U.S. patent application number 16/385678 was filed with the patent office on 2019-08-08 for method for evaluating and monitoring formation fracture treatment using fluid pressure waves.
The applicant listed for this patent is Seismos Inc.. Invention is credited to Panagiotis Adamopoulos, Jakub Felkl, Kaitlyn Christine Mascher-Mace, Youli Quan, Junwei Zhang.
Application Number | 20190242253 16/385678 |
Document ID | / |
Family ID | 65365393 |
Filed Date | 2019-08-08 |
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United States Patent
Application |
20190242253 |
Kind Code |
A1 |
Felkl; Jakub ; et
al. |
August 8, 2019 |
METHOD FOR EVALUATING AND MONITORING FORMATION FRACTURE TREATMENT
USING FLUID PRESSURE WAVES
Abstract
A method for characterizing a hydraulic fracture in a subsurface
formation includes inducing a pressure change in a well drilled
through the subsurface formation. At least one of pressure and
pressure time derivative are measured in or at a location proximate
to a wellhead for a selected length of time. At least one of a
physical parameter, a time derivative, and a change in the
parameter with respect to time of the physical parameter of at
least one fracture is determined using the measured at least one of
pressure and the time derivative of pressure.
Inventors: |
Felkl; Jakub; (Austin,
TX) ; Quan; Youli; (Houston, TX) ; Zhang;
Junwei; (Austin, TX) ; Mascher-Mace; Kaitlyn
Christine; (Aurora, CO) ; Adamopoulos;
Panagiotis; (Lakeway, TX) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Seismos Inc. |
Austin |
TX |
US |
|
|
Family ID: |
65365393 |
Appl. No.: |
16/385678 |
Filed: |
April 16, 2019 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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15810817 |
Nov 13, 2017 |
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16385678 |
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PCT/US2017/031507 |
May 8, 2017 |
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15810817 |
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62376475 |
Aug 18, 2016 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01V 2210/54 20130101;
E21B 47/06 20130101; E21B 49/00 20130101; G01V 1/40 20130101; G01V
2210/1234 20130101; E21B 43/26 20130101; G01V 2210/121 20130101;
E21B 47/117 20200501; E21B 49/008 20130101; E21B 43/267 20130101;
G01V 1/48 20130101; G01V 1/50 20130101; G01V 2210/646 20130101;
G01V 99/005 20130101; G01V 2210/123 20130101 |
International
Class: |
E21B 49/00 20060101
E21B049/00; E21B 43/267 20060101 E21B043/267; G01V 1/48 20060101
G01V001/48; G01V 1/40 20060101 G01V001/40; E21B 43/26 20060101
E21B043/26; E21B 47/06 20060101 E21B047/06; G01V 1/50 20060101
G01V001/50 |
Claims
1. A method for predicting characteristics of a hydraulic fracture
in a subsurface formation, comprising: inducing a pressure change
in a well drilled through the subsurface formation; determining at
least one of a physical parameter, and a time derivative, and a
change in the parameter with respect to time, of at least one
fracture, using the measured at least one of pressure and the time
derivative of pressure, and correlating the at least one of a
physical parameter, and a time derivative, and a change in the
physical parameter with respect to time, of at least one fracture
with at least one of a lithological description of the subsurface
formation, and at least one characteristics of the manner in which
the hydraulic fracture was created, and predicting at least one of
a physical parameter, a time derivative, and a change in the
physical parameter with respect to time, of at least one fracture,
to be created in another part of the same, or a similar, subsurface
formation.
2. The method of claim 1 wherein the at least one of a lithological
description of the subsurface formation, and at least one
characteristics of the manner in which the hydraulic fracture was
created comprises the pumping rate with which the hydraulic
fracture was created.
3. The method of claim 1 wherein the at least one of a lithological
description, or localized stress of the subsurface formation, and
at least one characteristics of the manner in which the hydraulic
fracture was created comprises the proppant concentration with
which the hydraulic fracture was created.
4. The method of claim 1 wherein the at least one of a lithological
description or localized stress of the subsurface formation, and at
least one characteristics of the manner in which the hydraulic
fracture was created comprises the silica content of the
formation.
5. The method of claim 1 wherein the at least one of a lithological
description or localized stress of the subsurface formation, and at
least one characteristics of the manner in which the hydraulic
fracture was created comprises the calcium content of the
formation.
6. The method of claim 1 wherein the at least one of a lithological
description or localized stress of the subsurface formation, and at
least one characteristics of the manner in which the hydraulic
fracture was created comprises the temporal changes in pumping rate
with which the hydraulic fracture was created.
7. The method of claim 1 wherein the at least one of a lithological
description or localized stress of the subsurface formation, and at
least one characteristics of the manner in which the hydraulic
fracture was created comprises the temporal changes in proppant
concentration with which the hydraulic fracture was created.
8. The method of claim 1 wherein the at least one of a lithological
description or localized stress of the subsurface formation, and at
least one characteristics of the manner in which the hydraulic
fracture was created comprises the temporal changes in proppant
type (size, hardness, abrasive properties, etc.) with which the
hydraulic fracture was created.
9. The method of claim 1 wherein the at least one of a lithological
description or localized stress of the subsurface formation, and at
least one characteristics of the manner in which the hydraulic
fracture was created comprises the perforation design within which
the hydraulic fracture was created.
10. The method of claim 1 wherein the at least one of a
lithological description or localized stress of the subsurface
formation, and at least one characteristics of the manner in which
the hydraulic fracture was created comprises a combination of
parameters for fracture treatment design.
11. The method of claim 1 wherein the at least one of a
lithological description or localized stress of the subsurface
formation, and at least one characteristics of the manner in which
the hydraulic fracture was created comprises a combination of
parameters for fracture treatment design such as Perforation
location, Number of perforations, Size of perforations, Depth of
Perforations, Viscosity of Fluid, Rate of Fluid, Temperature of
Fluid, Amount of Proppant, Density of Proppant, Injection Density
of Proppant, Size of Proppant, Injection Rate of Fluid, Chemical
content of pumped fluid, Rate of Change in the viscosity of fluid,
Rate of Change in the change of velocity of fluid, co-injection of
energized gases (nitrogen, CO2, Propane, Methane) in both liquid
and gas phases, Injection of Petroleum distillates, or pH of
injection fluid (Acid/Base).
