U.S. patent number 10,385,670 [Application Number 15/222,426] was granted by the patent office on 2019-08-20 for completions index analysis.
This patent grant is currently assigned to EOG RESOURCES, INC.. The grantee listed for this patent is EOG RESOURCES, INC.. Invention is credited to Oscar A. Bustos, Evan Daniel Gilmore, Christopher Michael James, Eric Robert Matus.
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United States Patent |
10,385,670 |
James , et al. |
August 20, 2019 |
Completions index analysis
Abstract
A method for determining a hydrocarbon-bearing reservoir quality
prior to a hydraulic fracture treatment based on completions index
is disclosed. The method comprises a step performing a test
determining a hydraulic pressure at which a hydrocarbon-bearing
reservoir will begin to fracture by pumping a fluid in a wellbore,
wherein the wellbore extends from a surface to the reservoir and
the wellbore has one or more perforations in communication with
reservoir; a step generating a pressure transient in the wellbore,
the pressure transient travels from the surface to the reservoir
through the perforations and reflects back the surface after
contacting the reservoir; a step measuring response of the pressure
transient at sufficiently high sampling frequency; a step
determining fracture hydraulic parameters of the perforations and
the reservoir using the measured response; and optimizing a
stimulation treatment to the reservoir based on the determined
fracture hydraulic parameters.
Inventors: |
James; Christopher Michael (San
Antonio, TX), Bustos; Oscar A. (San Antonio, TX),
Gilmore; Evan Daniel (Forth Worth, TX), Matus; Eric
Robert (Midland, TX) |
Applicant: |
Name |
City |
State |
Country |
Type |
EOG RESOURCES, INC. |
Houston |
TX |
US |
|
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Assignee: |
EOG RESOURCES, INC. (Houston,
TX)
|
Family
ID: |
57276682 |
Appl.
No.: |
15/222,426 |
Filed: |
July 28, 2016 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20160333684 A1 |
Nov 17, 2016 |
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Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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14526288 |
Oct 28, 2014 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
E21B
43/26 (20130101); E21B 49/008 (20130101) |
Current International
Class: |
E21B
43/26 (20060101); E21B 49/00 (20060101) |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Terry O. Anderson et al., A Study of Induced Fracturing Using an
Instrumental Approach, Journal of Petroleum Tecnology, pp. 261-267
(1967). cited by applicant .
Mohamed S. Ghidaoui et al., A Review of Water Hammer Theory and
Practice, Applied Mechanics. vol. 58, pp. 49-76 (2005). cited by
applicant .
Tadeusz W. Patzek et al., Lossy Transmission Line Model of
Hydrofractured Well Dynamics, Journal of Petroleum Science and
Engineering, vol. 25, pp. 59-77 (2000). cited by applicant .
International Search Report & Written Opinion,
PCT/US2015/048714, dated Jan. 19, 2016. cited by applicant .
International Preliminary Search Report (IPRP) PCT/US2015/48714
dated Nov. 23, 2016. cited by applicant.
|
Primary Examiner: Seo; Justin
Assistant Examiner: Royston; John M
Attorney, Agent or Firm: Winston & Strawn LLP
Parent Case Text
CROSS-REFERENCE TO RELATED APPLICATION
This application is a continuation-in-part of U.S. Nonprovisional
application Ser. No. 14/526,288, filed Oct. 28, 2014, the entirety
of which is herein incorporated by reference.
Claims
What is claimed is:
1. A method for determining a hydrocarbon-bearing reservoir quality
comprising: performing a test determining a hydraulic pressure at
which a hydrocarbon-bearing reservoir will begin to fracture by
pumping a fluid in a wellbore, wherein the wellbore extends from a
surface to the reservoir and the wellbore has one or more
perforations in communication with the reservoir; generating a
pressure transient in the wellbore, the pressure transient
traveling from the surface to the reservoir through the
perforations and reflecting back to the surface after contacting
the reservoir; measuring the response of the pressure transient at
a sampling frequency, wherein the measured response includes
pressure measurement over a period of time; and determining a
hydraulic parameter of the perforations, wherein the step of
determining a hydraulic parameter of the perforations includes
transforming the measured response to produce a transformed
response, wherein the step of transforming includes providing a
window having a time duration that is shorter than the period of
time in the measured response, applying the window to the measured
response to encompass a portion of the measured response, and
determining maximum and minimum pressure in the measured response
encompassed by the window, and; calculating rate of decay of the
transformed response.
2. The method of claim 1, wherein the step of transforming the
measured response further comprises calculating the difference
between the maximum pressure and the minimum pressure.
3. The method of claim 2, wherein the difference is produced as
part of the transformed response.
4. The method of claim 1, wherein the time duration of the window
is 1 second.
5. The method of claim 1, the step of transforming the measured
response further comprises sliding the window over the measured
response at an increment of time to transform the entire measured
response.
6. The method of claim 5, wherein the step of transforming the
measured response further comprises determining maximum and minimum
pressure in the portion encompassed by the window for each
increment of time.
7. The method of claim 6, wherein the step of transforming the
measured response further comprises calculating the difference
between the maximum pressure and the minimum pressure in the
portion encompassed by the window for each increment of time.
8. The method of claim 7, wherein the differences are produced as
part of the transformed response.
9. The method of claim 5, wherein the increment of time is 0.01
second.
10. The method of claim 1, wherein the step of calculating rate of
decay of the transformed response comprises finding peaks of the
transformed response and fitting an exponential decay to the
peaks.
11. The method of claim 1, wherein the method further comprises
calculating a reflection half-life from the rate of decay.
12. The method of claim 11, wherein the method further comprises
correlating the reflection half-life to a modeled hydraulic
resistance.
13. The method of claim 12, wherein the modeled hydraulic
resistance is obtained from adjusting an element of an electrical
model representing the wellbore over a range of values.
14. The method of claim 13, wherein the element is a resistor.
15. The method of claim 1, wherein the measured response provides
pressure information over a period of time and the transformed
response provides pressure information different from the pressure
information provided by the measured response over the same period
of time.
