U.S. patent application number 14/578922 was filed with the patent office on 2015-07-09 for method of subsurface reservoir fracturing using electromagnetic pulse energy.
The applicant listed for this patent is Husky Oil Operations Limited. Invention is credited to Amin Saeedfar.
Application Number | 20150192005 14/578922 |
Document ID | / |
Family ID | 53494768 |
Filed Date | 2015-07-09 |
United States Patent
Application |
20150192005 |
Kind Code |
A1 |
Saeedfar; Amin |
July 9, 2015 |
METHOD OF SUBSURFACE RESERVOIR FRACTURING USING ELECTROMAGNETIC
PULSE ENERGY
Abstract
A method for initiating and/or propagating fractures in a
hydrocarbon reservoir, to improve fluid-flow permeability and
hydrocarbon production. The method comprises the use of at least
one electromagnetic energy pulse to both heat the reservoir rock
and water within, causing thermal pressurization, and initiate
electrokinetic pressurization.
Inventors: |
Saeedfar; Amin; (Calgary,
CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Husky Oil Operations Limited |
Calgary |
|
CA |
|
|
Family ID: |
53494768 |
Appl. No.: |
14/578922 |
Filed: |
December 22, 2014 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61924919 |
Jan 8, 2014 |
|
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|
Current U.S.
Class: |
166/248 |
Current CPC
Class: |
E21B 47/13 20200501;
E21B 43/26 20130101; E21B 36/00 20130101; E21B 43/24 20130101; E21B
43/2401 20130101; H01Q 1/04 20130101 |
International
Class: |
E21B 43/26 20060101
E21B043/26 |
Claims
1. A method for initiating and propagating fractures in a
hydrocarbon reservoir, the method comprising the steps of: a.
applying at least one electromagnetic energy pulse to a portion of
the reservoir; b. allowing application of the at least one
electromagnetic energy pulse to expand pore fluids within the
portion of the reservoir; c. allowing the expansion of the pore
fluids to increase pore pressure; and d. allowing the increased
pore pressure to create mechanical stresses in the portion of the
reservoir exceeding fracture stress of the portion of the
reservoir, initiating and propagating fractures in the
reservoir.
2. The method of claim 1 wherein a series of the electromagnetic
energy pulses are applied to the portion of the reservoir.
3. The method of claim 1 wherein a plurality of the electromagnetic
energy pulses are applied to the portion of the reservoir.
4. The method of claim 1 wherein the electromagnetic energy pulses
are periodically applied to the portion of the reservoir.
5. The method of claim 1 further comprising the step before step a
of determining a suitable pulse strength for the at least one
electromagnetic energy pulse.
6. The method of claim 1 wherein the at least one electromagnetic
energy pulse is applied by radiating the at least one
electromagnetic energy pulse so as to propagate the at least one
electromagnetic energy pulse at least partially through the portion
of the reservoir.
7. The method of claim 1 wherein the expansion of the pore fluids
results from thermal pressurization and electrokinetic
pressurization.
8. The method of claim 1 wherein the expansion of the pore fluids
results at least partially from vaporization of connate water in
the portion of the reservoir.
9. The method of claim 1 wherein the fractures comprise
micro-cracks.
10. The method of claim 9 wherein the micro-cracks reduce strength
of the portion of the reservoir, enabling propagation of the
fractures.
11. A method for improving permeability in a hydrocarbon reservoir,
the method comprising the steps of: a. applying at least one
electromagnetic energy pulse to a portion of the reservoir; b.
allowing application of the at least one electromagnetic energy
pulse to expand pore fluids within the portion of the reservoir; c.
allowing the expansion of the pore fluids to increase pore
pressure; and d. allowing the increased pore pressure to create
mechanical stresses in the portion of the reservoir exceeding
fracture stress of the portion of the reservoir, fracturing the
portion of the reservoir to improve the permeability.
12. The method of claim 11 wherein a series of the electromagnetic
energy pulses are applied to the portion of the reservoir.
13. The method of claim 11 wherein a plurality of the
electromagnetic energy pulses are applied to the portion of the
reservoir.
14. The method of claim 11 wherein the electromagnetic energy
pulses are periodically applied to the portion of the
reservoir.
15. The method of claim 11 further comprising the step before step
a of determining a suitable pulse strength for the at least one
electromagnetic energy pulse.
16. The method of claim 11 wherein the at least one electromagnetic
energy pulse is applied by radiating the at least one
electromagnetic energy pulse so as to propagate the at least one
electromagnetic energy pulse at least partially through the portion
of the reservoir.
