
an essential part of the invention claimed. Optimization of the dispersant
type and concentration will
reduce viscosity. Dispersants may be selected based on cost, availability and
effectiveness in reducing
viscosity of a selected slurry. Dispersants that may be used to reduce the
viscosity of slurries include
sodium silicate, ammonium polyacrylate, sodium polymethacrylate, sodium
citrate, sodium
polysulfonate and hexametaphosphate.
The commonly used reactant chemical in the slurry in feed tank 14 is sodium
alginate. This is
a naturally occurring polysaccharide that is soluble in water as the sodium
salt but is cross-linked to
form a gel as the calcium salt. Alginate is typically added to the slurry at
levels of 0.1% to 1.0%
(weight percent alginate solid to total slurry). Coagulation tank 17 normally
contains a coagulation
liquid 19 which gels the reactant chemical in the slurry 15. The commonly used
coagulation liquid for
sodium alginate is a calcium chloride solution at concentration levels of 0.5%
to 10% by weight. A
variety of reactants in the slurry flowing through nozzle 12 and in the
coagulation vessel 17 may be
used. This may include other polysaccharides and other cross-linking compounds
such as polyvinyl
alcohol or borate fluids.
The diameter of nozzle 12, the viscosity of slurry 15, the ceramic particle
content of slurry
15, pressure to feed the slurry to the nozzle, along with the frequency and
amplitude of vibration
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applied by vibrator source 17 are adjusted to produce droplets having a
desired size. These variables
are preferably set at a constant value as spheres are produced to be formed
into a batch of pellets of
propping material. Different batches may be produced having different size
pellets. Preferably, each
batch will be monosized (i.e., contained on a single sieve such as passing
through a 20 mesh sieve but
staying on a 25 mesh sieve). The pressure used to feed slurry to the nozzle is
adjusted to create
laminar flow through the nozzle. The feed pressure can range from 1 to 50 psi.
The frequency is
adjusted for each set of slurry conditions such that a resonance is
established in the slurry stream
exiting the nozzle that then produces spherical droplets. The frequency can
range from 10 to 20,000
Hz. The pressure and frequency are optimized iteratively to create uniform
spherical shapes. The
amplitude is adjusted to improve the uniform shape of the spherical droplets
formed. The flow rate of
the slurry through a nozzle is a function of the nozzle diameter, slurry feed
pressure, and the slurry
properties such as viscosity and density. For example, for kaolin and alumina
slurries through nozzles
up to 500 microns in diameter the flow rate per nozzle can range from 0.2 to 3
kg/hr.
The distance between nozzle 12 and the top of the liquid 19 in coagulation
vessel 17 is
selected to allow droplets to become spherical before reaching the top of the
liquid. The distance can
be from 1 to 20 cm, but is more typically in the range of 1 to 5 cm so as to
reduce distortion of the
droplet shape upon impact with the liquid surface, thereby eliminating the
need for a reaction gas,
foam layer, or tangentially directed reaction liquid prior to the droplets
entering the coagulation vessel
17. The reactant chemical in the droplets of slurry reacts with the
coagulation liquid 19 in the
coagulation vessel 17 and a semi-solid surface is formed on the droplets,
which helps retain the
spherical shape and prevents agglomeration of the pellets. Preferably, the
residence time of pellets in
coagulation vessel 17 is sufficient to allow pellets to become rigid enough to
prevent deformation of
the spherical shape when they are removed and dried, i.e., semi-rigid. In some
embodiments, pellets
may fall into a coagulation liquid solution flowing vertically upward so that
settling of the particle
through the liquid will be retarded to produce a longer residence time in the
coagulation vessel.
Pellets formed using the apparatus of FIG. 1 are washed to remove excess
coagulation agent
and conveyed to other devices where they are dried and later sintered, using
well known processes in
the industry.
FIG. 3 illustrates a multi-nozzle apparatus, which is required to apply the
process on a
commercial scale. Multiple nozzles 32 are placed in vessel 30, which operates
under a controlled
pressure to flow sluiTy through the nozzles. Large numbers of nozzles are
required for commercial
production of proppant particles. Vessel 30 is vibrated to cause vibration of
nozzles, as described
above. Alternatively, variable pressure may be induced in the sluny to cause
formation of uniform
sized droplets. The droplets are collected as described before.
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Pellets produced by the process described in FIGS. 1-3 are near uniform in
size. For example,
Table 1 compares the pellet size distributions for sintered alumina proppant
produced by the dry
mixing process and by the drip casting process described herein, without
screening of the green
pellets. Without screening of the green pellets, dry mixing produces fired
proppant with a distribution
across six screens, whereas drip casting produces fired proppant substantially
on one screen.