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] Division of U.S. application Ser. No. 15/810,817 filed on
Nov. 13, 2017, which application is a Continuation of International
(PCT) Application No. PCT/US2017/031507 filed on May 8, 2017.
Priority is ultimately claimed from U.S. Provisional Application
No. 62/376,465 filed on Aug. 18, 2016.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
[0002] Not Applicable
NAMES OF THE PARTIES TO A JOINT RESEARCH AGREEMENT
[0003] Not Applicable.
BACKGROUND
[0004] This disclosure relates to the field of borehole acoustic
analysis and hydraulic fractures as well as hydraulic fracturing
process monitoring and evaluation. In particular, the monitoring
can be in real time while hydraulic stimulation takes place, while
additional analysis of the data or comparisons with prior models
can also be performed at another time.
[0005] This disclosure also relates to the field of seismic
analysis of hydraulic fractures. More specifically, the disclosure
relates to method for analyzing geophysical properties of hydraulic
fracture by analysis of pressure wave reflection and resonance.
[0006] Furthermore, this disclosure also relates to measurements of
fracture (network) connectivity to wellbore and fracture (network)
connectivity to the external reservoir volume.
[0007] Hydraulic fracturing has recently accounted for a
significant growth of unconventional (tight, shale) reservoir
production in the United States. During hydraulic fracturing, fluid
under high pressure is pumped into a low permeability reservoir to
initiate fractures that tend to propagate based on dominant stress
geometries and stress distribution in the reservoir. To maintain
connectivity and potential fluid (reservoir hydrocarbons and
trapped fluids) flow through the fractures created by the fluid
under pressure, proppant is carried with the fracturing fluid.
Proppant includes specific-sized sand or engineered (e.g. to
withstand very high pressure) compounds such as ceramics, coated
sands, and others. The proppant is injected along with the
fracturing fluid (typically water and some chemicals that may
include friction reducers, viscosifiers, gels, acid to help
dissolve rock, etc.). Even though simulations and rock
physics/fracture propagation models have shed some light on
fracture creation and growth, many parameters of and for
successful/productive fracturing in terms of ultimate hydrocarbon
production and recovery have typically been determined
experimentally and often by trial and error.
[0008] There are several ways known to create fracture networks in
"stages" or sections moving from toe to heel (deepest point and the
beginning of the horizontal section of a highly inclined or
horizontal well), typically referred to as "plug and perf" and
sliding sleeve (or similar) methods, that open only a small portion
or section of the well or of perforations (openings) to the
formation. Methods according to the present disclosure are
applicable to plug and perf as well as sliding sleeve methods
because measurements can take place before, during and after the
pumping of fracturing fluid irrespective of the specific pumping
method used in a given section of a well.
[0009] Despite recent improvements in understanding production from
unconventional fractured reservoirs, current monitoring methods and
analysis, such as the passive or "microseismic" monitoring have
been less than optimal in obtaining efficient fluid recovery. It
has been estimated that only a fraction of stages in a multiple
stage fractured well contribute significantly to ultimate
hydrocarbon production. Moreover, fracture connectivity (related to
permeability) and near well-bore fracture complexity (affecting
efficient drainage) seem to show impact on ultimate recovery but
are difficult to both infer/measure and design with currently
available methods.
[0010] The problem of efficient monitoring to optimize fracture
treatment design has been approached in many different ways using
microseismic and other forms of monitoring (electromagnetic,
downhole measurements and logs, or, for example analysis using
conductive or activated proppants). Such methods provide some level
of information and detail, but have several drawbacks. Typical
microseismic or electromagnetic monitoring methods require many
sensors, significant processing time and computing resources, and
can be labor intensive. In general, such methods can add
significant cost, time and labor to the process. In particular,
additional significant post-acquisition processing of acquired data
to obtain results makes real-time information availability limited
or impracticable.
[0011] U.S. Patent Application Publication No. 2013/0079935 A1 by
Kabannik et al. describes a method using geophones and locates
sensors inside a wellbore. The disclosed method does not require
any downhole sensors, even though such implementation may enhance
some results and requires microseismic data acquisition to take
place. Any downhole sensors are operationally difficult and
increase costs of measurements. Moreover, the method disclosed in
the '935 publication relies on more complex models and required
interrupting fracture pumping operations. Furthermore, the first
part of the presently disclosed method is not concerned with
determining the location of microseismic events, only their
detection.
[0012] A method for hydraulic impedance testing disclosed in
Holzhausen, U.S. Pat. No. 4,802,144, relates to a method for
analysis of free oscillations of a connected well-fracture system,
the latter of which is assumed to support wave propagation, to
obtain fracture geometry (such as length, height and width) by
matching the data to pre-existing models or by inversion for the
fracture geometry. The '144 patent does not describe either the
effects of fracture permeability, nor inversion for wellbore-only
parameters, such as tube wave velocity and attenuation.
[0013] With reference to U.S. Patent Application Publication No.
2011/0272147 A1, by Beasley et al., the focus of such publication
is on sensors disposed near a reservoir but not necessarily sensors
hydraulically connected to the reservoir. Beasley et al. discloses
performing measurement before and post hydraulic
fracturing/stimulation operation. Moreover, the method disclosed in
the '147 publication may not be suitable for rapid
interpretation.
[0014] U.S. Patent Application Publication No. 2012/0069707
discloses using multiple receivers that are ground based, not
connected hydraulically to the wellbore, while also requiring
reference data and models.
[0015] U.S. Patent Application Publication No. 2014/0216729 by
McKenna focuses on determining a fracture network volume using
microseismic event triangulation and detection from surface based
ground sensors, rather than from a direct fluid connectivity of
wellbore fluid with the fracture network as the present
invention.