17. The method of claim 11 wherein the expansion of the pore fluids
results from thermal pressurization and electrokinetic
pressurization.
18. The method of claim 11 wherein the expansion of the pore fluids
results at least partially from vaporization of connate water in
the portion of the reservoir.
19. The method of claim 11 wherein the mechanical stresses reduce
shear strength of the portion of the reservoir, causing the
fracturing.
20. The method of claim 11 wherein the mechanical stresses cause
tensile failure of the portion of the reservoir, causing the
fracturing.
21. A method for improving production of hydrocarbon from a
reservoir, the method comprising the steps of: a. applying at least
one electromagnetic energy pulse to a portion of the reservoir; b.
allowing application of the at least one electromagnetic energy
pulse to expand pore fluids within the portion of the reservoir; c.
allowing the expansion of the pore fluids to increase pore
pressure; d. allowing the increased pore pressure to create
mechanical stresses in the portion of the reservoir exceeding
fracture stress of the portion of the reservoir, initiating and
propagating fractures in the reservoir; and e. producing the
hydrocarbon through the fractures.
22. The method of claim 21 wherein a series of the electromagnetic
energy pulses are applied to the portion of the reservoir.
23. The method of claim 21 wherein a plurality of the
electromagnetic energy pulses are applied to the portion of the
reservoir.
24. The method of claim 21 wherein the electromagnetic energy
pulses are periodically applied to the portion of the
reservoir.
25. The method of claim 21 further comprising the step before step
a of determining a suitable pulse strength for the at least one
electromagnetic energy pulse.
26. The method of claim 21 wherein the at least one electromagnetic
energy pulse is applied by radiating the at least one
electromagnetic energy pulse so as to propagate the at least one
electromagnetic energy pulse at least partially through the portion
of the reservoir.
27. The method of claim 21 wherein the expansion of the pore fluids
results from thermal pressurization and electrokinetic
pressurization.
28. The method of claim 21 wherein the expansion of the pore fluids
results at least partially from vaporization of connate water in
the portion of the reservoir.
29. The method of claim 21 wherein the fractures comprise
micro-cracks.
30. The method of claim 29 wherein the micro-cracks reduce strength
of the portion of the reservoir, enabling propagation of the
fractures.
31. A method of hydrocarbon reservoir stimulation, the method
comprising the steps of: a. applying at least one electromagnetic
energy pulse to a portion of a reservoir; b. allowing application
of the at least one electromagnetic energy pulse to expand pore
fluids within the portion of the reservoir; c. allowing the
expansion of the pore fluids to increase pore pressure; d. allowing
the increased pore pressure to create mechanical stresses in the
portion of the reservoir exceeding fracture stress of the portion
of the reservoir, initiating and propagating fractures in the
reservoir; and e. producing hydrocarbon through the fractures.
32. The method of claim 31 wherein a series of the electromagnetic
energy pulses are applied to the portion of the reservoir.
33. The method of claim 31 wherein a plurality of the
electromagnetic energy pulses are applied to the portion of the
reservoir.
34. The method of claim 31 wherein the electromagnetic energy
pulses are periodically applied to the portion of the
reservoir.
35. The method of claim 31 further comprising the step before step
a of determining a suitable pulse strength for the at least one
electromagnetic energy pulse.
36. The method of claim 31 wherein the at least one electromagnetic
energy pulse is applied by radiating the at least one
electromagnetic energy pulse so as to propagate the at least one
electromagnetic energy pulse at least partially through the portion
of the reservoir.
37. The method of claim 31 wherein the expansion of the pore fluids
results from thermal pressurization and electrokinetic
pressurization.
38. The method of claim 31 wherein the expansion of the pore fluids
results at least partially from vaporization of connate water in
the portion of the reservoir.
39. The method of claim 31 wherein the fractures comprise
micro-cracks.
40. The method of claim 39 wherein the micro-cracks reduce strength
of the portion of the reservoir, enabling propagation of the
fractures.
Description
FIELD OF THE INVENTION
[0001] The present invention relates to methods to enhance
hydrocarbon reservoir permeability and hydrocarbon production, and
specifically to methods for fracturing a hydrocarbon reservoir.
BACKGROUND OF THE INVENTION
[0002] The availability of an efficient fracturing method for
separating constituents of a rock is of interest for recovering
useful materials such as hydrocarbons. Common to all subsurface
formation fracturing techniques is the creation of mechanical
stresses that exceed the fracture stress of a given formation rock.
This leads to generation of micro-cracks in the rock, which
consequently results in a significant loss of strength in the
formation rock and its fracturing.