Therefore, in a manufacturing process for proppant, drip casting does not
require sieving the green
pellets to select the size range desired and then recycling the material in
green pellets outside the
selected size range. The size pellets to be sintered into proppant are
selected by controlling the
diameter of nozzle 12 or 32, the viscosity of slurry 15, the ceramic particle
content of slurry 15,
pressure to feed the slurry to the nozzle, along with the frequency and
amplitude of vibration applied
by vibrator source 17. The sintered pellets or proppant particles produced by
the process described in
FIGS. 1-3 can have any suitable size. The proppant particles produced by the
process described in
FIGS. 1-3 can have a size of at least about 100 mesh, at least about 80 mesh,
at least about 60 mesh,
at least about 50 mesh, or at least about 40 mesh. For example, the proppant
particles can have a size
from about 115 mesh to about 2 mesh, about 100 mesh to about 3 mesh, about 80
mesh to about 5
mesh, about 80 mesh to about 10 mesh, about 60 mesh to about 12 mesh, about 50
mesh to about 14
mesh, about 40 mesh to about 16 mesh, or about 35 mesh to about 18 mesh.
Table 1
Sieve Distribution of Sintered Pellets (Proppant Particles) formed by Dry
Mixing and Drip Casting
16 Mesh 20 Mesh 25 Mesh 30 Mesh 35 Mesh 40 Mesh 50 Mesh
Pan
Dry
0% 17.8% 23.9% 24.3% 18.4% 10.6% 4.9% 0%
Mixing
Drip 0% 0% 0.2% 99.8% 0% 0% 0% 0%
Casting
The proppant particles produced by the process described in FIGS. 1-3 can have
any suitable
composition. The proppant particles can be or include silica and/or alumina in
any suitable amounts.
According to one or more embodiments, the proppant particles include less than
80 wt %, less than 60
wt %, less than 40 wt %, less than 30 wt %, less than 20 wt %, less than 10 wt
%, or less than 5 wt %
silica based on the total weight of the proppant particles. According to one
or more embodiments, the
proppant particles include from about 0.1 wt % to about 70 wt % silica, from
about 1 wt % to about
60 wt % silica, from about 2.5 wt % to about 50 wt % silica, from about 5 wt %
to about 40 wt %
silica, or from about 10 wt % to about 30 wt % silica. According to one or
more embodiments, the
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proppant particles include at least about 30 wt %, at least about 50 wt %, at
least about 60 wt %, at
least about 70 wt %, at least about 80 wt %, at least about 90 wt %, or at
least about 95 wt % alumina
based on the total weight of the proppant particles. According to one or more
embodiments, the
proppant particles include from about 30 wt % to about 99.9 wt % alumina, from
about 40 wt % to
about 99 wt % alumina, from about 50 wt % to about 97 wt % alumina, from about
60 wt % to about
95 wt % alumina, or from about 70 wt % to about 90 wt % alumina. In one or
more embodiments, the
proppant particles produced by the process described in FIGS. 1-3 can include
alumina, bauxite, or
kaolin, or any mixture thereof. For example, the proppant particles can be
composed entirely of or
composed essentially of alumina, bauxite, or kaolin, or any mixture thereof.
The term "kaolin" is well
known in the art and can include a raw material having an alumina content of
at least about 40 wt %
on a calcined basis and a silica content of at least about 40 wt % on a
calcined basis. The term
"bauxite" is well known in the art and can be or include a raw material having
an alumina content of
at least about 55 wt % on a calcined basis.
The proppant particles produced by the process described in FIGS. 1-3 can have
any suitable
specific gravity. The proppant particles can have a specific gravity of at
least about 2.5, at least about
2.7, at least about 3, at least about 3.3, or at least about 3.5. For example,
the proppant particles can
have a specific gravity of about 2.5 to about 4.0, about 2.7 to about 3.8,
about 3.5 to about 4.2, about
3.8 to about 4.4, or about 3.0 to about 3.5.
FIGS. 4(a-e) show photographs of alumina, bauxite, and kaolin proppant
particles produced
by the apparatus of FIG. 1 and by prior art methods. FIG. 4(a) shows an
alumina proppant particle
made by drip casting, as illustrated in FIG. 1, which has high sphericity and
a very smooth surface.
FIG. 4(b) shows an alumina proppant particle made by an Eirich mixer. The
surfaces of the particles
are rough and the shapes are generally oblate. FIG. 4(c) shows a bauxite
proppant particle made by
drip casting and FIG. 4(d) shows a bauxite proppant particle made by a
commercial prior art process
using an Eirich mixer (CARBO HSP , sold by CARBO Ceramics Inc., Houston,
Tex.). FIG. 4(e)
shows a kaolin proppant particle made by drip casting and FIG. 4(f) shows a
kaolin proppant particle
made by a pilot scale fluidized bed process.