16. The method of claim 15, wherein the pressure information
provided by the transformed response includes a plurality of peaks
and the rate of decay is calculated based on the peaks.
17. The method of claim 1, wherein the hydraulic parameter is flow
resistance.
18. The method of claim 1, wherein the sampling frequency is more
than 2 Hz.
19. The method of claim 1, the step of transforming the measured
response further comprises applying the window to the measured
response at an increment of time to encompass a next portion of the
measured response.
20. The method of claim 19, wherein the step of transforming the
measured response further comprises determining maximum and minimum
pressure in the next portion of the measured response encompassed
by the window.
Description
FIELD OF THE INVENTION
The present invention relates to a method for determining a
hydrocarbon-bearing reservoir quality, and in particular, to a
method for determining a hydrocarbon-bearing reservoir quality
prior to a hydraulic fracture treatment based on a completions
index.
BACKGROUND OF THE INVENTION
Hydraulic fracturing is a technique of fracturing rock formations
by a pressurized fluid in order to extract oil and natural gas
contained in the formations. A fluid, which usually is water mixed
with sand and chemicals, is injected into a wellbore under
considerable pressure to create fractures in the formations. When
the pressure is removed from the wellbore, the sand props the
fractures open allowing the oil and gas contained in the formations
to more readily flow into the well for extraction. This technique
has revolutionized oil and gas development, especially is shale
formations, because it permits extraction of formerly inaccessible
hydrocarbons. As a result, it has helped push U.S. oil production
to a new high and generate billions of revenues to mineral rights
owners, oil companies, as well federal, state, and local
governments.
Hydraulic fracturing, however, can be a very expensive process,
especially if the quality of the formations is unknown, in a
horizontally drilled oil well, hydraulic fracturing generally is
performed in several stages along the horizontal portion of the
well. Typically, the horizontal portion of the well is stimulated
in stages about every 200 to 250 feet. Although the horizontal
portion of the well generally extends through a given hydrocarbon
hearing formation, the lithology or rock quality may vary along the
length of the wellbore. When oil companies conduct a frac treatment
at a section of the formations that is sub-optimal, the stimulation
may be ineffective or produce marginal gains in productivity for
that particular stage. Assuming that the average cost for each
hydraulic fracture treatment is approximately $100,000 and that
some formations may have up to 80% of its sections be sub-optimal,
the cost and time spent in fracturing sub-optimal sections or in
determining whether to move onto another section can be
substantial. In one year, an energy consulting company estimated
that about $31 billion was spent in sub-optimal fracturing across
26,100 U.S. oil wells.
Moreover, even if the oil drilling companies treat a section of the
formation that happens to be optimal, the treatments may not have
been the optimal size. In other words, the treatment may have been
too small given the favorable rock qualities that existed for that
particular stage and that the well could have been even more
productive and the return on the investment of the stimulation
could have been even higher had a larger stimulation been pumped,
or had a different stimulation fluid or amount of proppant been
pumped. As such, knowing the quality of the formations prior to a
hydraulic fracture treatment is beneficial to stimulation
treatments.
A method called Distributed Fiber Optic Sensing has been developed
to provide this information. This method is based on either
temperature or acoustic sensing. In the method based on temperature
sensing, a unit including a laser source and a photodetector is
placed on the surface and a glass fiber is permanently installed in
the well. The laser source sends laser pulses down the glass fiber
and the temperature of the formations can affect the glass fiber
and locally change the characteristics of light transmission in the
glass fiber. The photodetector measures the laser light reflections
from different spots in the glass fiber due to the temperature and
the spectrum of the laser light reflections can used to determine
the properties of the formations. The method based on acoustic
sensing is similar to the temperature sensing one except that this
method employs a unit that includes an acoustic signal generator
and an acoustic signal receiver and that this method measures the
reflected acoustic signals based on the strain or pressure of the
formations exerted on and along various points of the glass fiber.
The measured acoustic signals may have various amplitude,
frequency, and phase attributes that can also be used to determine
the properties of the formations.
The Distributed Fiber Optic Sensing method, however, has several
drawbacks. First, this method requires running a glass fiber into
the well that complicates the installation process. Second, this
method usually costs around $600,000 to implement and the
investment is only for one single well and is permanent. Third,
this method is not economically practical on smaller reservoir
wells. Fourth, to protect the fragile glass fiber, the glass fiber
is typically placed within a stainless steel sheath that can
attenuate the temperature or strain response, reducing accuracy of
the measurement.
Accordingly, there is a need for an improved method for determining
the quality of the rock formations prior to a hydraulic fracture
treatment.
SUMMARY
In accordance with one embodiment of the present invention, a
method for determining a hydrocarbon-bearing reservoir quality is
described. The method may comprise performing a test determining a
hydraulic pressure at which a hydrocarbon-bearing reservoir will
begin to fracture by pumping a fluid in a wellbore, wherein the
wellbore extends from a surface to the reservoir and the wellbore
has one or more perforations in communication with the reservoir;
generating a pressure transient in the wellbore, the pressure
transient traveling from the surface to the reservoir through the
perforations and reflecting back to the surface after contacting
the reservoir; measuring the response of the pressure transient at
a sufficiently high sampling frequency; and determining a hydraulic
parameter of the perforations by transforming the measured response
to produce a transformed response and calculating rate of decay of
the transformed response.
In a preferred embodiment, the step of transforming the measured
response may comprise generating a window defining a period of time
over the measured response. This step may also comprise determining
maximum and minimum pressure in the period of time defined by the
window. This step may further comprise calculating the difference
between the maximum pressure and the minimum pressure. The
difference may be produced as part of the transformed response. The
window may define a period of 1 second. Moreover, this step may
comprise sliding the window over the measured response at an
increment of time to transform the entire measured response.
In a preferred embodiment, the step of transforming the measured
response may comprise determining maximum and minimum pressure in
the period of time defined by the window for each increment of
time. This step may also comprise calculating the difference
between the maximum pressure and the minimum pressure for each
increment of time. The differences may be produced as part of the
transformed response. The increment of time may be 0.01 second.