[0003] Hydraulic fracturing is one form of fracturing that is
commonly applied for hydrocarbon reservoir stimulation, especially
for tight reservoirs and/or interbedding shale. By creating and/or
extending a fracture from a borehole into the reservoir formations,
target hydrocarbons such as oil and gas can be produced from the
formation towards the borehole with much less flow resistance.
Conventionally, in hydraulic fracturing a pressurized fluid used to
create and/or widen the fracture is provided with a special type of
material such as proppant, which proppant remains in the fracture
after injection of the fluid to keep the fracture flow-conductive
after relieving fluid pressure.
[0004] Other types of fracturing are known in the art. For example,
U.S. patent application Ser. No. 13/231,912 to Sultenfuss et al.
teaches a method of applying steady-state radiofrequency (RF)
heating to fracture a reservoir for a steam-assisted gravity
drainage (SAGD) application. Notwithstanding the exploration of
alternative fracturing methods and techniques, hydraulic fracturing
remains a standard and ubiquitous reservoir stimulation method.
[0005] However, it is known that hydraulic fracturing techniques
have been subject to criticism on environmental grounds, and they
can also be undesirably expensive to implement.
[0006] What is needed, therefore, is a method for fracturing
reservoir rock that can reduce the environmental impact and the
associated costs.
SUMMARY OF THE INVENTION
[0007] The present invention therefore seeks to provide a method
for applying electromagnetic energy to a reservoir in such a way
that it fractures the reservoir, opening up permeability and
enhancing production, while reducing or eliminating the need for
conventional hydraulic fracturing techniques.
[0008] According to a first broad aspect of the present invention,
there is provided a method for initiating and propagating fractures
in a hydrocarbon reservoir, the method comprising the steps of:
[0009] a. applying at least one electromagnetic energy pulse to a
portion of the reservoir;
[0010] b. allowing application of the at least one electromagnetic
energy pulse to expand pore fluids within the portion of the
reservoir;
[0011] c. allowing the expansion of the pore fluids to increase
pore pressure; and
[0012] d. allowing the increased pore pressure to create mechanical
stresses in the portion of the reservoir exceeding fracture stress
of the portion of the reservoir, initiating and propagating
fractures in the reservoir.
[0013] According to a second broad aspect of the present invention,
there is provided a method for improving permeability in a
hydrocarbon reservoir, the method comprising the steps of:
[0014] a. applying at least one electromagnetic energy pulse to a
portion of the reservoir;
[0015] b. allowing application of the at least one electromagnetic
energy pulse to expand pore fluids within the portion of the
reservoir;
[0016] c. allowing the expansion of the pore fluids to increase
pore pressure; and
[0017] d. allowing the increased pore pressure to create mechanical
stresses in the portion of the reservoir exceeding fracture stress
of the portion of the reservoir, fracturing the portion of the
reservoir to improve the permeability.
[0018] According to a third broad aspect of the present invention,
there is provided a method for improving production of hydrocarbon
from a reservoir, the method comprising the steps of:
[0019] a. applying at least one electromagnetic energy pulse to a
portion of the reservoir;
[0020] b. allowing application of the at least one electromagnetic
energy pulse to expand pore fluids within the portion of the
reservoir;
[0021] c. allowing the expansion of the pore fluids to increase
pore pressure;
[0022] d. allowing the increased pore pressure to create mechanical
stresses in the portion of the reservoir exceeding fracture stress
of the portion of the reservoir, initiating and propagating
fractures in the reservoir; and
[0023] e. producing the hydrocarbon through the fractures.
[0024] According to a fourth broad aspect of the present invention,
there is provided a method of hydrocarbon reservoir stimulation,
the method comprising the steps of:
[0025] a. applying at least one electromagnetic energy pulse to a
portion of a reservoir;
[0026] b. allowing application of the at least one electromagnetic
energy pulse to expand pore fluids within the portion of the
reservoir;
[0027] c. allowing the expansion of the pore fluids to increase
pore pressure;
[0028] d. allowing the increased pore pressure to create mechanical
stresses in the portion of the reservoir exceeding fracture stress
of the portion of the reservoir, initiating and propagating
fractures in the reservoir; and
[0029] e. producing hydrocarbon through the fractures.
[0030] In some exemplary embodiments of the above aspects, a series
of the electromagnetic energy pulses are applied to the portion of
the reservoir, or a plurality of the electromagnetic energy pulses
are applied to the portion of the reservoir, or the electromagnetic
energy pulses are periodically applied to the portion of the
reservoir. The preferred methods further comprise the step before
step a of determining a suitable pulse strength for the at least
one electromagnetic energy pulse. The at least one electromagnetic
energy pulse is preferably applied by radiating the at least one
electromagnetic energy pulse so as to propagate the at least one
electromagnetic energy pulse at least partially through the portion
of the reservoir.