The proppant particles produced by the process described in FIGS. 1-3 can have
any suitable
surface roughness. The proppant particles can have a surface roughness of less
than 5 gm, less than 4
gm, less than 3 gm, less than 2.5 gm, less than 2 gm, less than 1.5 gm, or
less than 1 gm For
example, the proppant particles can have a surface roughness of about 0.1 gm
to about 4.5 gm, about
0.4 gm to about 3.5 gm, or about 0.8 gm to about 2.8 pm
The surface roughness of each whole proppant particle shown in FIGS. 4(a-f)
was measured.
A smooth, convex perimeter was drawn around each proppant particle,
establishing an average
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surface level that mimicked the actual proppant particle surface as closely as
possible while still
remaining convex. Then the separation between the actual surface and the
smooth, average surface
was measured around the entire perimeter at intervals of 100 gm at 100×
magnification used in
FIG. 4, the separation could be measured with a precision of about 0.5 gm The
average of the
measurements from the entire perimeter is representative of the surface
roughness of the proppant
particle. Table 2 shows that proppant particles formed by dry mixing and spray
fluidized bed have
surface roughness from three to seven times as large as their drip cast
counterparts.
Table 2
Surface Roughness of Drip Cast and Conventionally-Formed Proppant Particles
Average Surface Roughness (gm)
Drip Cast Alumina (FIG. 4a) 1.4
Dry Mixing-Formed Alumina (FIG. 4b) 5.8
Drip Cast Bauxite (FIG. 4c) 1.6
Dry Mixing-Formed Bauxite (FIG. 4d) 4.9
Drip Cast Kaolin (FIG. 4e) 0.8
Spray Fluid Bed-Formed Kaolin (FIG. 40 5.7
FIG. 5 compares the permeability of proppant particles formed in the apparatus
of FIG. 1
compared with proppant particles formed by the dry mixing process. The
proppant particles from the
two processes are identical in size and composition, both being a high purity
(99+%) alumina. The
only variable is the pellet formation process. The permeabilities were
measured in accordance with
ISO 13503-5: "Procedures for Measuring the Long-term Conductivity of
Proppants," except that steel
wafers were used rather than sandstone wafers. The long term conductivity
apparatus described in
ISO 13503-5 utilizes a steel conductivity cell that contains an internal slot
of dimensions 7 inches in
length by 1.5 inches in width. An open port is placed in the cell extending
from the each end of the
slot to the exterior of the cell to allow for fluid flow through the slot.
Other ports are placed along the
length of the slot also extending to the exterior of the cell for the
measurement of the internal pressure
of the slot. Into this slot are fitted a lower and upper piston, the lengths
which extend out beyond the
dimensions of the cell such that a load may be applied directly to the pistons
by a hydraulic load
frame. To load the conductivity cell for the measurement of conductivity the
lower piston is first
secured into the cell so as not to obstruct the fluid or pressure ports. A
seal ring is installed to prevent
pressure or fluid leakage between slot and the piston wall. A slot sized metal
shim and a sandstone
wafer are then placed on the lower piston. Alternatively a steel wafer may
replace the sandstone wafer
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(as was the case here). A set amount of proppant is then placed on the wafer.
In this case equal
volumes of the two proppants were loaded representing initial pack widths of
about 0.19 inches. The
proppant is leveled. Then on top of the proppant is placed a second steel
wafer, metal shim, seal ring,
and the upper piston. An initial load is applied to the pistons and fluid is
flowed through the proppant
pack while pressure is measured. The temperature of the fluid and cell was
maintained at 250 F
Measurement of the rate of fluid flow and pressure loss provides a measure of
the proppant pack
conductivity in millidarcy-feet. The permeability of the proppant pack is
calculated by dividing the
conductivity by the measured width of the pack, which was about 0.16-0.19 inch
for the data shown
in FIG. 5. The flowing fluid was a silica saturated deoxygenated aqueous
solution of 2% KC1.
Conductivity was measured at stresses of 2,000 psi to 20,000 psi in increments
of 2,000 psi. In each
case the stress was held for 50 hours before measuring the conductivity.
Permeability of a proppant
pack decreases as closure stress increases due to failure of the proppant
grains. Stronger pellets will
result in a higher permeability. As can be seen in FIG. 5, proppant particles
made by dry mixing (line
2) lose 78% of their permeability as the closure stress increases from 2,000
psi to 20,000 psi. By
contrast the proppant particles made from the apparatus in FIG. 1 (line 1)
lose only 31% of their
permeability--less than one half of the permeability loss of the proppant
particles made by dry
mixing. This higher permeability of the proppant particles made from the
apparatus of FIG. 1 is due
to the improved strength of the proppant particle.