In a preferred embodiment, the step of calculating rate of decay of
the transformed response may comprise finding peaks of the
transformed response and fitting an exponential decay to the
peaks.
In a preferred embodiment, the method may further comprise
calculating a reflection half-life from the rate of decay. The
reflection half-life may be correlated to a modeled hydraulic
resistance. The modeled hydraulic resistance may be obtained from
adjusting an element of an electrical model representing the
wellbore over a range of values. The element may be a resistor.
In a preferred embodiment, the measured response may provide
pressure information over a period of time and the transformed
response may provide pressure information different from the
pressure information provided by the measured response over the
same period of time. The pressure information provided by the
transformed response may include a plurality of peaks and the rate
of decay is calculated based on the peaks.
In a preferred embodiment, the hydraulic parameter may be flow
resistance.
In a preferred embodiment, the sufficiently high sampling frequency
may be more than 2 Hz.
BRIEF DESCRIPTION OF THE DRAWINGS
For the purposes of illustrating the present invention, there is
shown in the drawings a form which is presently preferred, it being
understood however, that the invention is not limited to the
precise form shown by the drawing in which;
FIG. 1 shows one embodiment of the method for determining a
hydrocarbon-bearing reservoir quality;
FIGS. 2 and 3 show an example of a fracturing treatment having a
leak-off test performed at the beginning of the fracturing
treatment, an initial water hammering effect of the leak-off test,
and a final water hammering effect after the fracturing
treatment;
FIG. 4 is a closer or detailed view of the leak-off test shown in
FIGS. 2 and 3;
FIG. 5 shows an example of measured pressure transient
response;
FIG. 6 shows an example of multiple pressure transients generated
during the pressure decline of the leakoff test;
FIG. 7 shows that the measured pressure transient response can
identify a hydrocarbon-bearing reservoir quality;
FIG. 8 shows at the measured pressure transient response can
determine if there is a hole in the casing;
FIG. 9 shows a small section of an equivalent per unit length
electrical model of a hydraulic wellbore/fracture system;
FIG. 10 shows matching between an electrical model response and an
actual measured response for two different stages;
FIG. 11 shows the comparison of high Efficiency Coefficient and low
Efficiency Coefficient;
FIG. 12 shows the comparison of high completions index and low
completions index.
FIG. 13 shows the slope ratio variable for calculating the
completions index and the correlation developed between slope
ratios, initial slope and stage depth;
FIG. 14 shows how the completions index changes throughout a
fracturing treatment;
FIG. 15 shows changes in Efficiency Coefficient and completions
index from initial water hammering to final water hammering;
FIGS. 16A-16D show an example measured pressure transient response
being transformed into a response having different pressure
data;
FIG. 17 shows the graphical representations of the measured
pressure transient response, the transformed response, and the
decay curve of the transformed response; and
FIG. 18 shows an example correlation between reflection half-life
and a modeled hydraulic resistance.
DETAILED DESCRIPTION OF THE INVENTION
Referring to FIG. 1, one embodiment of the method for determining a
hydrocarbon-bearing reservoir quality 100 is illustrated. The
method 100 comprises steps of performing a test determining a
hydraulic pressure at which the reservoir will begin to fracture
110, generating a pressure transient during the test 120, measuring
response of the pressure transient 130, determining fracture
hydraulic parameters using the measured response 140, and
optimizing a stimulation treatment to the hydrocarbon-bearing
reservoir based on the determined fracture hydraulic parameters
150.
The step of performing a test determining a hydraulic pressure at
which the reservoir will begin to fracture, or a leak-off test, 110
involves pumping a fluid, for example a hydraulic fracturing fluid,
into a wellbore using a pressure pumping equipment. The wellbore
extends from a surface to a reservoir and has one or more
perforations extending through the production casing in
communication with the reservoir. The pressure pumping equipment
may be any equipment that is capable of pumping the fracturing
fluid at a pressure into the wellbore. In addition to determining
the hydraulic pressure at which the reservoir will begin to
fracture, the leak-off test can also determine if the perforations
are sufficiently open to establish communication with the
reservoir. From the leak-off test, the ball seating pressure, the
fracturing gradient (FG) of the formation, and the fracture closure
time can be determined. A leak-off test is illustrated in FIGS. 2
and 3.
FIGS. 2 and 3 show an example of a fracturing treatment having a
leak-off test performed at the beginning of the fracturing
treatment, an initial water hammering effect of the leak-off test,
and a final water hammering effect after the fracturing treatment.
Referring to FIG. 2, the fracturing treatment in which the leak-off
test is performed has a duration of approximately three hours from
start to finish. FIG. 3 is a breakdown of FIG. 2 that shows the
treatment rate (the top graph), the treatment pressure (the middle
graph), and the proppant concentration (the bottom graph) of the
fracturing treatment. The treatment rate in this example is
approximately 32 barrels per minute between about 0.45 hour and
3.15 hour. The treating pressure is between 2,000 and 3,000 PSI
from about 0.45 hour to 3.15 hour. The proppant concentration is
between 0.5 and 1 pound per gallon (PPA) from about 0.6 hour to 0.9
hour, and between 1.5 and 2 PPA from about 0.9 hour to 3 hour. The
leak-off test is labeled as the "acid and leak-off test" in FIG. 2
or the graph prior to the "rise" or "step" at approximately 0.45
hour in the treatment rate and the treatment pressure graphs. The
leak-off test is initiated and concluded within approximately 30
minutes, or at about 0.5 hour, from the start of the fracturing
treatment. After the leak-off test, and for the remaining two and
half hours, water with chemicals is pumping into the wellbore and
proppant is slowly added into the water to inject the stimulation
fluid into the fractures in the reservoir.