[0031] The expansion of the pore fluids may result from thermal
pressurization and electrokinetic pressurization. The expansion of
the pore fluids can result at least partially from vaporization of
connate water in the portion of the reservoir. The fractures may
comprise micro-cracks, such that the micro-cracks reduce strength
of the portion of the reservoir, enabling propagation of the
fractures. The mechanical stresses reduce shear strength of the
portion of the reservoir, and cause tensile failure of the portion
of the reservoir, causing the fracturing.
[0032] A detailed description of exemplary embodiments of the
present invention is given in the following. It is to be
understood, however, that the invention is not to be construed as
being limited to these embodiments.
BRIEF DESCRIPTION OF THE DRAWINGS
[0033] In the accompanying drawings, which illustrate exemplary
embodiments of the present invention:
[0034] FIG. 1 is an illustration of an electric double layer in a
fluid-saturated porous medium;
[0035] FIG. 2 is a simplified view of an electromagnetic (EM) pulse
generator in a wellbore, according to an exemplary embodiment of
the present invention;
[0036] FIG. 3 is a chart illustrating real and imaginary parts of
the impedance of a reservoir formation;
[0037] FIG. 4 is a simplified circuit model of a reservoir
formation;
[0038] FIG. 5 is a chart illustrating a single EM energy pulse;
[0039] FIG. 6 is an illustration of a periodic pulse wave with a
smaller frequency than the cosine wave; and
[0040] FIG. 7 is an illustration of a periodic pulse wave with a
frequency equal to the cosine wave.
[0041] Exemplary embodiments of the present invention will now be
described with reference to the accompanying drawings.
DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS
[0042] Throughout the following description specific details are
set forth in order to provide a more thorough understanding to
persons skilled in the art. However, well known elements may not
have been shown or described in detail to avoid unnecessarily
obscuring the disclosure. The following description of examples of
the invention is not intended to be exhaustive or to limit the
invention to the precise forms of any exemplary embodiment.
Accordingly, the description and drawings are to be regarded in an
illustrative, rather than a restrictive, sense.
[0043] Unlike conventional hydraulic fracturing, the
electromagnetic pulse energy (EMPE) method disclosed herein
involves a process of fracture initiation and propagation by a
joint thermal-electrokinetic pressurization mechanism that
preferably occurs in a relatively short period of time, which
results in thermal-pressure shock. Such rapid pressurization may
generate multiple fractures, which can be beneficial to reservoir
stimulation, particularly in relatively tight formations.
[0044] According to some embodiments of the present invention, for
general applications and processes (for example, thermal
recoveries, CHOPS, conventional recoveries, carbonate reservoirs,
clastics reservoirs, shale oil/gas reservoirs, heavy oil
reservoirs, etc.), near-instantaneous thermal and pressure stress
in the reservoir rock can be introduced through: [0045] 1) rapid
electromagnetic heating and thermal pressurization of the rock and
the water contained within it, and [0046] 2) electrokinetic
pressurization by means of one or more electromagnetic pulses using
high power signals.
[0047] In those areas of a target reservoir formation having low
permeability, the pore pressure resulting from the electro-thermal
expansion of pore fluids and the electrokinetic mechanism may not
be balanced with the fluid flow and the fluid volume increment
resulting from pore-space dilation. If the pore pressure is created
in a relatively short period of time through exerting a pulsed
power, particularly an electromagnetic pulse, the described
mechanism will be more rapid and dramatic, which can lead to shear
or tensile failure of formation rock and creation of desirable
micro-cracks and fractures.
[0048] EM Rapid Heating:
[0049] EM heating can be generally divided into two main categories
based on the frequency of the electrical current used by the
source, (i) direct (DC)/low frequency currents, and (ii) high
frequency (radio frequency (RF), microwave) currents, which may be
employed depending on reservoir fluid properties (e.g.,
resistivity, dielectric permittivity) and other formation
characteristics. Two different electromagnetic mechanisms underlie
the electromagnetic heating using different kinds of EM sources.
When a DC or a low frequency current source is applied, the joule
heating based on the electric conduction in materials, is dominant.
In this low frequency mechanism, charged particles in an electric
circuit are accelerated by an electric field but give up some of
their kinetic energy each time they collide with a particle. The
increase in the kinetic energy of these particles manifests itself
as heat and a rise in the temperature of the conducting material.