The proppant particles formed by the drip cast methods disclosed herein can
have any
appropriate permeability. Proppant particles formed by the drip cast methods
and having a specific
gravity of about 2.7 can have a long term permeability greater than about 130
darcies, about 150
darcies, about 170 darcies, about 190 darcies, about 195 darcies, about 200
darcies, about 225 darcies,
or about 250 darcies at a stress of 10,000 psi and a temperature of 250 F, as
measured in accord with
ISO 13503-5. Proppant particles formed by the drip cast methods and having a
specific gravity of
about 3.3 can have a long term permeability greater than about 110 darcies,
about 120 darcies, about
130 darcies, about 140 darcies, about 150 darcies, about 155 darcies, about
165 darcies, or about 170
darcies at a stress of 14,000 psi and a temperature of 250 F, as measured in
accord with ISO 13503-5.
Proppant particles formed by the drip cast methods and having a specific
gravity of about 3.5 can
have a long term permeability greater than about 80 darcies, about 90 darcies,
about 100 darcies,
about 110 darcies, about 115 darcies, about 120 darcies, about 130 darcies,
about 140 darcies, about
150 darcies, about 160 darcies, about 170 darcies, or about 185 darcies at a
stress of 20,000 psi and a
temperature of 250 F, as measured in accord with ISO 13503-5.
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The proppant particles formed by the drip cast methods disclosed herein can
have any
appropriate strength. An appropriate strength can include a decrease of less
than 85%, less than 80%,
or less than 75% of long term liquid permeability, as measured in accord with
ISO 13503-5 at 250 F,
of a pack of test particles, the test particles having the same composition
and method of making as the
proppant particles, when a stress applied to the pack of test particles
increases from 2,000 psi to
12,000 psi and the test particles are in the size range of 20-40 mesh and have
a specific gravity of
about 2.7. An appropriate strength can also include a decrease of less than
75%, less than 65%, or less
than 55% of long term liquid permeability, as measured in accord with ISO
13503-5 at 250 F, of a
pack of test particles, the test particles having the same composition and
method of making as the
proppant particles, when a stress applied to the pack of test particles
increases from 2,000 psi to
14,000 psi and the test particles are in the size range of 20-40 mesh and have
a specific gravity of
about 3.3. An appropriate strength can also include a decrease of less than
90%, less than 80%, less
than 75%, less than 70%, less than 65%, or less than 60% of long term liquid
permeability, as
measured in accord with ISO 13503-5 at 250 F, of a pack of test particles, the
test particles having the
same composition and method of making as the proppant particles, when a stress
applied to the pack
of test particles increases from 12,000 psi to 20,000 psi and the test
particles are in the size range of
20-40 mesh and have a specific gravity of above about 3.5.
The strength of a proppant particle can be indicated from the proppant crush
resistance test
described in ISO 13503-2: "Measurement of Properties of Proppants Used in
Hydraulic Fracturing
and Gravel-packing Operations." In this test a sample of proppant is first
sieved to remove any fines
(undersized pellets or fragments that may be present), then placed in a crush
cell where a piston is
then used to apply a confined closure stress of some magnitude above the
failure point of some
fraction of the proppant particles. The sample is then re-sieved and weight
percent of fines generated
as a result of proppant particle failure is reported as percent crush. A
comparison the percent crush of
two equally sized samples is a method of gauging the relative strength. For
the two samples of
proppant particles used in the conductivity test described above the weight
percent crush at 15,000 psi
of the proppant particles produced by dry mixing was 2.7% as compared to 0.8%
for the drip cast
proppant particles. This again indicates that drip casting produces a stronger
proppant particles.
Relative proppant strength can also be determined from single proppant
particle strength
measurements. Strength distributions of forty proppant particles from each of
the two samples of
proppant used in the conductivity test described above were measured,
tabulated, and analyzed using
Weibull statistics for the determination of a characteristic strength. The
characteristic strength of the
drip cast proppant particles so determined was 184 MPa as compared to 151 MPa
for the proppant
particles made by dry mixing.
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The proppant particles formed by the drip cast methods disclosed herein can
have any
suitable pore size distribution. For example, the proppant particles can have
a standard deviation in
pore size of less than 6 gm, less than 4 gm, less than 3 gm, less than 2.5 gm,
less than 2 gm, less than
1.5 gm, or less than 1 gm The proppant particles formed by the drip cast
methods disclosed herein
can have any suitable average maximum or largest pore size. For example, the
proppant particles can
have an average largest pore size of less than about 25 gm, less than about 20
gm, less than about 18
gm, less than about 16 fiM, less than about 14 gm, or less than about 12 gm
The proppant particles
formed by the drip cast methods disclosed herein can have any suitable
concentration of pores. For
example, the proppant particles can have less than 5,000, less than 4,500,
less than 4,000, less than
3,500, less than 3,000, less than 2,500, or less than 2,200 visible pores at a
magnification of
500× per square millimeter of proppant particulate.
Fracture mechanics teaches that particles fail under stress from the largest
flaw in the particle.
In proppant particles, the largest flaw is believed to be the largest pore.
Therefore, the stress at failure
is inversely proportional to the square root of the size of the largest flaw.