[0016] U.S. Pat. Nos. 4,907,204 and 7,035,165 B2 are both based on
active seismic well sources and well logging inside a wellbore,
which uses wireline or similar devices to traverse a borehole and
as such may be significantly more expensive and complex to
implement in comparison with a single (or only a few) surface based
borehole sensor(s).
BRIEF DESCRIPTION OF THE DRAWINGS
[0017] FIG. 1 shows an example embodiment of a data acquisition
system that may be used in accordance with the present
disclosure.
[0018] FIG. 2 shows an example geophysical model of subsurface
formations being fractured and measurements made according to the
disclosure to characterize the fractures. It also shows the
resonances driven in fractures through pumping and microseismic
activity.
[0019] FIG. 3 shows an example of data recording and analysis. The
top frame shows pressure at a selected position in or along a well
(arbitrary units), the middle frame shows hydrophone or acoustic
pressure change (time derivative) data, the bottom frame (pg 4/8)
shows examples of characteristic times and events.
[0020] FIG. 4A shows a graph of a representative active source
hydrophone time series.
[0021] FIG. 4B illustrates how conductivity kw affects
waveforms.
[0022] FIG. 4C shows how the reflection coefficient R depends on
kw.
[0023] FIG. 5A shows the hydrophone Fourier spectrum from water
hammer.
[0024] FIG. 5B shows the sensitivity of modeled spectra to fracture
conductivity kw.
[0025] FIG. 6 shows an example embodiment of a computer system that
may be used in some embodiments.
DETAILED DESCRIPTION
[0026] The discussion below uses specific examples but is not
necessarily the only intended or possible implementation or use of
the disclosed methods. A person having skill in the art can devise
similar implementations to the same goals. Methods according to
this disclosure make practical use of pressure waves and pressure
disturbances in fracture(s), including the resonance of the
combined well-fracture network system, to determine hydraulic
fracture network parameters.
[0027] During hydraulic fracturing, formations crack or fracture,
and fluid with proppant is injected in the opened cracks or
fractures. Because fractures may create an interconnected network,
the terms "fracture" and "fracture network" may be used
synonymously in the description below. Note that given the quantity
of injected fluids, there is a geostatistical component and
superposition to the sum of fracture sizes and distribution. Also
note that this method is applicable to vertical, horizontal, or any
other deviated well that undergoes hydraulic fracturing
(stimulation) treatment.
[0028] Active sources can be water hammer, fracture treatment
pumps, pistons, or other type sources specifically designed to
generate tube waves or borehole resonances, etc. as described
herein below.
[0029] Continuous/passive sources are embedded in the operation
itself and may include general pumping noise, microseismic events,
other geological phenomena not generally related to the fracturing
operation (e.g. natural seismicity).
[0030] Fractures created during hydraulic fracture fluid pumping
may be connected to the wellbore through casing perforations, or
slotted-sleeve ports integrated into the completion and, if
existing, any previously created or naturally existing fracture
network. Logically, only fractures that remain propped/open will
contribute significantly to ultimate production from the well.
Moreover, fracture geometry has importance in ultimate recovery,
well spacing design, well orientation, and even in-stage (within a
single well) spacing or perforation designs and spacing. For
example, stress shadowing from one fracture, perforation cluster,
or fracture network can reduce recovery or propensity to fracture
of another nearby stage, cluster, or adjacent well. Note that
because methods according to the present disclosure rely on
information traveling predominantly through the fluid and
interfaces, a hydraulically connected volume is where measurements
may be made.
[0031] Continuously measuring pressure-related signals and also the
rate of change of pressure (these can be pressure fluctuations, or
rates of change in pressure such as provided by pressure
gauges/transducers and/or hydrophones), how they change, their
frequency characteristics, overall phase shift and time of travel,
may be related to instantaneous fracture geometry. Comparing
measured values with theoretical speed of the wave given the
proppant size (which puts a lower limit on a single fracture
thickness), fracture geometry and other geophysical parameters can
be determined.
[0032] The quality factor (Q=resonant (maximum amplitude)
frequency/resonance spectral width at half maximum amplitude
frequency) of resonances may be estimated and used to infer the
fluid communication of fracture networks to the well.
[0033] In an embodiment according to the present disclosure,
sensors are placed on the surface near, at, or contacting the fluid
inside the well. The sensors may include but are not limited to
hydrophones that are connected to the wellbore fluid when pumping,
other acoustic measurement sensors (to measure ambient noises),
accelerometers, pressure transducers, jerk-meters (measure
derivative of acceleration), geophones, microphones, or similar
sensors. Other physical quantities can also be measured, such as
temperature or fluid composition to provide temperature corrections
and calibrations or for data consistency checks for all the
sensors. Measuring nearby ambient surface noise using microphones,
geophones, accelerometers or similar sensors can help in
attenuation of noise in fluid pressure or pressure time derivative
sensor data (i.e. pump noise as contrasted with fluid resonances
due to fractures). Sensors measuring chemical composition and
density of the pumped fluid may be used to improve analysis and are
therefore implemented in some embodiments. An example arrangement
of sensors is shown in FIG. 1. Sensors may be placed on and near
(surface or subsurface) a well W as well as an adjacent well W1.
The various sensor locations are shown at S1 through S6. Sensors
S1, S2, S4, S5, and S6 may be exposed to fluid being pumped
throughout a fracturing operation. A pressure or seismic source S
may be disposed at or near the position of sensor S1 and may be
connected to the well W only when necessary to activate it; it may
also be located near a wellbore not directly contacting fluid but
generating pressure or seismic signals in the said wellbore.
Sensor(s) S3 (surface-based) may be one or more seismic sensors
disposed on the ground within about 100 meter(s) of the well W,
depending on available access.
[0034] Sensor(s) S1 on the wellhead may measure, e.g., pressure,
pressure time derivative, temperature. Sensor(s) S2 located near
fracture treatment pumps may measure pressure, pressure time
derivative, chemical composition, temperature.