With a higher frequency electromagnetic source, the dielectric
heating prevails in which dipoles formed by the molecules tend to
align themselves with the electric field (called dielectric
polarization) with a velocity proportional to the frequency of the
field's alternation. This molecular movement can result in
significant heating, as seen in commercial microwave ovens. The key
requirement for dielectric polarization is that the frequency range
of the external oscillating field should enable adequate
inter-particle interaction. The larger the masses involved, the
slower the response upon applying or removing of the external EM
field. As the frequency goes higher, the slower polarization
mechanisms for heavier particles fail to follow. From the
dependency of characteristic relaxation frequency and particle
mass, it can be deduced that at higher frequencies, heating is
achieved mostly by polarization mechanisms and local oscillation of
charged particles. In contrast, as the frequency decreases, free
charge/ionic conduction plays a dominant role in the heating
process. Back to the reservoir scale, through the relatively rapid
heating, the internal pore pressure of the reservoir rock (for
example, interbedding shale) increases, thereby causing the
fracturing. When an electromagnetic pulse is utilized (as opposed
to steady-state RF heating), rapid heating occurs even faster and
the fracturing process is more efficient. Also, an instantaneous
input power with greater amplitude can be applied during the EMPE
process, which introduces a greater heat rate to the reservoir and
further improves the fracturing performance, yet maintains energy
efficiency when compared to steady-state radio frequency (RF)
heating, which will be described below. Fracturing is achieved by
rapid heating through the radiation of electromagnetic high-power
pulse signals and consequent near-instantaneous vaporization of the
connate water trapped in the reservoir rock, which introduces
thermal pressurization and mechanical fracture as a result. While
vaporization will take place depending on the heat introduced at a
particular point in the reservoir (which depends on distance from
the antenna or the location of the electromagnetic beam),
vaporization per se does not necessarily have to occur, as dilation
pressure can occur due simply to differential thermal expansion
coefficients between the pore matrix and the pore space components.
In other words, thermal pressurization is overpressure of the pore
fluids caused by thermal expansion, which either quickly dissipates
in high permeability formations or accumulates in low permeability
areas. Thermal pressurization occurs when the thermal expansion of
pore fluids exceeds that of the pore space. In this case, the
pore-space stiffness acts against the expansion of the pore-fluid
volume and compresses the fluid by increasing pore pressure to
minimize its increase in volume, which results in a reduction of
the effective stress. This reduces the shear strength of the
formation rock which may lead to fracturing. This pore
pressurization may also induce tensile failure.
[0050] Electrokinetic Mechanism:
[0051] The electrokinetic mechanism is based on the fact that
mechanical (acoustic pressure) and electromagnetic energies are
generally coupled in wetted porous rocks. In a subsurface
formation, electrokinetic phenomena arise from the bound charges on
a solid surface in contact with an electrically conductive fluid.
As a result the electric charges within the fluid separate into an
electric double layer (EDL), as is illustrated in FIG. 1. The inner
layer consists of ions absorbed onto the solid surface, while the
outer layer is formed by ions under the combined influence of
ordering electrical and disordering thermal forces. A low frequency
electromagnetic wave that propagates through such a fluid-saturated
porous medium will produce an electric current (called the
streaming current) by applying electromagnetic forces on outer
layer ions of the EDL. This creates a mechanical disturbance in the
fluid and therefore a pressure gradient. By taking this effect into
account, the pressure response resulting from low frequency
electromagnetic (EM) energy can contribute to the fluid
pressurization in a porous media and consequently the fracturing
process.
[0052] An illustration of an exemplary process is shown in FIG. 2,
where an EM pulse generator (generating a periodic pulse wave of
any shape) located on the surface is connected to an EM applicator
in a wellbore (which wellbore may be single/multiple, vertical or
horizontal, as would be known to those skilled in the art) through
an appropriate transmission line. An EM field is thus propagating
through the formation, but its amplitude is attenuating due to the
electrical properties and skin depth effect of the reservoir
formation; therefore, a single pulse is likely not adequate to
create the necessary pressure in some cases for fracturing
purposes, and multiple or periodic pulse waves are therefore
recommended for consideration. It is possible to combine this
aspect of the present invention with various EM sources, such as
induction coils as a low frequency EM source or an antennae array
as a radio frequency EM source, to focus the beam of the
electromagnetic pulse on the area that is to be fractured, in a
known manner. It is also possible to use acoustic pulses
simultaneously to expedite the fracturing process, again in a
manner that would be clear to those skilled in the art.