So, the ratio (R) of the stress
at failure of a drip cast proppant (DC) formed by the apparatus disclosed
herein to a conventionally
(CONY) made proppant (dry mixing or spray fluid bed processes) would be:
R=(Max pore sizepc/Max pore sizecoNv)1/2
Proppant particles made by the drip casting process and prior art processes
were examined by
a scanning electron microscope (SEM) at a magnification of 500x. To measure
pore size distribution
in particles, cross-sections of alumina, bauxite and kaolin proppant particles
made by each process
were examined in the SEM. For each sample, a random area of approximately 252
gm x171 gm from
each of ten different pellets was photographed. The ten largest pores in each
area were measured and
the equation above was used to calculate the theoretical ratio of stress at
failure of drip cast proppant
particles versus conventionally made proppant particles. The results are
presented in Table 3. For
example, the average maximum pore size in the drip cast alumina proppant
particles was 16.3 gm and
for the dry mixing process alumina proppant particles average maximum pore
size was 40.8 gm
Using the equation above, the ratio of the stress to failure of the drip cast
proppant particles to the dry
mixing process proppant particles is 1.6. Thus fracture mechanics predicts
that drip cast high alumina
proppant particles should withstand approximately 1.6 times more stress
without fracturing than dry
mixing process made proppant particles.
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Table 3
Pore Sizes of Proppant Particles Formed by Drip Casting, Dry Mixing, and Spray
Fluid Bed
Alumina Bauxite Kaolin
Drip Dry Drip Dry Drip
Dry
Cast Mixed Cast Mixed Cast Mixed
Average Largest Pore (gm) 16.3 40.8 14.3 37.5 11.1
56.0
Average of 10 Largest Pores (gm) 10.4 19.1 9.1 20.5 6.0
18.4
Theoretical Ratio of Drip Cast Strength
to Conventional Strength (gm) 1.6x 1.6x 2.2x
Additional measurements were carried out on the kaolin samples. In these,
every visible pore
was measured and the composite data from all ten areas was used to calculate
average pore size,
standard deviation in pore size, and number of pores per square millimeter, as
well as the largest pore
data, which are presented in Table 3. A summary of the data is presented in
Table 4, and FIG. 6
shows plots of the pore size distributions for drip cast kaolin (Curve 1) and
spray fluid bed kaolin
(Curve 2). The small percentage of very large pores generated by the spray
fluid bed process shown
in FIG. 6 (Curve 2) is readily visible in the microstructures in FIG. 4f. The
lack of large pores in the
drip cast material provides the strength advantage discussed above.
Table 4
Additional Pore Size Measurements for Drip Cast and Spray Fluid Bed Kaolin
Drip Cast Kaolin Spray Fluid Bed Kaolin
Average Pore Size (gm) 2.0 2.8
Standard Deviation in Pore Size ( m) 1.8 6.4
Average Number of Pores Per Square Millimeter 2121 5133
Proppant made from kaolin has a cost advantage over proppant containing higher
alumina
contents, which are made from higher-cost ores containing higher percentages
of alumina. Four
proppant products having three ranges of alumina content are sold by Carbo
Ceramics, for example
(data from vvww.carboceramics.com, searched Dec. 19, 2011). Higher alumina
content proppants
generally sell for higher prices and cost more to manufacture. The lowest
alumina contents are in the
products ECONOPROP and CARBOLITE, in which the alumina content is about 48 and
51 percent,
respectively. A higher alumina content is in CARBOPROP, in which the alumina
content is about 72
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percent. The CARBOPROP is a more expensive product to make primarily because
of higher raw
material costs.
The property of a proppant that is most directly related to its performance in
hydraulic
fractures is permeability under stress. Long-term permeability data for pure
alumina proppant made
by a prior art method and by the drip-casting process disclosed herein are
shown in FIG. 5. FIG. 7
shows long-term permeability data, measured using the same procedures as used
to obtain the data in
FIG. 5, for proppant having different alumina contents and made by different
processes. Curve 1
represents published permeability of 20/40 mesh ECONOPROP proppant (made from
kaolin, having
an alumina content of about 48 percent) made by the Eirich-mixer process
described above. Curve 2
represents permeability of 20/40 mesh CARBOPROP proppant (made from a mixture
of ores having
an alumina content of about 72 percent). Curve 3 represents the average
permeability vs stress of 15
samples of proppant (made from kaolin, having an alumina content of about 48
percent) made by the
drip cast method disclosed herein. The drip cast process produces a proppant
made from kaolin that
has about the same permeability under stress as the higher-cost product
containing 72 percent
alumina. The average long-term permeability measured at 10,000 psi stress of
15 samples was 173
darcies. This is far above the published long-term permeability at 10,000 psi
stress (85 darcies) of the
commercial proppant (ECONOPROP) having about the same alumina content, as can
be seen by
comparing Curve 3 and Curve 1.