Near the end of the leak-off test, a response or water hammering
effect can be measured by generating a pressure transient and
monitoring how the pressure transient declines with time. The very
first 15 to 30 seconds after generating the pressure transient
shows a lot of noise when the pressure transient is measured under
low sampling frequency, such as 1 Hz, and that is the water
hammering effect of the pressure transient. The pressure transient
propagates to the perforations, reflects back to the surface, and
travels in this manner back and forth until it attenuates
completely. This response is shown as the initial water hammering
graph in FIGS. 2 and 3. The same response may also be measured at
the end of the fracturing treatment and is shown as the final water
hammering graph in the same figures. The final water hammering
graph shows more response or bounces because the fractures in the
reservoir have been opened.
FIG. 4 is a closer or detailed view of the leak-off test shown in
FIGS. 2 and 3. When the water hammering effect is measured at
sufficiently high sampling frequency, such as sampling frequencies
higher than 2 Hz up to 500 Hz, more water hammering effect can be
seen from the measurement as shown in the plot labeled as "Water
Hammering." The shape of the water hammering effect signal is
directly depending upon the type of rock in the reservoir in
communication with the perforations and is an indication of the
rock quality. Therefore, when the water hammering effect signal is
showing a good shape, i.e., more fluctuations and slower
attenuation, the oil company can pump in more stimulation fluid in
that stage to extract more oil and gas. If the water hammering
effect is showing a had signal, i.e., less fluctuations and faster
attenuation, the oil company can skip that stage or reduce the
treatment size for that stage saving thousands of dollars in
fracturing treatment and move onto the next stage. As such, the
present invention provides real-time knowledge about the rock
quality that can vary in each stimulation treatment stage of
horizontal wellbores before the stimulation treatment is performed.
By understanding the water hammering effect signal in each stage,
oil companies can know when to pump more and when the pump less of
the stimulation treatment.
A leak off test, which is also known as mini-frac, is a pumping
sequence aimed to establish a hydraulic fracture, to understand,
among other things, what is the pressure required to propagate a
hydraulic fracture, and to estimate the minimum pressure at which
the hydraulic fracture closes. A critical component of the test is
the pressure monitoring after pumps as shut-down, which is commonly
known as leakoff period or pressure fall off. During this period,
fluid inside the open hydraulic fracture will leak off into the
formation, continues until this process reaches a point that all
fluid is leaked off and the hydraulic fracture closes. Another
component of the test is the "step rate test," whereby the rate of
fluid is gradually increased at the beginning of the test until a
fracture is established or reaches the fracturing extension
pressure and is reduced in a step down fashion at the end of the
test. This test allows engineers to calculate the total pressure
loss in between the rate steps so that the total number of
perforations hydraulically connected to the fracture can be
calculated. After the pumps are shut down, pressure is monitored
for some time to determine fracture hydraulic parameters such as
fracture closure pressure, presence of natural fractures, and
leakoff coefficient for the fluid. Pressure may be monitored from
several minutes to several hours and the fracture hydraulic
parameters may be determined by using a "G" function.
Referring back to FIG. 1, the step of generating a pressure
transient 120, the pressure transient is preferably generated by
stopping or substantially reducing the pump rate of the pressure
pumping equipment. But optionally, the pressure transient can be
introduced by other methods that generate a pressure wave from the
change of the inertia of the fluid, such as rapidly opening and
closing a valve on the injection well head, or by other devices,
such as a pressure oscillator or a mechanical shutter. The pressure
transient travels from the surface to the reservoir through the
perforations and reflects back to the surface after contacting the
reservoir at the speed of sound in the wellbore fluid (normally
water). Preferably, the pressure transient is generated within the
first 15 to 30 seconds of the test determining a hydraulic pressure
at which the reservoir will begin to fracture. After the pressure
transient attenuates, additional pressure transients can be
generated if desired (during the leak off test).
The response of the pressure transient, or the reflected pressure
transient, is measured at sufficiently high sampling frequency such
as at least 5 Hz. Alternatively, sample frequencies higher than 2
Hz up to 500 Hz may be used. The response is measured by a pressure
transducer. An example of the measured response in high sampling
frequency is shown in FIG. 5. The measured response is presented in
a pressure-time plot. This measured response is also known as the
water hammering effect. The y-axis is the pressure in pounds per
square inch (PSI) and the x-axis is the time in minutes. The
rounded dot represents the number of bounces from the surface. "t"
represents the travel time of the pressure transient in sonic speed
from the surface to the reservoir and then back to the surface
through the wellbore fluid, which is the time between a peak and a
trough on the plot. Such information can also be used to determine
the distance of the perforations from the surface since the time
between bounces is directly related to the distance to the
perforations. A1 represents the initial decreasing amplitude of the
waveform and A2 represents the next decreasing amplitude. A1
generally has a larger amplitude than A2. Based on A1 and A2, the
initial rate of decay, or Efficiency Coefficient (EC), can be
calculated by the following equation: EC= {square root over
(A2/A1)}
Although FIG. 5 shows that A1 and A2 are the preferred amplitudes,
any two successive decreasing amplitudes may also be used. With the
measured response in FIG. 5, fracture hydraulic parameters such as
fracture closure pressure, fracture closure time, presence of
natural fractures, and resistance of the perforations can be
determined. Additionally, the shape of the waveform, which is
determined by the combination of t, amplitudes, slopes on the
waveform from the ISP (Instantaneous Shut-in Pressure) up to the A2
amplitude, can be used to calculate the fracture capacitance of the
reservoir. While FIG. 5 shows only one pressure transient response,
multiple pressure transients can be generated in each stimulation
stage to obtain multiple responses for determining closure of the
fractures in the reservoir. This determination is based on the
comparison of the multiple responses with each other or the
comparison of the most recently obtained response (or the most
recently obtained flow resistance and fracture capacitance, which
are described below) with a prior obtained response (or prior
obtained flow resistance and fracturing capacitance). FIG. 6 shows
an example of thirteen (13) pressure transients generated during
the pressure decline of the leakoff test. The closure of the
fractures can be observed from the reduction of the Efficiency
Coefficient of each pressure transient versus time (or until the
Efficiency Coefficient and fracture capacitance of each pressure
transient no longer change with time). The figure shows responses
measured at 1 Hz and 250 Hz sampling frequencies. Responses showing
inconspicuous fluctuations correspond to measurement at 1 Hz
sampling frequency and responses showing pronounced fluctuations
correspond to measurement at 250 Hz sampling frequency.