[0035] More than one sensor on the wellhead (e.g., at S1) is not
required, however additional sensors placed proximate to the
wellhead can provide higher accuracy, such as directionality of
propagating signals, ambient noise records for noise cancelling,
ground vibration measurements, steel casing vibrations, etc. and
thus methods according to the present disclosure may benefit from
using such sensors. In some embodiments all the sensors should have
substantial response at .about.1 kHz or above.
[0036] The signals from the sensors are amplified, filtered,
captured, digitized, recorded, stored, and transferred to a
computer or similar device for processing, e.g., in a recording
unit R which may be disposed proximate the well W. Such recording
unit R may be further connected with a control system CS of the
entire fracturing operation to detect sensor measurements, analyze
the measurements and provide possible feedback control loops to
optimize operations and correlate multitude of data streams for
final processing (pump rotation speeds, pumping rates, chemical
input rates, blender rates, fluid density, sand concentration,
etc.).
[0037] Although data of primary interest can only be obtained in
certain intervals of interest, a continuous stream of data acquired
at reasonably high frequencies (up to approximately .about.100 kHz)
may be beneficial to further analysis and a continuous or near
continuous, or continuously-pulsed measurement stream is desirable
for microseismic event rate monitoring. In particular, measurements
of signals at relatively low and subsonic frequencies (less than
about 5 kHz and 20 Hz respectively) are important for fracture
characteristic analysis and provide some of the frequency domain
information. Higher frequencies may provide higher spatial and time
resolution into the fractures and of seismic and other subsurface
events, while their penetration depth away from the wellbore may
not be as large. The accurate recording of low frequencies is also
important in order to detect large fractures (natural or
human-made) and larger-scale stimulated reservoir volumes.
[0038] Such sensor attachments and connections as described may be
made safely using common practices and design principles even
though fracturing pressures are very high. Spacing of the sensors
and available connections will be specific to a fracturing
well-configuration, but in general a sensor should be connected
very close to the formation (farther from the fracturing pumps,
e.g. on a wellhead) or close to the master valve and hydraulically
connected to the formation. Exceptions may include secondary
sensor(s), e.g., S2 on the pumping flowline, that can be correlated
with the measurements made by a sensor, e.g., at S1 (S1.fwdarw.S2
or S2.fwdarw.S1) to infer traveling wave linear directionality in
the flowline and thus in the well.
[0039] As stated above, more than one sensor is not required,
however additional sensors can provide higher accuracy, such as
directionality of propagating signals, ambient noise records for
noise cancelling, ground vibrations, steel casing vibrations, etc.
Thus having more than one sensor is included in FIG. 1.
Measurements from the various sensors may be time synchronized. One
method of synchronizing sensors is using GPS time signals at the
sensors or on the recording system R (if the sensors are far
apart). Combining all real-time sensor measurement streams into a
single common data acquisition unit, e.g. the recording unit R
could obtain the same objective.
[0040] Sources of signals that excite resonant frequencies in the
combined well-fracture network will come from, including but not
limited to: pumping and pumping changes; performing nearby
perforations; nearby geologic activity; AND surface or
borehole-based time-limited/pulsed energy sources. In addition,
continuous sources (valves, pumps such as are already used), or
micro-seismic events, microseismic/fracture activity are broadband
sources well-suited to excite such resonant frequencies. In
particular, inside reservoir induced (by ongoing hydraulic
fracturing operation in the well of interest or a nearby well while
pumping) microseismic activity, is important in generating some of
the signals and fracture waves.
[0041] FIG. 2 shows an example geophysical model of the well
traversing subsurface formations, fractures 24 created by or
enhanced by fracture treatment pumping, measurements obtained using
a method according to the present disclosure and analysis of the
measurements. Traveling fluid pressure waves are shown
schematically at R1 in the graph at 20 being reflected pressure
wave in the wellbore, and T representing transmitted pressure waves
in the wellbore with time difference of .tau..sub.0. FIG. 2 shows
graphic representations of the transmitted pressure wave T with
respect to time superimposed on the reflected pressure wave R1 and
its reverberations on the graph at 20. Frequency domain analysis is
shown schematically on the graph at 22.
[0042] Measurements acquired during a fracture treatment pumping
stage may be similar in characteristics to what is shown in FIG. 3.
Note that a rapid pressure change generates an acoustic signal (can
be subsonic <20 Hz, or supersonic >20 kHz) and often may be
referred to as such. This signal in turn, may generate an "echo"
returning from the subsurface region of the well (a representative
single pulse in FIG. 4A.).
[0043] The upper frame 30 in FIG. 3 shows pressure applied to a
well with respect to time as measured, e.g., at sensor S1 in FIG. 1
over a longer time period (hundreds of seconds). The middle frame
32 shows a graph of the time derivative of the measured pressure.
The lower frame 34 shows graphs of time derivative of the measured
pressure with reference to specific events occurring in the well
and in the formations penetrated by the well. During a common
hydraulic fracturing operation, a ball-seating plug is set at a
selected depth in the well, then a sealing ball is pumped down the
well at a modest rate (few or tens of barrels per minute, e.g., 100
seconds in the upper frame 30), slowing down before the ball
engages a plug (e.g., at 195 seconds in FIG. 3). Immediately after
the ball seats--at which point if chosen based on formation
composition, properly used and spotted, acid would reach the area
of perforations in the well casing and the formation--the pressure
builds up. At .about.200 seconds in FIG. 3, the pressure rises to
the point where fractures in the newly pressured fracture treatment
stage start to open. A steep pressure increase shown in the upper
frame 30 indicates that the present fracture treatment stage is
hydraulically isolated from the previous fracture treatment
stage.
[0044] As more fracturing fluid is pumped and the fluid pumping
rate increases, fractures continue propagating in the formation.