FIG. 8 shows long-term permeability data, measured by the same procedures as
used to
obtain the data in FIGS. 5 and 7, for proppant having different alumina
contents and made by
different processes. Curve 1 represents published permeability data for 20/40
mesh CARBOPROP
proppant formed by the Eirich mixer process described above (made from a
mixture of ores having an
alumina content of about 72 percent). Curve 2 represents permeability data for
proppant (primarily
sieved on a 25-mesh screen) made by the drip cast method disclosed herein
using bauxite with an
alumina content of 70 percent. Curve 3 represents permeability data for 20/40
mesh proppant made
by the Eirich mixer process and having an alumina content of about 83 percent
alumina. The
permeability of the proppant made by the drip cast method and having an
alumina content of only 70
percent exhibits practically the same permeability behavior as the prior art
proppant made with an
Eirich mixer and having about 83 percent alumina. Since alumina is a more
expensive component of
proppants, there is considerable saving by using lower cost raw materials and
the drip cast process
disclosed herein. Comparison of Curves 1 and 2 shows the benefits of the drip
cast process with about
the same alumina content in the proppant.
Methods of hydraulic fracturing using the proppant particulates disclosed
herein are also
provided. The methods can include injecting a hydraulic fluid into a
subterranean formation at a rate
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and pressure sufficient to open a fracture therein and injecting the proppant
particulates disclosed
herein into the fracture of the subterranean formation. Downhole tools and
equipment in place during
fracturing operations oftentimes erode due at least in part to proppant
particles impinging onto the
metallic surfaces of the downhole tools and equipment when injected during the
hydraulic fracturing
operation. These proppant particles oftentimes travel at high velocities,
sufficient to damage or
destroy the downhole tools and equipment. These downhole tools and equipment
include, but are not
limited to, the well casing, measurement tools, bridge plugs, frac plugs,
setting tools, packers, and
gravel pack and frac-pack assemblies and the like. Applicants have discovered
that hydraulic
fracturing with the proppant produced by the drip cast methods disclosed
herein instead of
conventionally made proppant particles demonstrates a surprising and
unexpected reduction in
erosion to the downhole tools and equipment. For example, replacing
conventionally made proppant
particles with proppant particles made by the drip cast methods disclosed
herein can result in at least a
10%, at least a 20%, at least a 30%, at least a 40%, or at least a 50%
reduction in erosivity to the
downhole tools and equipment under same or similar hydraulic fracturing
conditions.
FIG. 9 is a graph of erosivity as a function of proppant velocity for bauxite
proppant formed
by conventional methods and alumina proppant formed by the drip cast method of
FIGS. 1-3. In this
testing the wear of flat targets made of mild steel was measured individually
for each proppant at
three separate proppant velocities. The proppant was fed into a 20' long tube
which had a nitrogen gas
stream of set velocity. The proppant was accelerated by the gas stream and
would exit the tube 1"
from the target at an incident angle of 45 degrees. The proppant was fed in
ten separate, 25 gram
increments for a total of 250 grams for each test. Three different nitrogen
gas velocities were used to
evaluate the wear caused by each of the proppant samples. The wear was
measured by measuring the
weight of the steel targets before and after impact by the proppant samples.
Erosivity was expressed
as the ratio of the weight loss of the target in milligrams to the weight of
proppant impacting the
target in kilograms. The results are shown in Table 5. The results show that
the use of the proppant
particles produced by the drip cast method of FIGS. 1-3 result in a reduction
of erosivity of up to
about 86%.
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Table 5
Sample Gas Pre-test Post-test Mass loss
Total mass of Erosivity
velocity coupon coupon (g) proppant
(mg/kg)
(m/s) mass (g) mass (g) propelled onto
coupon (g)
Conventional 150 54.5619 54.5592 0.0027 250
10.8
Proppant 200 57.757 57.7455 0.0115 250
46
260 56.8724 56.8306 0.0418 250 167.2
Drip Cast 150 57.7018 57.7011 0.0007 250
2.8
Proppant 200 53.0541 53.0525 0.0016 250
6.4
260 52.3513 52.3327 0.0186 250 74.4
Impinging the gas-entrained proppant particles formed by the drip cast methods
at a velocity
of about 160 meters per second (m/s) onto a flat mild steel target can result
in an erosivity of about
0.01 milligrams lost from the flat mild steel target per kilogram of proppant
contacting the target
(mg/kg), about 0.05 mg/kg, about 0.1 mg/kg, about 0.5 mg/kg, about 1 mg/kg, or
about 2 mg/kg to
about 5 mg/kg, about 7 mg/kg, about 10 mg/kg, about 12 mg/kg, or about 15
mg/kg. Impinging the
gas-entrained proppant particles formed by the drip cast methods at a velocity
of about 200 m/s onto
the flat mild steel target can result in an erosivity of about 0.01 mg/kg,
about 0.05 mg/kg, about 0.1
mg/kg, about 0.5 mg/kg, about 1 mg/kg, or about 2 mg/kg to about 5 mg/kg,
about 7 mg/kg, about 10
mg/kg, about 12 mg/kg, or about 15 mg/kg. Impinging the gas-entrained proppant
particles formed by
the drip cast methods at a velocity of about 260 m/s onto the flat mild steel
target can result in an
erosivity of about 1 mg/kg, about 5 mg/kg, about 10 mg/kg, about 20 mg/kg,
about 40 mg/kg, or
about 60 mg/kg to about 65 mg/kg, about 70 mg/kg, about 80 mg/kg, about 90
mg/kg, or about 100
mg/kg.