The measured response can identify reservoir quality. Measured
responses show significant differences for different reservoirs or
rocks having similar wellbores (for example, multiple wells in a
given field), as the pressure transient travels outside the
wellbore through the perforations of the wellbore and into the
adjacent formation/rocks. If the transient pressure did not travel
outside the wellbore, the expected responses would be similar for
comparable wellbores. This also proves that the perforations are
open and in communication with the formation. This identification
ability is shown in FIG. 7. On the left of FIG. 7, a siliceous rich
mud rock (shale), which has a lower Young's modulus and a lower
fracturing gradient, produces a lot of fluctuations or hammering
(higher capacitance). On the right of FIG. 7, a carbonate rich mud
rock (shale), which has a higher Young's modulus and a higher
fracturing gradient, produces a lot less hammering (lower
capacitance Thus, based the amount of hammering, one can obtain an
initial impression of whether the rocks are prone to simple or
complex fracturing.
The measured response can also be used to determine if there is a
hole in the casing. Referring to FIG. 8, two wells A and B are
plotted. Well A is represented by lighter-colored dots whereas Well
B is represented by darker-colored dots. Well A has a casing
without any holes and its plot shows a pattern close to a linear
line for the various stages where pressure transients were
measured. The slope m of the linear line may be determined by the
following equation:
.DELTA..function..times..times..times..times..DELTA..times..times.
##EQU00001##
MD top perforation is the measured depth to the top perforation.
The slope m is measuring the change in measured distance to the top
perforation for successive stages in the well divided by the change
in time. The slope m may also be determined by dividing the speed
of sound C by 2.
Well B, on the other hand, has a casing with a hole and its dots
spread everywhere on the chart without a general pattern. Based on
the measured response, it was confirmed by a downhole camera ran on
this well that a hole was located in the casing at a measured depth
of 6987 feet.
For every hydraulic wellbore/fracture model, there is an equivalent
electrical model. The wellbore or casing may be modeled as a lossy
transmission line using resistors, capacitors, and inductors. The
values of all these electrical components are known if one knows
the depth of the well, the size of the casing, and the temperature
and type of the fluid used in the well. Some or all of these values
may be lumped into an impedance representing the electrical
property or mechanical property of the wellbore. The generated
pressure transient inside the casing may be modeled as an input
voltage on the transmission line. The perforations of the casing,
which provide communication to the reservoir, may be modeled as a
resistor. If the perforations are small, the resistance is high and
vice versa. The reservoir itself or the quality of the reservoir
may be modeled as a capacitor.
FIG. 9 represents a small section of an equivalent per unit length
electrical model. This small section of the electrical model
corresponds to a small section of the horizontal portion of the
wellbore. This small section of the electrical model is divided
into three (3) nodes ((x-1), (x), and (x+1)) and each node is
associated with a stub that is spaced along the horizontal portion
of the wellbore for example, every 30 feet. The stub associated
with each node is used to represent an area of the reservoir and
any changes in casing properties, otherwise the impedance of the
stub, Zs, is set sufficiently high such that no current flows into
the stub. A simulated response similar to the actual measured
response can be obtained from each node by generating an input
voltage, or simulated pressure transient, to the electrical model
or circuit. A stub modeling a fracture, for instance, Zs(x+1) and
Rs(x+1), represents fracture capacitance Zs(x+1) and flow
resistance Rs(x+1). Each impedance, Zs(x-1), Zs(x), Zs(x+1),
Z(x-1), Z(x), or Z(x+1), has an inductive component and a
capacitive component and they are configured to be the equivalent
circuit of a transmission line (not shown). While fracture
capacitance appears to be impedance, or Zs, in the figure, the
value of the impedance is essentially capacitance. When the
electrical model in FIG. 9 is simulated, the inductive component of
Zs is treated as if it has little to no inductance, and therefore,
the impedance becomes a capacitor representing an area of the
reservoir or the fractures in that area of the reservoir. In other
words, the electrical model by default presents or sees an area of
the reservoir or the fractures in that area of the reservoir as
impedance but the value of the impedance is simulated to be based
on a capacitor. Although this figure shows only three nodes, there
can be more nodes as this figure represents only a small section of
the electrical model or the horizontal portion of the wellbore. The
distance between two adjacent nodes typically can range from 10 to
250 feet. Other ranges are also possible depending on the scale of
the hydraulic wellbore system.
R(x-1), Z(x-1), and R(x) (and R(x), Z(x), and R(x+1), etc) are
lumped impedance representative of a transmission line (Z(x-1)) and
resistance (R(x-1) and R(x)) values and they represent a lateral
portion of the casing connecting adjacent nodes or adjacent areas
of the reservoir. All these values are fixed and can be determined
based on the depth of the well, the size of the casing, and the
fluid in the casing.
Therefore, by using an equivalent electrical model, one can obtain
a simulated response similar to the actual measured response for
each stage of the horizontal portion of the wellbore. A simulated
response can be created to match the actual measured response by
adjusting the resistor in the stub and the capacitor of the
impedance component in the stub or by solving their resistance and
capacitance through numerical optimization. Once the simulated
response matches to the actual measured response, the obtained
resistance is known as the flow resistance and the obtained
capacitance is known as the fracture capacitance. FIG. 10 shows
such matching for two different stages. At stage X, the simulated
response (the top graph) matches to the actual measured response
(the bottom graph) when the resistance is 33 ohm and the
capacitance is 0.1 farad. At stage Y, the simulated response
matches to the actual measured response when the resistance is 18
ohm and the capacitance is 1 farad.