[0053] To illustrate the potential utility of embodiments of the
present invention, it is important to note that the soils,
unconsolidated sediments, and rocks of the crust of the Earth are
principally composed of silicate minerals, which are electrical
insulators. Their electrical resistivities are typically greater
than 1010 Ohm-m and they carry no current. However, at high
temperatures these minerals begin to dissociate and current can be
carried by their ions in the pore solutions.
[0054] For most rocks and soils where current is carried by ions in
the pore fluid, the resistivity depends on the rock properties such
as porosity, pore fluid resistivity/salinity, temperature, pore
fluid saturation, and pressure. Electrical resistivity or the
apparent resistivity is also a function of the frequency of the
applied current called electrical impedance, which is a complex
number, i.e., the measured voltage has a component in phase with
the current and a component 90 degrees out of phase (in quadrature)
with the current. The real and imaginary components of V/I
(proportional to the resistivity) have the form illustrated in FIG.
3.
[0055] It has also been observed in field measurements employing a
switched DC current that the voltage across the measuring
electrodes decayed slowly after the current was shut off. This
suggests an energy storage mechanism in the subsurface material.
Qualitatively, the transient and frequency domain observations for
the resistivity are compatible with the response of the
resistor-capacitor circuit analog illustrated in FIG. 4.
[0056] At DC the capacitor is an open circuit and all the current
passes through the sum of R1 and R2, developing a voltage
V=I.times.(R1+R2). As the frequency increases, current can flow
through the capacitor, which decreases the overall resistance.
Finally, at high frequency the current is effectively short
circuited by the capacitor and the voltage developed is simply
V=I.times.R1. Between the DC and high frequency limits the voltage
across the capacitor is phase shifted 90.degree. from the current
and so adds an imaginary component to the total voltage measured
across the circuit, which peaks midway between the low and high
frequency asymptotes. Thus it can be seen that the illustrated
circuit reproduces the key features observed in measurements. The
electric circuit representation of subsurface formation rock is a
simplified model of the rock electrical behaviour. While more
complicated circuit representations could be developed based on
other electrical mechanisms in rocks, the basic model in FIG. 4 is
employed for simplicity. However, the proposed methodology can be
employed for other types of electric circuit representations.
[0057] To begin, the impedance of the circuit model at given
angular frequency, .omega.=2.pi.f, is written as
V I = Z = Z ( .omega. ) j.PHI. ( .omega. ) = R 1 + 1 1 R 2 +
j.omega. C = R 1 + R 2 + j.omega. CR 1 R 2 1 + j.omega. CR 2 ( 1 )
##EQU00001##
where j= {square root over (-1)}. If the applied voltage is a
single frequency cosine wave (steady-state source), then the
time-averaged power being consumed by the electric circuit (turned
to heat in the rock) is given by
p s = 1 2 Re { V 0 I * } = 1 2 Re { V 0 2 Z * } = V 0 2 2 1 k 1 k 2
+ .omega. 2 CR 2 k 2 2 + .omega. 2 ( 2 ) where k 1 = CR 1 R 2 , k 2
= R 1 + R 2 CR 1 R 2 ( 3 ) ##EQU00002##
as the time domain input voltage is defined as
v.sub.s(t)=V.sub.0 cos(.omega..sub.0t) (4)
and the instantaneous power delivered to the circuit can be written
as follows
p s ( t ) = v s ( t ) i s ( t ) = V 0 2 Z ( .omega. 0 ) cos (
.omega. 0 t ) cos ( .omega. 0 t - .PHI. ( .omega. 0 ) ) = 1 2 V 0 2
Z ( .omega. 0 ) [ cos ( 2 .omega. 0 t - .PHI. ( .omega. 0 ) ) + cos
( .PHI. ( .omega. 0 ) ) ] ( 5 ) ##EQU00003##
[0058] Therefore the maximum instantaneous power is given by
max t p s ( t ) = 1 2 V 0 2 Z ( .omega. 0 ) [ 1 + cos ( .PHI. (
.omega. 0 ) ) ] ( 6 ) ##EQU00004##
[0059] In the case of a single pulse (for example, a rectangular
pulse as illustrated in FIG. 5), the frequency spectrum is wide
band and continuous. In this case, the instantaneous power could be
greater than the single frequency time harmonic wave, but for the
EMPE fracturing to be more effective the source has to emit
multiple pulses, which lead to a periodic pulse emission from the
EM applicator.