In the normal operation of hydraulically fractured oil and gas wells the
operating pressures
occurring in the well can vary significantly. For example, oil and gas wells
can cycle from a shut-in
condition, in which the pressure within the well is maintained at a maximum,
to a producing
condition, in which the pressure within the well is much lower. Further, the
flowing conditions can
change resulting in cycles of a higher or lower pressure within the well. This
"pressure cycling" of a
hydraulically fractured well is known to cause damage to proppant in the
fracture due to
rearrangement and re-stressing of the proppant grains. This results in a less
conductive proppant pack
in the fracture and adversely impacts production performance of the well.
Consequently a proppant
that is resistant to pressure cycling conductivity loss is desirable.
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A pack of the proppant particles formed by the drip cast methods disclosed
herein can also
have increased conductivity after cyclic loading conditions when compared to a
pack of
conventionally made proppant particles. For example, a pack of the proppant
particles with a specific
gravity above 3.5 formed by conventional methods can lose at least 16% of its
conductivity at 20,000
psi after being subjected to 5 cycles of cyclic loading under stresses from
about 12,000 psi to about
20,000 psi. Also, a pack of the proppant particles with a specific gravity
above 3.5 formed by
conventional methods can lose at least 10% of its conductivity at 14,000 psi
after being subjected to 5
cycles of cyclic loading under stresses from about 6,000 psi to about 14,000
psi. A pack of the
proppant particles with a specific gravity above 3.5 formed by the drip cast
methods disclosed herein
can lose less than 15%, less than 12%, less than 10%, or less than 8% of its
conductivity at 20,000 psi
after being subjected to 5 cycles of cyclic loading under stresses from about
12,000 psi to about
20,000 psi. Also, a pack of the proppant particles with a specific gravity
above 3.5 formed by the drip
cast methods disclosed herein can lose less than 10%, less than 8%, less than
6%, less than 4%, less
than 2%, less than 1%, or less than 0.1% of its conductivity at 14,000 psi
after being subjected to 5
cycles of cyclic loading under stresses from about 6,000 psi to about 14,000
psi.
FIG. 10 is a graph showing the long term conductivity of conventional bauxite
proppant and
drip cast alumina, each of 20/40 mesh sizing, after subjecting each to 50
hours of 20,000 psi closure
stress, followed by 5 cycles of cyclic loading under stresses from about
12,000 psi to about 20,000
psi, and finally re-measuring each under 20,000 psi closure stress to
determine a decrease in
conductivity due to cycling. First, it can be observed that the conductivity
of the drip cast proppant is
substantially greater at 20,000 psi than the two conventional proppants.
Second, it can be seen that the
drip cast proppant lost only 7% of its conductivity due to the stress cycling
whereas the two
conventional bauxite proppants lost 17% of their conductivity. Similarly, FIG.
11 is a graph showing
the long term conductivity of conventional bauxite proppant and drip cast
alumina, each of 20/40
mesh sizing, after subjecting each to 50 hours of 14,000 psi closure stress,
followed by 5 cycles of
cyclic loading under stresses from about 6,000 psi to about 14,000 psi, and
finally re-measuring each
under 14,000 psi closure stress to determine a decrease in conductivity due to
cycling. First, it can be
observed that the conductivity of the drip cast proppant is substantially
greater at 14,000 psi than the
two conventional proppants. Second, it can be seen that the drip cast proppant
exhibited essentially no
loss of conductivity due to the stress cycling whereas the two conventional
bauxite proppant lost 10%
of their conductivity. Also, FIG. 12 is a graph showing the long term
conductivity of conventional
bauxite proppant and drip cast alumina, each of 30/50 mesh sizing, after
subjecting each to 50 hours
of 20,000 psi closure stress, followed by 5 cycles of cyclic loading under
stresses from about 12,000
psi to about 20,000 psi, and finally re-measuring each under 20,000 psi
closure stress to determine a
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decrease in conductivity due to cycling. First, it can be observed that the
conductivity of the drip cast
proppant is substantially greater at 20,000 psi than the conventional
proppant. Second, it can be seen
that the drip cast proppant exhibited 5% loss of conductivity due to the
stress cycling whereas the
conventional bauxite proppant lost 20%.