Thus, by using an electrical model, simulated responses with their
associated flow resistances and fracture capacitances can be
obtained for previous actual fracture stimulation operations,
future actual stimulation operations, and any other stimulation
operations that one may encounter since the information regarding
the well, the casing, and the fluid are already known, will be
known, or can be predicted in advance. All these simulated
responses, flow resistances, and fracture capacitances may be saved
in a database or lookup table for comparison with future
stimulation operations. In one embodiment, the comparison may be
performed by adjusting the resistor in the electrical model first
to determine the flow resistance and then adjusting the capacitor
to determine the fracture capacitance. Therefore, it is possible to
model every expected response and different combination of depth,
fracture flow resistance, fracture capacitance, and response at the
surface in terms of the pressure transient that is generated at the
surface for a given field. The benefit is that hydraulic properties
of the fracture system of the reservoir can be inferred by just
looking at the pressure responses observed at the surface during
the water hammering. The model allows one to infer the flow
resistance and the hydraulic capacitance of the fracture based on
the pressure response measured at the surface. In other words, if
the comparison shows a match, the flow resistance and fracture
capacitance of the actual fracture stimulation operation can be
obtained from the flow resistance and fracture capacitance of the
matched simulated response. With this lookup table, one does not
need to manually change the resistance and capacitance in the
electrical model for matching its simulated response to every
measured response. The benefit of having the lookup table or
database allows an operator to calculate these parameters very
quickly. The operator can get the transient response from the
initial injection or leak off test before the primary stimulation
of every stage in a horizontal wellbore, thereby providing the
operator valuable information needed on a near real time basis to
optimize each particular stage before pumping any proppant.
The flow resistance can also be approximated by the Efficiency
Coefficient. The Efficiency Coefficient is determined by how fast
the measured response decays (i.e., the initial rate of decay) and
the number of bounces the measured response contains. These
determining factors are directly related to the near wellbore flow
resistance or the flow through the perforations. High Efficiency
Coefficient means that the perforations are open and have less
resistance, and low Efficiency Coefficient means that the
perforations are narrow and have more resistance or that there is a
tortuous path connecting the wellbore with the hydraulic fracture.
This is shown in FIG. 11.
The fracture capacitance is also known as the completions index.
This value is directly related to the slope (darkened line) of the
simulated response as shown in FIG. 12, and it indicates whether
the reservoir is a compliant or non-compliant system. Referring to
FIG. 12, a positive slope is considered as high index and it
indicates that the reservoir is a compliant system. A negative
slope is considered as low index and it indicates that the
reservoir is a non-compliant system. A compliant or non-compliant
system provides information regarding how rigid the reservoir is. A
compliant system means that the reservoir is less rigid (presence
of natural fractures), the volume of a bounded fluid would expand
rapidly with increase in pressure and contact more surface area
inside the reservoir. A non-compliant system means that the
reservoir is more rigid, the volume of a bounded fluid would remain
relatively static with increase in pressure and contact less area
inside the reservoir. Generally, a rock showing a compliant system
is considered as good rock quality and is more ideal for a
stimulation treatment. Conversely, a rocking showing a
non-compliant system is considered as lower rock quality and is
less ideal for a stimulation treatment. As such, when one obtains
the completions index, or the value of the capacitance in the
simulated response, quality information of the reservoir is also
obtained.
In addition to obtaining the fracture capacitance by comparing the
simulated responses to the measured response in the manner
discussed above, one can also obtain the fracture capacitance
through numerical optimization. One way of performing numerical
optimization is via a neural network. In this invention, the neural
network is a computational model configured to receive four
variables extracted from the measured response, compares those
variables to the same variables in the simulated responses, and
calculates the completions index if the comparison matches. These
four variables are the depth of the stimulation stage, the
Efficiency Coefficient, the slope ratio, which is m1/m2 as shown in
FIG. 13, and the initial pressure drop in the test of determining a
hydraulic pressure at which the reservoir will begin to fracture.
FIG. 13 also shows the correlation developed between slope ratios,
the initial slope, and the stage depth. The neural network compares
the variables and calculates the completions index based on
training weights obtained from simulations and previous
measurements (optimizing a numerical model to match the measured
response). During this optimization, the Efficiency Coefficient and
the completions index are optimized together or simultaneously. The
optimization of the Efficiency Coefficient simultaneously optimizes
the completions index and vice versa. The neural network may also
be utilized to determine the fracture capacitance by interpolation.
The employment of a neural network provides speedy comparison and
calculation of the completions index.
Another way of performing numerical optimization to obtain the
fracture capacitance is via, numerical simulation of the electrical
model in FIG. 9. One can use numerical optimization to match the
electrical model output to find a best fit to the measured field
data. Using the equivalent per unit length electrical model shown
in FIG. 9, one can determine the correct flow resistance and
completions index in order to match the observed field response.
These values are found through a process of numerical optimization,
wherein a numerical simulator solves many iterations of the
electrical model output with varying flow resistance and
completions index values. Each iteration is assigned a fitness or a
numerical value corresponding to the quality of the match to the
measured field response. The numerical simulator then outputs the
values of the flow resistance and completion index with the best
fitness values. Like the numerical optimization based on a neural
network, the flow resistance and fracture capacitance are also
optimized together or simultaneously. The optimization of the flow
resistance simultaneously optimizes the fracture capacitance and
vice versa.
Therefore, referring to the step of determining fracture hydraulic
parameters using the measured response 140 in FIG. 1, one can
determine flow resistance and fracture capacitance by either
comparing the simulated response to the measured response with help
from a lookup table or employing numerical optimization. Based on
the determined flow resistance and fracture capacitance, one can
optimize a stimulation treatment to the reservoir 150. The
stimulation treatment may be a hydraulic fracturing treatment. The
optimization of the stimulation treatment may be adjusting the
volume, properties or rate (i.e., number of barrels per minute) of
the fracturing fluid is required to fracture the reservoir,
adjusting the volume, size or type of proppant carried by the
fracturing fluid, or omitting a hydraulic fracturing treatment
altogether for a given stage.