[0060] In the case of a general periodic pulse voltage, Fourier
expansion is required to calculate the maximum and average power to
the load. The frequency of the periodic pulse wave is selected in
the same way that it is done for the single frequency time harmonic
wave, which is based on electrical properties, electromagnetic loss
tangent and skin depth of the reservoir formation. However, it is
recommended that the frequency of the periodic pulse wave be less
than (as in FIG. 6) or equal to (as in FIG. 7) the reference
frequency of the time harmonic wave. This will adjust the frequency
contents of the periodic pulse wave source so that it can
contribute in both low frequency electrokinetic and wide range
frequency thermal mechanisms in reservoir formations.
[0061] The time-domain representation of a generic periodic pulse
is given by
v T ( t ) = n = - .infin. + .infin. a n j n .omega. 0 t ( 7 )
##EQU00005##
and its Fourier spectrum is then given by
V T ( .omega. ) = n = - .infin. + .infin. 2 .pi. a n .delta. (
.omega. - n .omega. 0 ) ( 8 ) ##EQU00006##
where .delta.(.omega.) is the Dirac-delta function. As it is seen
from (8), unlike the single frequency cosine wave, a generic
periodic pulse voltage has an infinite number of frequency
components. As such, higher frequency components can contribute to
dielectric heating and lower frequency components can contribute to
both resistive heating and the electrokinetic process. As described
above, all these mechanisms may be beneficial for the thermal and
hydro pressurization of a fluid saturated porous medium to create
fractures.
[0062] Now, using Parseval's theorem, it can be easily shown that
the time-average power consumed by the load for a generic periodic
pulse is calculated by
p T = a 0 2 Z ( 0 ) + 2 n = 0 + .infin. a n 2 Z ( n .omega. 0 ) Re
{ Z ( n .omega. 0 ) } ( 9 ) ##EQU00007##
[0063] In the following workflow, from an energy transport
perspective, it will be shown why EM pulse energy is more effective
than steady-state single frequency EM wave for rapid heating
purposes. To create a pulse voltage that can provide greater heat
(and consequently thermal pressurization) than a single frequency
cosine wave at a given frequency, the periodic pulse with a given
shape can be designed so that time-average power consumed by the
load is the same for the periodic pulse wave and single frequency
cosine wave but the instantaneous power delivered to the load by
the periodic pulse wave is greater than that of the single
frequency cosine wave, i.e.,
{ p T = p s max t p T ( t ) max t p s ( t ) ( 10 ) ##EQU00008##
[0064] By imposing the conditions in (10), the total input energy
provided by both types of source of voltages are the same but the
instantaneous power which provides thermal shock and kinetic
pressurization is greater for the periodic pulse wave than single
frequency cosine wave. Here, this process is described for the
rectangular pulse and cosine wave shown in FIG. 6 or 7. However,
the same procedure can be done for any type of periodic pulse wave
and time-harmonic single frequency wave form.
[0065] To then obtain the time-average power delivered to the
circuit shown in FIG. 4 from a periodic pulse voltage source as
show in FIGS. 6 and 7, one will first calculate the electric
current from a voltage source as shown in FIG. 5, which is one
single pulse from the periodic waveform.
[0066] Using the fundamentals of electric circuits theory, one can
show that the electric current is obtained by
i ( t ) = V m [ 1 R 1 + R 2 + ( 1 R 1 - 1 R 1 + R 2 ) - k 2 t ] u (
t ) - V m [ 1 R 1 + R 2 + ( 1 R 1 - 1 R 1 + R 2 ) - k 2 ( t - .tau.
) ] u ( t - .tau. ) ( 11 ) ##EQU00009##
where u(t) is the Heaviside step function. Using the theory of a
linear time-invariant system, it can be shown then that the
electrical current as the response of periodic pulse is given
by
i T ( t ) = n = - .infin. + .infin. i ( t + nT ) ( 12 )
##EQU00010##
[0067] Therefore, the time-average power delivered to the circuit
is given by
p T = 1 T .intg. T v T ( t ) i T ( t ) t = V m 2 T [ .tau. R 1 + R
2 + 1 k 2 1 - - k 2 .tau. 1 - - k 2 T ( 1 R 1 - 1 R 1 + R 2 ) - 1 k
2 1 - - k 2 .tau. 1 - - k 2 T ( 1 R 1 - 1 R 1 + R 2 ) - k 2 ( T -
.tau. ) ] ( 13 ) ##EQU00011##
[0068] For a sufficiently large amplification coefficient, G, the
following selection is made so that the instantaneous power
delivered by periodic pulse waveform becomes greater than single
frequency cosine wave (steady-state source)
V m = G ( R 1 + R 2 ) max t p s ( t ) = G ( R 1 + R 2 ) 2 V 0 2 Z (
.omega. 0 ) [ 1 + cos ( .PHI. ( .omega. 0 ) ) ] ( 14 )
##EQU00012##
[0069] Now, for this value of V.sub.m, the following nonlinear
algebraic equation has to be solved for .tau. (.tau.<T) to find
the appropriate duty cycle for the periodic pulse wave so the
time-average power from both voltage sources become equal.