The flow of reservoir fluids through the proppant pack in a hydraulic fracture
generally
occurs at velocities that are much greater than those occurring in the
reservoirs. At these very low
fluid velocities occurring in the reservoir pressure drops are dominated by
viscous flow behavior.
This permits the pressure behavior to be adequately described by Darcy's law
as shown:
Ap/L= pv/k, where:
Ap/L is the change in pressure per unit length, µ is the fluid viscosity, v
is the fluid
velocity and k is the permeability of the pack. However, inertial flow effects
dominate the velocities
oftentimes found in the fracture and the Forchheimer equation is therefore
employed:
Ap/L = ,uv/k + 13pv2
The first term in the Forchheimer equation is identical to Darcy's law. The
Forchheimer
equation adds an inertial pressure drop term that includes a velocity squared
function, v2, and the
density of the fluid, p. At high velocities this inertial teim will dominate
the pressure drop and thus
dictate fluid flow. Also included in the inertial term is the Forchheimer beta
factor, (-3. Similar to
permeability, the beta factor is an intrinsic property of the porous media
that will vary as a function of
confining stress. As shown by the Forchheimer equation, pressure change (Ap)
decreases as
permeability increases and beta factor decreases. Thus in high fluid velocity
conditions, such as those
in a propped hydraulic fracture where inertial forces will dominate, a low
beta factor will reduce
pressure losses in the fracture resulting in higher flow rates.
A pack of the proppant particles formed by the drip cast methods disclosed
herein can also
have a reduced beta factor after cyclic loading conditions when compared to
conventionally made
proppant. For example, a pack of the proppant particles formed by conventional
methods in the size
range of 20/40 mesh can have an increase in beta factor at least 0.0004 at
20,000 psi after being
subjected to 5 cycles of cyclic loading under stresses from about 12,000 psi
to about 20,000 psi. Also,
a pack of the proppant particles formed by conventional methods in the size
range of 30/50 mesh can
have an increase in beta factor of at least 0.0004 at 20,000 psi after being
subjected to 5 cycles of
cyclic loading under stresses from about 12,000 psi to about 20,000 psi. A
pack of the proppant
CA 02963249 2017-03-30
WO 2016/054022 PCT/US2015/052912
particles formed by the drip cast methods disclosed herein in the size range
of 20/40 mesh can have
an increase in beta factor of less than 0.0005, less than 0.0002, less than
0.0001, less than 0.00005, or
less than 0.00001 at 20,000 psi after being subjected to 5 cycles of cyclic
loading under stresses from
about 12,000 psi to about 20,000 psi. Also, a pack of the proppant particles
formed by the drip cast
methods disclosed herein in the size range of 30/50 mesh can have an increase
in beta factor of less
than 0.0006, less than 0.0004, or less than 0.0002 at 20,000 psi after being
subjected to 5 cycles of
cyclic loading under stresses from about 12,000 psi to about 20,000 psi.
FIG. 13 is a graph showing the beta factors of conventional bauxite proppant
and drip cast
alumina, each of 20/40 mesh sizing, after subjecting each to 50 hours of
20,000 psi closure stress,
followed by 5 cycles of cyclic loading under stresses from about 12,000 psi to
about 20,000 psi, and
finally re-measuring each under 20,000 psi closure stress to determine an
increase in beta factors due
to cycling. First, it can be observed that the beta factor of the drip cast
proppant is substantially lower
at 20,000 psi than the two conventional proppants. Second, it can be seen that
the beta factor for the
drip cast proppant increased only slightly when compared to the increase in
post cycling beta factor
for the two conventional bauxites. Similarly, FIG. 14 is a graph showing the
beta factors of
conventional bauxite proppant and drip cast alumina, each of 30/50 mesh
sizing, after subjecting each
to 50 hours of 20,000 psi closure stress, followed by 5 cycles of cyclic
loading under stresses from
about 12,000 psi to about 20,000 psi, and finally re-measuring each under
20,000 psi closure stress to
determine an increase in beta factors due to cycling. First, it can be
observed that the beta factor of the
drip cast proppant is substantially lower at 20,000 psi than the two
conventional proppants. Second, it
can be seen that the beta factor for the drip cast proppant increased only
slightly when compared to
the increase in beta post cycling for the two conventional bauxites.
It is understood that modifications to the invention may be made as might
occur to one skilled
in the field of the invention within the scope of the appended claims. All
embodiments contemplated
hereunder which achieve the objects of the invention have not been shown in
complete detail. Other
embodiments may be developed without departing from the spirit of the
invention or from the scope
of the appended claims. Although the present invention has been described with
respect to specific
details, it is not intended that such details should be regarded as
limitations on the scope of the
invention, except to the extent that they are included in the accompanying
claims.
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