FIG. 14 shows how the completions index changes throughout a
fracturing treatment. In this example, the fracturing treatment is
divided into three phases instead of one single continuous
fracturing treatment to better observe capacitance change and to
adjust stimulation fluid accordingly. Before any treatment is
performed, the reservoir initially has a completions index of 0.03.
After the first phase of the fracturing treatment is performed by
pumping stimulation fluid with 92,000 lbs. of sand and the pumping
is shut down, which corresponds to the step of the pressure
waveform to the left most of the plot, the completions index or
capacitance rises quickly to 0.087. This change in capacitance is
an indication of the rock quality and can be used to optimize the
fracturing treatment for a particular stage. The subsequent phases
of the fracturing treatment show that increasing the amount of
proppant yields minor increase in capacitance. As such, an operator
knows how rigid the rock is and the optimal amount of proppant to
fracture the rock in this particular stage. Based on this figure,
the operator may not want to add any more proppant into the fluid
after the second phase or after the third phase since the
completions index would not change much and the cost of fracturing
treatment can be reduced. By analyzing the completions index to
determine reservoir quality, the method is also known as
Completions Index Analysis.
While FIG. 14 shows that the method of the present invention is
conducted during a fracturing treatment, the method may also be
performed after the fracturing treatment to provide indications on
the quality of the fracturing treatment just performed.
Based on the foregoing, using the measured responses from the water
hammering effect allows an operator to see the variations in the
rock quality so one can recognize the good pan of the lateral
(i.e., horizontal wellbore) and what is the poor part of the
lateral. Knowing this information, the operator can make near real
time decisions to optimize the stimulation treatments of the
various stages of a wellbore. Thus, an operator can determine which
sections of the wellbore may justify an even larger treatment than
was originally planned and which sections could be omitted, thereby
reducing the overall cost of the treatment and/or improving the
effectiveness of the treatment.
FIG. 15 shows a comparison of the initial water hammering effect
and the final water hammering effect for a stimulation stage based
on the Efficiency Coefficient and the completions index. The
initial water hammering effect is the effect measured prior a
fracture treatment whereas the final water hammering effect is the
effect measured after the fracture treatment. Both have similar
input slopes or utilize similar pressure transients. The final
water hammering effect shows that the signal decays much slower
after the fracture treatment, which indicates that the fracturing
fluid and the perforations have a better connection to the
reservoir. The fracture treatment has eroded the tortuous path of
the fractures and it becomes easier to establish a communication
from the wellbore to the reservoir. As such, both the Efficiency
Coefficient and the completions index are higher after the fracture
treatment. The Efficiency Coefficient before and after the fracture
treatment are 0.814 and 0.897, respectively. The completions index
before and after the fracture treatment are 0.235 and 0.820,
respectively.
As discussed above, the flow resistance can be determined by the
rate of decay of the measured pressure transient response and the
rate of decay can be calculated from two successive decreasing
amplitudes. Alternatively, the rate of decay can be calculated by
transforming the measured pressure transient response to produce a
transformed response and calculating the rate of decay of the
transformed response. The measured pressure transient response or
simply the measured response) provides pressure information over a
period of time. The transformed response provides pressure
information different from that of the measured response over the
same period of time (e.g., different pressure behavior over the
same period of time).
In one embodiment, the measured response may be transformed by
generating a window defining a period of time over the measured
response, determining the maximum pressure and the minimum pressure
in the period of time defined by the window, calculating the
difference between the maximum pressure and the minimum pressure,
and producing the difference as a data point of the transformed
response. The window may define a period of time such as 0.5
second, 1 second, 2 seconds, or any other duration. The measured
response may have pressure data measured at a frequency. The
frequency may be 0.005, 0.008 second, 0.01 second, 0.05 second, or
any other frequency. Preferably, the window has a duration of 1
second and a frequency of 0.01 second. Within the time duration of
the window, there are a number of pressure measurements in the
measured response with each measured at the specified frequency,
and the maximum pressure and the minimum pressure are determined
from those pressure measurements. The difference between the
maximum pressure and the minimum pressure is a data point of the
transformed response, and it corresponds to the first data point of
the measured response in the window or the data point of the
measured response that is first in time in the window. The
determination of the maximum pressure and the minimum pressure and
the calculation of the difference starts from the beginning of the
measured response or 0 second. A data point refers to a measurement
at a specific time whereas data refers two or more measurements or
all the measurements collectively.
The window may slide on the measured response at an increment of
time to determine the maximum pressure and the minimum pressure in
the period of time defined by the slided window and to calculate
the difference between the maximum pressure and the minimum
pressure in the slided window. The window slides without changing
its time duration (e.g., the time duration of the window is the
same before and after sliding). The increment of time and the
frequency may be the same (e.g., 0.01 second). The determination of
the maximum pressure and the minimum pressure and the calculation
of their difference in the slided window involve the same
computations as those discussed above. The window may continue to
slide, determine the respective maximum pressure and the respective
minimum pressure, and calculate the respective difference for the
entire measured response. The differences collectively create the
transformed response with each difference being a data point of the
transformed response.
FIGS. 16A-16D show pressure data of an example measured response
1605 and pressure data of an example transformed response 1610. In
these Figures, the transformed response 1610 (or the differences)
is obtained by using a window A having a 1 second duration and by
sliding the window at an increment of 0.01 second over the measured
response 1605. The measured response 1605 had the pressure measured
at a frequency of 0.01 second. Given the length of the measured
response and the frequency/increment used, only part of the
measured response and part of the transformed response are shown
(up to 1.11 second).
The measured response 1605 includes a number of measurements with
each conducted at every 0.01 second starting from 0 second. The
transformation starts from the beginning of the measured response
and determines the maximum pressure and the minimum pressure in the
1-second duration of the window A (see FIGS. 16A and 16D). In that
window, e.g., from 0 second to 1 second defined by window A.sub.1,
the minimum pressure in the measured response 1605 is 500.6 PSI and
the maximum pressure in the measured response 1605 is 2624.2 PSI.