Operators typically increase the rate of pumping until a target
rate is reached (tens, sometimes about 100 barrels per minute-bpm),
which also generally increases the fluid pressure and the pressure
exerted on the subsurface formation. Once a target planned "sweet
spot" or optimized pumping rate is reached, the operator may
maintain that pumping rate unless unexpected behavior (pump
failures, screen-out, or unexpected pressure rise) and safety
considerations or feedback from methods as disclosed herein dictate
otherwise. For example pressure and pumping rate can be changed to
overcome friction and to mitigate growth of fractures. During this
time, proppant is typically added to the pumped fluid to keep
fractures open after the pressure on the fracturing fluid is
relieved.
[0045] In FIG. 3, note in the lower frame 34 measurements
corresponding to pump noise, pressure changes with ball seating, a
microseismic event identified around 420.5 seconds and a stabilized
pumping noise and pressure signals during this time. Measuring,
detecting, and providing real-time feedback of the microseismic
events thus detected may also be valuable. Coming from a single or
a small number of sensors, this data can be made readily available
and processed in real-time.
[0046] In its simple form, only knowing how many
formation-breaking, i.e. microseismic, events occur per unit time
may show how much the formation has been fractured and can be
combined with additional information (such as but not limited to
fully passive microseismic analysis) for even more comprehensive
understanding. Real-time aspects of the pressure and pressure time
derivative measurements can be useful as the operator may want to
maintain a certain formation-breaking/fracture creating rate
(microseismic events per unit time interval) to optimize fracture
creation for maximum hydrocarbon recovery.
[0047] Time-frequency analysis may be used to show change of the
pressure wave spectrum over time. Frequency domain analysis, such
as may be provided by a Fourier transform can then have a better
resolution in the time-frequency stationary period.
[0048] In some embodiments, measurements from a plurality of
sensors such as shown in FIG. 1 comprising pressure transducers,
accelerometers, hydrophones, or geophones may be used to reduce
surface-based noise, reconfirm the existence of strong events,
and/or to eliminate certain frequencies in the signals such as
those originating from the pumps or surface activity instead of the
reservoir and/or fractures or subsurface signals carried though the
wellbore.
Inversion of the Measurement
[0049] The inversion of the measurement to determine physical
parameters describing the fractures and fracture network requires a
description of how pressure disturbance(s) interact(s) with the
fractures, the fracture network, the wellbore and the system
comprised by these parts. Within all elements of the system and its
component parts pressure disturbances obey a second-order in time
differential equation composed of terms that describe wave
propagation and terms that describe diffusion behavior. The
relative amplitude of each of these terms differs in the wellbore
and in the fracture and fracture network.
[0050] In the wellbore, the wave propagation terms dominate and the
pressure disturbance propagates as a wave with relatively little
attenuation. Except in unusual circumstances in the fracture and
fracture networks, the diffusion terms dominate and the amplitude
of the pressure disturbance decays rapidly with relatively little
wave-like nature. Only in unusual circumstances are interface
waves, such as Stoneley waves, Scholte waves, Rayleigh waves, Love
waves and Krauklis waves, excited, and such waves propagate within
the fractures and fracture network.
[0051] A specific method will now be explained to invert the data
based on the above understanding. Those skilled in the art will
understand that the specific method may be modified or extended in
whole or in part. The method, which inverts the data based on the
above understanding, will now be explained. The explanation of an
example embodiment of the method uses a model (see, e.g., Mathieu
and Toksoz, 1984; Hornby et al., 1989; Kostek et al., 1998a; Henry,
2005), to describe tube wave reflection from fractures. Important
elements of this disclosure refer to complex-valued frequency
dependent reflection coefficient, proppant filled Darcy flow, and
elastic compliance of the fractures as described in paragraphs
below. Tube waves at the frequencies of interest are idealized as
pressure waves obeying the wave equation with speed c.sub.T (Biot,
1952). Attenuation during propagation is accounted for using a
frequency-independent quality factor Q.sub.T, not to be confused
with wellhead flow rate Q(t).
[0052] The borehole may be sealed with a packer, and fractures have
been created through several perforation clusters in the casing. At
low frequencies of interest, wavelengths of tube waves are
sufficiently large that it may be assumed that all fractures
effectively experience the same pressure at their junction with the
borehole. Tube waves thus reflect from the set of fractures and
packer collectively, rather than from individual fractures. The
tube wave reflection coefficient for this geometry may be
determined by the expression:
R ( .omega. ) = Z f ( .omega. ) - Z T Z f ( .omega. ) + Z - T , ( 1
) ##EQU00001##
[0053] where Z.sub.T=r.sub.T c.sub.T/A.sub.T is the tube wave
hydraulic impedance (for a borehole fluid density r.sub.T, tube
wave speed c.sub.T, and borehole cross-sectional area A.sub.T) and
Z.sub.f (.omega.) is the hydraulic impedance of the set of
fractures and packer that terminates the portion of the borehole
that is hydraulically connected to the wellhead.
[0054] Here, R(.omega.) is a complex-valued, frequency-dependent
reflection coefficient, and hydraulic impedance Z is defined as the
ratio of pressure change to change in volumetric flow rate. The
wellhead pressure with respect to time P(t), in response to an
imposed wellhead flow rate Q(t), may be expressed in the frequency
domain as:
P ^ ( .omega. ) = Z T Q ^ ( .omega. ) 1 + g ( .omega. ) R ( .omega.
) 1 - g ( .omega. ) R ( .omega. ) = Z T Q ^ ( .omega. ) { 1 + 2 n =
1 .infin. [ g ( .omega. ) R ( .omega. ) ] n } , ( 2 )
##EQU00002##
for reflection coefficient R(.omega.) given in Eq. (1) and two-way
travel time factor g(.omega.) that accounts for attenuation and
causality preserving dispersion (See, e.g., Aki and Richards,
2009):
g ( .omega. ) = exp ( 2 i .omega. h c T [ 1 - ln ( .omega. /
.omega. 0 ) .pi. Q T ] - [ .omega. ] h c T Q T ) , ( 3 )
##EQU00003##
where h is the borehole length and .omega..sub.0 is a reference
angular frequency at which the tube wave phase velocity equals
c.sub.T. The second form of Eq. (2) highlights the infinite
sequence of reflections. In numerical time-domain examples to
follow, we construct the solution first in the frequency domain and
then invert the transform using a fast Fourier transform.