V m 2 T [ .tau. R 1 + R 2 + 1 k 2 1 - - k 2 .tau. 1 - - k 2 T ( 1 R
1 - 1 R 1 + R 2 ) - 1 k 2 1 - - k 2 .tau. 1 - - k 2 T ( 1 R 1 - 1 R
1 + R 2 ) - k 2 ( T - .tau. ) ] = V 0 2 2 1 k 1 k 2 + .omega. 2 CR
2 k 2 2 + .omega. 2 ( 15 ) ##EQU00013##
[0070] Thus, a periodic pulse wave can be designed by a skilled
person based on this teaching which can provide greater
instantaneous power to the load compared to a single frequency time
harmonic wave for a given frequency and yet, maintain an equal
total input power.
[0071] Similarly, a system can be designed so that the maximum
instantaneous power delivered by a periodic pulse wave and a single
frequency time harmonic wave are equal but the time-average power
delivered by the periodic pulse wave becomes much less than that of
single frequency time harmonic wave, i.e.,
{ p T p s max t p T ( t ) = max t p s ( t ) ( 16 ) ##EQU00014##
[0072] The potential benefit of using a periodic pulse wave over a
single frequency time harmonic wave is also demonstrated, where
less input power from a periodic pulse wave source gives the same
maximum instantaneous dissipated power that can be transformed to
equal thermal shock for fracturing purposes.
[0073] This proposed technique is potentially both more
environmentally friendly than conventional hydraulic fracturing and
less expensive. However, this invention can potentially be combined
with standard hydraulic fracturing techniques to improve the
process. The performance can be evaluated and dynamically tracked
through a micro-seismic monitoring system installed nearby.
[0074] As will be clear from the above, those skilled in the art
would be readily able to determine obvious variants capable of
providing the described functionality, and all such variants and
functional equivalents are intended to fall within the scope of the
present invention.
[0075] Specific examples have been described herein for purposes of
illustration. These are only examples. The technology provided
herein can be applied to contexts other than the exemplary contexts
described above. Many alterations, modifications, additions,
omissions and permutations are possible within the practice of this
invention. This invention includes variations on described
embodiments that would be apparent to the skilled person, including
variations obtained by: replacing features, elements and/or acts
with equivalent features, elements and/or acts; mixing and matching
of features, elements and/or acts from different embodiments;
combining features, elements and/or acts from embodiments as
described herein with features, elements and/or acts of other
technology; and/or omitting combining features, elements and/or
acts from described embodiments.
[0076] The foregoing is considered as illustrative only of the
principles of the invention. The scope of the claims should not be
limited by the exemplary embodiments set forth in the foregoing,
but should be given the broadest interpretation consistent with the
specification as a whole.
[0077] It should be understood that every maximum numerical
limitation given throughout this specification includes every lower
numerical limitation, as if such lower numerical limitations were
expressly written herein. Every minimum numerical limitation given
throughout this specification will include every higher numerical
limitation, as if such higher numerical limitations were expressly
written herein. Every numerical range given throughout this
specification will include every narrower numerical range that
falls within such broader numerical range, as if such narrower
numerical ranges were all expressly written herein.
[0078] The dimensions and values disclosed herein are not to be
understood as being strictly limited to the exact numerical values
recited. Instead, unless otherwise specified, each such dimension
is intended to mean both the recited value and a functionally
equivalent range surrounding that value. For example, a dimension
disclosed as "20 mm" is intended to mean "about 20 mm."
[0079] Every document cited herein, including any cross referenced
or related patent or application, is hereby incorporated herein by
reference in its entirety unless expressly excluded or otherwise
limited. The citation of any document is not an admission that it
is prior art with respect to any invention disclosed or claimed
herein or that it alone, or in any combination with any other
reference or references, teaches, suggests or discloses any such
invention. Further, to the extent that any meaning or definition of
a term in this document conflicts with any meaning or definition of
the same term in a document incorporated by reference, the meaning
or definition assigned to that term in this document shall
govern.
[0080] While particular embodiments of the present invention have
been illustrated and described, it would be obvious to those
skilled in the art that various other changes and modifications can
be made without departing from the spirit and scope of the
invention. It is therefore intended to cover in the appended claims
all such changes and modifications that are within the scope of
this invention.
* * * * *