The difference between the two pressures is 2123.6 PSI. The
difference corresponds to the first data point in the transformed
response 1610 or the first data point (e.g., 2612.1 PSI) of the
measured response 1605 in the window A.sub.1. The transformation
then slides the window A by an increment of 0.01 second. In that
window, e.g., from 0.01 second to 1.01 second defined by window
A.sub.2, the minimum pressure in the measured response 1605 is
still 500.6 PSI and the maximum pressure in the measured response
1605 is still 2624.2 PSI. Accordingly, the difference between the
two pressures is also still 2123.6 PSI. The difference corresponds
to the second data point in the transformed response 1610 or the
first data point (e.g., 2563 PSI) of the measured response 1605 in
the window or the slided window A.sub.2.
The transformation may continue to slide the window A at the
specified increment. When the window A reaches to 0.06 second,
which covers the measured response from 0.06 second to 1.06 second
defined by window A.sub.7, the minimum pressure in the measured
response 1605 is 494.4 PSI and the maximum pressure in the measured
response 1605 is 2618.4 PSI. The difference between the two
pressures is 2124 PSI. The difference corresponds to the seventh
data point in the transformed response 1610 or the first data point
(e.g., 2618.4 PSI) of the measured response 1605 in the window or
the slided window A.sub.7. The transformation may continue to slide
the window A until the entire measured response is transformed. The
transformed response may be a response produced for the same period
of time from which the measured response is obtained (e.g., if the
measured response is obtained for 1.11 second, or from 0 to 1.11
second, then the transformed response is also obtained for that
1.11 second), but has a different pressure behavior in time (e.g.,
the response or the signal forms a different shape). The
transformed response is a new time series curve. Each measurement
in the measured response 1605 has a corresponding transformed data
point. The transformation process may be known as a rolling max-min
technique. FIG. 17 shows the graphical representations of the
measured pressure transient response 1705 and the transformed
response 1710.
Windows A.sub.1, A.sub.2, and A.sub.7 all refer to the same window
having the same duration. The subscripted number is used merely to
differentiate their positions on the measured response 1605.
The rate of decay of the transformed response 1710 is then
determined. The rate of decay is determined by finding the peaks of
the transformed response 1710 and fitting an exponential decay to
the peaks to produce a decay curve 1715, which is also shown in
FIG. 17. The exponential decay or the decay curve 1715 indicates
how quickly in time the transformed response decays. This rate of
decay is then used to calculate a reflection half-life or a
parameter that measures flow resistance.
In particular, the rate of decay Y of the transformed response 1710
may be determined by an exponential function that has the following
form: Y=Ae.sup.-Cx
where A is the initial quantity (i.e., the quantity at time t=0), C
is the decay constant, and x is the number of cycles or
reflections. The number of reflections is also the number of peaks
in the transformed response 1710. The amplitude (or pressure) of
each peak is selected and the plurality of amplitudes are graphed
with respect to the number of peaks. The exponential decay is
fitted to this function rather than to a function of time. The
exponential decay is not fitted as a function of time because the
depth of a given completion stage is going to drive the time
required for the pressure transient to reach the perforations and
reflect back to the surface, thereby increasing or decreasing the
time between pulses of the measured response. After fitting the
exponential decay, the number of peaks required for the amplitude
of the transformed response 1710 to decay by one-half is
calculated. The number of peaks can be calculated by solving x in
the above equation when Y=1/2A. The solved x is the reflection
half-life. The reflection half-life describes the decay
characteristics for different water hammer responses. A higher
reflection half-life indicates that the water hammer response (or
the measured response) takes more reflections to decay and
correlates to a lower hydraulic resistance. A lower reflection
half-life indicates that the water hammer response decays more
quickly and correlates to a higher hydraulic resistance.
The reflection half-life (solid line) can be correlated to a
modeled hydraulic resistance (dotted lines) as shown in FIG. 18.
The modeled hydraulic resistance is an element of the electrical
model that is varied over a range to observe how it affects the
rate of decay of the measured response. For example, the electrical
model may be the model shown in FIG. 9 and the modeled hydraulic
resistance may be determined by adjusting the resistor Rs(x-1),
Rs(x), or Rs(x+1) over a range of values when the other valuables
are known or fixed to obtain several responses. This resistance,
for example Rs(x+1), can represent the hydraulic resistance at the
casing to fracture system interface. This is also modeled at the
depth of the perforations for a given completion. The other
resistance values in FIG. 9 are used to capture the hydraulic
impedance of the casing and are not varied for a fixed diameter
casing. The reflection half-life can be correlated to those
responses over a range of Rs(x+1). This correlation allows for the
constraint of the numerical optimization or can be used directly to
evaluate the flow resistance of the measured response. Hydraulic
resistance also refers to the flow resistance of the perforations
between the wellbore and the reservoir.
The transformation, the calculation of the decay rate, the
calculation of the reflection half-life/parameter, and the
correlation between the reflection half-life/parameter and the
modeled hydraulic resistance can be performed by a processor (e.g.,
CPU) or a specialized processor (e.g., signal processor) configured
to perform the above described steps or by a system including such
a processor or specialized processor.
The other steps, processes, and methods discussed in this
application may also be performed by the same processor,
specialized processor, or system that is further configured to
perform those other steps, processes, and methods. The other steps,
processes, and methods may also be performed by a separate
processor, a separate specialized processor, or a separate system
including such a processor or specialized processor that is
configured to perform only those other steps, processes, and
methods.
While the disclosure has been provided and illustrated in
connection with a specific embodiment, many variations and
modifications may be made without departing from the spirit and
scope of the invention(s) disclosed herein. The disclosure and
invention(s) are therefore not to be limited to the exact
components or details of methodology or construction set forth
above. Except to the extent necessary or inherent in the methods
themselves, no particular order to steps or stages of methods
described in this disclosure, including the Figures, is intended or
implied. In many cases the order of method steps may be varied
without changing the purpose, effect, or import of the methods
described. The scope of the claims is to be defined solely by the
appended claims, giving due consideration to the doctrine of
equivalents and related doctrines.
* * * * *