[0055] Single Fracture
[0056] Consider a single, one-sided fracture as a planar crack
extending in the positive x direction away from the borehole to a
distance L. The fracture has cross-sectional area A in the y-z
plane (e.g., for an elliptical cross-section, A=.pi.wH/4, with
maximum width w and height H). The fluid pressure p is assumed to
be uniform across this cross-section, but is permitted to vary in
the x direction; i.e., p=p(x; t). The fracture is filled with
proppant (porosity .PHI. and permeability k) and fluid (density
.rho. and dynamic viscosity .mu.). The volumetric flow rate of
fluid along the fracture in the x direction is denoted as q(x; t).
The hydraulic impedance of this fracture is defined using pressure
and volumetric flow rate at the fracture mouth, p.sub.0(t)=p(0,t)
and q.sub.0(t)=q(0, t), respectively, as
Z.sub.0(.omega.)=p.sub.0(.omega.)/q.sub.0(.omega.).
[0057] An objective is to derive Z.sub.0(.omega.) for a single,
one-sided fracture. Conservation of fluid mass may be represented
as:
.differential. ( .rho..phi. A ) .differential. t + .differential. (
.rho. q ) .differential. x = 0 , ( 4 ) ##EQU00004##
assuming negligible leak-off over the short time scales of
interest. Next, we rewrite (4) as an equation for pressure
perturbation p(x, t) within the fracture. Perturbations are assumed
sufficiently small so as to justify linearization. Following
standard procedures in linear poromechanics, it may be assumed that
r and f depend on the local pressure p, and define fluid and pore
compressibilities as
.beta..sub.f=.rho..sup.-1(.differential..rho./.differential.p) and
.beta..sub.f=.PHI..sup.-1(.differential..PHI./.differential.p)
respectively.
[0058] It may also be assumed that a local elasticity relation in
which changes in A depend only on the local pressure. This
assumption is used in several simple models of hydraulic fractures
(e.g., the PKN model, see, Nordgren, 1972). With this assumption,
the crack compliance may be defined as
.beta..sub.A=A.sup.-1(.differential.A/.differential.p). As an
example, if it is assumed that the fracture height H is much less
than wavelengths characterizing the pressure perturbations in the x
direction, then plane strain conditions prevail within the plane of
the cross-section. This permits use of the standard solution for a
uniformly pressurized mode I crack, for which changes in width
.DELTA.w are related to changes in pressure .DELTA.p by
.DELTA.w=(H/G*)/.DELTA.p with G*=G/(1-v) for solid shear modulus G
and Poisson's ratio v. It follows that the crack compliance is
.beta..sub.A=(H/w)(G*).sup.-1.
[0059] The general definitions of compressibilities and the crack
compliance are then used to rewrite the first term in the mass
balance Eq. (4) in terms of the pressurization rate
.differential.p/.differential.t. In addition, Darcy's law states
that:
q = - kA .mu. .differential. p .differential. x . ( 5 )
##EQU00005##
[0060] With these substitutions, the mass balance in Eq. (4)
becomes the diffusion equation for pressure perturbation p(x; t)
within the fracture:
.rho..phi. A .beta. .differential. p .differential. t =
.differential. .differential. x ( .rho. kA .mu. .differential. p
.differential. x ) , ( 6 ) ##EQU00006##
where .beta.=.beta..sub.f+.beta..sub.f+.beta..sub.A is the total
compressibility/compliance. The diffusivity and diffusion length
are, respectively:
D = k .mu..phi. .beta. and L D = D / .omega. . ( 7 )
##EQU00007##
Consistent with the assumption of small perturbations, Eq. (6) is
linearized and all coefficients (i.e., S, .rho., k, A and .mu.) are
evaluated at reference conditions. In all examples below, one may
assume spatially uniform properties.
[0061] When the fracture is much longer than the diffusion length
(L.sub.D<<L), as is typically the case in our experience, the
solution to Eq. (6) for imposed volumetric flow rate q.sub.0(t) at
the fracture mouth x=0 is, in the frequency domain:
p ^ ( x , .omega. ) = q ^ 0 ( .omega. ) .mu. kA D - i .omega. exp (
- - i .omega. D x ) . ( 8 ) ##EQU00008##
The hydraulic impedance of this single, one-sided fracture is:
Z 0 ( .omega. ) = .mu. kA D - i .omega. = .mu. - i .omega. .phi.
.beta. k A 2 . ( 9 ) ##EQU00009##
Multiple Fractures
[0062] Now consider a small section of the borehole hydraulically
connected to a set of N fractures, each extending bilaterally away
from the borehole, and terminated by an impermeable, rigid plug.
Elastic interactions between the fractures are neglected. It may be
assumed that all fractures experience the same pressure p.sub.0(t)
at their junction with the borehole, and one may define q.sub.i(t)
as the volumetric flow rate into fracture i (i=1, . . . , N). The
hydraulic impedance of the fracture set is:
Z f ( .omega. ) = p ^ 0 ( .omega. ) 2 i = 1 N q ^ i ( .omega. ) , (
10 ) ##EQU00010##
where the denominator in Eq. (10) is the total volumetric flow rate
into all N fractures, and the factor of two is because the
fractures extend laterally from both sides of the borehole (x>0
and x<0). If it is further assumed that all fractures are
effectively identical, each having hydraulic impedance
Z.sub.0(.omega.), then Z.sub.f(.omega.)=Z.sub.0(.omega.)/2N.
[0063] Compliant, Elliptical Crack Model
[0064] As a specific example, suppose that the compressibility or
compliance b is dominated by the crack compliance .beta..sub.A,
such that .beta..about.(H/w)(G*).sup.-1. Using this expression, and
assuming elliptical cross-section (A=.pi.wH/4), the hydraulic
impedance of N bilateral fractures, in the small diffusion length
limit of Eq. (9), reduces to
Z f ( .omega. ) = 2 .pi. N G * .mu. .phi. - i .omega. kwH 3 . ( 11
) ##EQU00011##
Eq. (11) will be used in the remainder of this disclosure, together
with Eq. (1) and Eq. (2), to interpret data.
Active Source Measurement
[0065] FIG. 4A shows a representative active source hydrophone time
series along with the best-fitting model. The source is idealized
as a Gaussian modulation of wellhead flow rate,
(t).about.exp(-(.omega.T).sup.2/2), for source duration T. Setting
representative values c.sub.T=1460 m/s, h=4805 m, G=13:3 GPa, N=6,
H=10 m, .PHI.=0.5, and .mu.=5.times.10.sup.-3 Pa s, one may then
vary the fracture conductivity kw, borehole quality factor .sub.T,
source duration T, and source amplitude to minimize the waveform
misfit in the L.sub.2 norm. It may be determined that
.sub.T.about.70, T.about.0.055 s, and kw.about.0.38 D m.
[0066] FIG. 4B illustrates how conductivity kw affects waveforms.
This is because the reflection coefficient R depends on kw as shown
in FIG. 4C. The real part of R is negative, and R.fwdarw.1 at high
frequencies and for highly conductive fractures (large kw). In this
limit, the fracture hydraulic impedance is much less than the tube
wave impedance (Z.sub.f<<Z.sub.T), such that waves reflect as
if from a constant pressure (i.e., "open") end. At lower
frequencies, and also for less conductive fractures (smaller kw),
the fracture hydraulic impedance increases, and the reflection
coefficient shows appreciable differences from the open-end limit.
For even smaller kw than shown in the FIG. 4C,
Z.sub.f>>Z.sub.T and R.fwdarw.1 (i.e., "closed" end).
[0067] The inferred value for conductivity, kw.about.0.38 D m, is
reasonably consistent with independent estimates of width w and
proppant pack permeability k. First, it should be emphasized that
the measurement alone cannot provide separate constraints on k and
w. For example, the inferred conductivity is consistent with w=1 mm
and k=400 D, w=1 cm and k=40 D, or w=0.1 m and k=4 D. Laboratory
measurements of proppant pack permeability (See, e.g., Lee et al.,
2010) show values around 100 D, for which the inferred width is 4
mm.
[0068] Water Hammer Measurement
[0069] Next, t data may be interpreted in the frequency domain.
FIG. 5A shows the hydrophone Fourier spectrum from water hammer
produced when pumps are shut off at the end of the stage (ISIP
water hammer). The multiple spectral peaks are the resonant modes
of the borehole-fracture system. The resonance frequencies of open-
and close-ended tubes are well known. The present example
embodiment of a model predicts a continuous transition between
these limits as the hydraulic impedance ratio, Z.sub.f/Z.sub.T, is
varied. FIG. 5B shows the sensitivity of modeled spectra to
fracture conductivity kw.
[0070] To demonstrate this, one may apply the model with the same
parameters as before but with the source flow rate Q(t) idealized
as a step function. FIG. 5B shows graphically how kw influences the
spectra. The resonance frequencies transition from the closed-end
limit for small kw to the open-end limit for large kw. Since the
actual source time function is more complicated than a step
function, the model may be fit to the data by matching the
frequencies and quality factors of individual resonances, rather
than attempting to directly match the spectrum. This procedure, not
illustrated here, provides values reasonably consistent with those
inferred from the active source full waveform inversion.
Interpretation of the Inversion Results
[0071] In the preceding section is described one specific method of
inverting the data for a parameter kw/.mu. which controls the rate
at which fluid flows into and out of the fracture and which may be
designated as the conductivity of the fracture or fracture network.
This is a relevant factor in the subsequent production of
hydrocarbons.
[0072] In addition, by repeating this measurements at least two
distinct times before, during or after the pumping of a fracture
treatment, it is possible to calculate the change, or rate of
change, of the conductivity which provides information on the
effectiveness of the fracturing treatment. The initial, "baseline"
measurement may also be taken from another dataset of similar
parameters of well and formation to estimate such a change.
[0073] In addition, by examining the conductivity calculated from
resonances at comparatively low frequencies, intermediate
frequencies and high frequencies can be analyzed. Different
frequencies are sensitive to different ranges of investigation with
low frequencies extending furthest and high frequencies extending
the least distances. Thus, from comparison of the conductivity
estimates made at different frequencies it is possible to estimate
the conductivity, conductivity changes and rates of conductivity
change at different distances from the perforations.
[0074] Thus, the calculation of conductivities and their change
with respect to time can be interpreted as originating from the
spatial distribution of changes in conductivity, and consequently
one can infer the distribution of proppant and its change with
time.
[0075] Furthermore, the distribution of proppant as a function of
distance from the perforation can be interpreted in terms of the
complexity of the fracture network. A situation where the known
total volume of proppant is distributed equally with respect to
distance from the well is expected to be the result of a relatively
simple fracture network. Conversely, when the known total volume of
proppant is highly concentrated near the well it is expected that a
complex fracture network exists. This complex fracture network
provides both the volume to contain the proppant and the complexity
which traps the proppant and prevents it from being carried further
from the well.
[0076] Furthermore, it is possible to identify segments of a
borehole (stages) that contain fractures that exhibit significantly
larger, or significantly smaller changes in conductivity caused by
hydraulic fracturing. These segments can be correlated, or
otherwise associated, with particular geological characteristics of
the formation in which the borehole is situated. These geological
characteristics are typically determined from lithological logs, or
other logs (e.g., rate-of-penetration logs) recorded while drilling
the borehole or using data acquired after drilling acquired on, for
example, wireline. Once this correlation, or association, of
fractures yielding high or low conductivities with particular
features of lithological or other logs has been established, it can
then be used to plan perforation and hydraulic fracture location in
other boreholes to optimize operations and production. For example,
if it is established by correlation or other comparison that
portions of the well that exhibited low rates-of-penetration while
drilling also tend to produce high conductivity fractures, then in
subsequent wells it may be possible to locate the perforations
(where the fractures originate) in segments of the well that
exhibited low rates-of-penetration when they were drilled. As
another example, if it is established that high conductivity
fractures are associated with silica-rich portions of the
formation, in future wells one can position the perforations
primarily in silica-rich segments of the well; then high
conductivity fractures may be expected in other wells drilled
through silica-rich formations or portions thereof. Many other
correlations between fracture characteristics and lithology
(formation mineral composition) or geomechanical characteristics
(e.g., bulk and elastic moduli, Poisson's ratio, compressive and
tensile strength) of the formation are possible.
[0077] FIG. 6 shows an example computing system 100 in accordance
with some embodiments. The computing system 100 may be an
individual computer system 101A or an arrangement of distributed
computer systems. The individual computer system 101A may include
one or more analysis modules 102 that may be configured to perform
various tasks according to some embodiments, such as the tasks
explained with reference to FIGS. 2, 3, 4A, 4B, 4C, 5A and 5B. To
perform these various tasks, the analysis module 102 may operate
independently or in coordination with one or more processors 104,
which may be connected to one or more storage media 106. A display
device 105 such as a graphic user interface of any known type may
be in signal communication with the processor 104 to enable user
entry of commands and/or data and to display results of execution
of a set of instructions according to the present disclosure.
[0078] The processor(s) 104 may also be connected to a network
interface 108 to allow the individual computer system 101A to
communicate over a data network 110 with one or more additional
individual computer systems and/or computing systems, such as 101B,
101C, and/or 101D (note that computer systems 101B, 101C and/or
101D may or may not share the same architecture as computer system
101A, and may be located in different physical locations, for
example, computer systems 101A and 101B may be at a well drilling
location, while in communication with one or more computer systems
such as 101C and/or 101D that may be located in one or more data
centers on shore, aboard ships, and/or located in varying countries
on different continents).
[0079] A processor may include, without limitation, a
microprocessor, microcontroller, processor module or subsystem,
programmable integrated circuit, programmable gate array, or
another control or computing device.
[0080] The storage media 106 may be implemented as one or more
computer-readable or machine-readable storage media. Note that
while in the example embodiment of FIG. 6 the storage media 106 are
shown as being disposed within the individual computer system 101A,
in some embodiments, the storage media 106 may be distributed
within and/or across multiple internal and/or external enclosures
of the individual computing system 101A and/or additional computing
systems, e.g., 101B, 101C, 101D. Storage media 106 may include,
without limitation, one or more different forms of memory including
semiconductor memory devices such as dynamic or static random
access memories (DRAMs or SRAMs), erasable and programmable
read-only memories (EPROMs), electrically erasable and programmable
read-only memories (EEPROMs) and flash memories; magnetic disks
such as fixed, floppy and removable disks; other magnetic media
including tape; optical media such as compact disks (CDs) or
digital video disks (DVDs); or other types of storage devices. Note
that computer instructions to cause any individual computer system
or a computing system to perform the tasks described above may be
provided on one computer-readable or machine-readable storage
medium, or may be provided on multiple computer-readable or
machine-readable storage media distributed in a multiple component
computing system having one or more nodes. Such computer-readable
or machine-readable storage medium or media may be considered to be
part of an article (or article of manufacture). An article or
article of manufacture can refer to any manufactured single
component or multiple components. The storage medium or media can
be located either in the machine running the machine-readable
instructions, or located at a remote site from which
machine-readable instructions can be downloaded over a network for
execution.
[0081] It should be appreciated that computing system 100 is only
one example of a computing system, and that any other embodiment of
a computing system may have more or fewer components than shown,
may combine additional components not shown in the example
embodiment of FIG. 6, and/or the computing system 100 may have a
different configuration or arrangement of the components shown in
FIG. 6. The various components shown in FIG. 6 may be implemented
in hardware, software, or a combination of both hardware and
software, including one or more signal processing and/or
application specific integrated circuits.
[0082] Further, the acts of the processing methods described above
may be implemented by running one or more functional modules in
information processing apparatus such as general purpose processors
or application specific chips, such as ASICs, FPGAs, PLDs, or other
appropriate devices. These modules, combinations of these modules,
and/or their combination with general hardware are all included
within the scope of the present disclosure.
REFERENCES CITED IN THIS DISCLOSURE
[0083] Aki, K., and P. G. Richards, 2009, Quantitative Seismology:
University Science Books. [0084] Biot, M., 1952, Propagation of
elastic waves in a cylindrical bore containing a fluid: Journal of
Applied Physics, 23, 997-1005. [0085] Henry, F., 2005,
Characterization of borehole fractures by the body and interface
waves: TU Delft, Delft University of Technology. [0086] Hornby, B.,
D. Johnson, K. Winkler, and R. Plumb, 1989, Fracture evaluation
using reflected Stoneley-wave arrivals: Geophysics, 54, 1274-1288.
[0087] Kostek, S., D. L. Johnson, and C. J. Randall, 1998a, The
interaction of tube waves with borehole fractures, part i:
Numerical models: Geophysics, 63, 800-808. [0088] Lee, D. S., D.
Elsworth, H. Yasuhara, J. D. Weaver, and R. Rickman, 2010,
Experiment and modeling to evaluate the effects of proppant-pack
diagenesis on fracture treatments: Journal of Petroleum Science and
Engineering, 74, 67-76. [0089] Mathieu, F., and M. Toksoz, 1984,
Application of full waveform acoustic logging data to the
estimation of reservoir permeability: Technical report,
Massachusetts Institute of Technology. Earth Resources Laboratory.
[0090] Nordgren, R., 1972, Propagation of a vertical hydraulic
fracture: Society of Petroleum Engineers, 12, 306-314.
[0091] Although only a few examples have been described in detail
above, those skilled in the art will readily appreciate that many
modifications are possible in the examples. Accordingly, all such
modifications are intended to be included within the scope of this
disclosure as defined in the following claims.
* * * * *