Note: Descriptions are shown in the official language in which they were submitted.
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EXTENT OF DETONATION DETERMINATION METHOD
USING SEISMIC ENERGY
TECHNICAL FIELD
The present invention relates to subterranean well drilling, well completion
and
maintenance. More particularly, the invention relates to procedures for
enhancing well
production and for verification of production zone perforation by shaped
charge
explosives.
BACKGROUND ART
Those in the petroleum industry are particularly concerned with extracting
petroleum by boring holes into deep underground rock formations. To improve
the
flow of hydrocarbon fluids into the borehole from the surrounding rock,
explosive
devices are placed in the borehole and detonated, causing piercement and
fracturing
of the rock. These explosive devices are called Perforating Guns and contain a
series of shaped charges, each with a primer connected by explosive cord
called
detonating cord. The detonating cord is also connected within the Perforating
Gun to
a detonator. The explosion is initiated by the detonator and travels along the
detonating cord and past the series of shaped charges, detonating each of them
in
turn, to the last shaped charge in the Perforating Gun. In a successful
detonation, all
of the shaped charges explode. Occasionally, the explosion sequence will
terminate
before all of the charges have detonated, against the desire and intent of the
operator. In a worst case, none of the explosive charges will detonate even
though
the operator has activated the firing sequence.
In the current state of the industry's technology, no method is available to
the
operator that can quickly and reliably provide a quantitative estimate of the
extent of
the detonation of the Perforating Gun. A quantitative estimate of extent of
detonation
would be one that provides the operator with the length of the Perforating Gun
that
detonated or a percentage of the total length of the Perforating Gun that
detonated.
At best, the operator may get an indication of a probable firing of the gun
from a
transducer positioned on the well structure at or near the well head.
Presumably, the
absence of a signal indicates a total misfire. This method often fails to give
correct
indications of gun firing or misfiring, as the case may be. Moreover, this
wellhead
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transducer method provides neither an indication of a partial misfire nor a
quantitative
estimate of the extent of detonation.
Tubing-conveyed Perforating Guns (TCP Guns) are typically detonated below
the packer and are intended to be permanently left in place as petroleum
production
ensues after detonation. In the case of TCP the operator thus may never team
from
retrieval and direct inspection of the gun that a partial detonation has
occurred. He
may suffer direct economic loss in that the productive rock formation is only
partially
perforated and petroleum production from the perforated borehole is
correspondingly
reduced. A potentially far greater economic loss may stem from the operators
resultant under-estimation of the production potential of the oil field, based
on the
lower production rate after a partial perforation that he believes to be a
complete
perforation of the formation. Under-estimation of the field's potential could
lead to a
Wrong decision such as to limit further drilling activity or even to abandon
the field
and the initial investment in that field.
Other types of Perforating Guns may be retrieved to the surface for inspection
after attempted detonation. The operator will be able to observe the extent of
detonation upon inspection. Even in this method of operation it would be
useful for
the operator to know, without waiting for withdrawal or inspection, the extent
of
detonation. If the operator knew immediately of a failed detonation he could
undertake appropriate remedial action as best available. Backup detonation
means
could be activated if available. Knowledge of the existence of unexploded
charges
could allow the operator to implement procedures designed to enhance safety of
workers in this situation.
Direct sensing of the detonation at the location of the gun itself is
impractical
in the case of TCP operations, in that no wire or cable can be conveniently
connected to the Perforating Gun.
Thus, there is a need in the petroleum industry for a method of indirect
remote
sensing of the detonation with a rapid and reliable determination of the
extent of
detonation of a Perforating Gun.
DISCLOSURE OF INVENTION
A preferred embodiment of the invention is a set of seismic receivers, a
seismic recording and control system linked to the Perforating Gun detonation
control
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system and containing a computer programmed to process and analyze the seismic
wave amplitudes enabling the practitioner to determine the extent of
detonation of a
subsurface borehole-emplaced Perforating Gun.
The seismic receivers consist of conventional geophones or other transducers
deployed singly or in arrays or sub-arrays of multiple transducers.
Emplacement of
the seismic receivers may be at or near the earth's surface or in boreholes
proximate
the vicinity of the Perforating Gun positioned to allow advantage in sensing
and
processing the directly arriving seismic waves from the Perforating Gun.
The Perforating Gun may be positioned as necessary to achieve its purpose
at any depth within a borehole and may be of any practicable length or style
of
construction. It may be detonated by any of the available means. The
detonation is
assumed to be initiated by a detonator and to progress away from ttie position
of the
detonator as it travels along the gun.
The axis of the borehole may be vertical, horizontal, linear, or curved, i.e.
of
any curvilinear shape.
Seismic waves caused by the progressive explosion travel in all
directions and arrive at the seismic receivers. Amplitudes of the seismic
waves are
detected, recorded and then processed to improve the signal-to-noise ratio and
form
a best signal estimate. A control and processing computer activates the
recording
prior to the instant of detonation, enabled to do so by a link to the
detonation control
system. The link may be an automated electronic link or may simply be voice
communication between human operators of the seismic recorder and the
detonation
system.
The best signal estimate is analyzed and a determination is made of the
extent-of-detonation (EOD) of the Perforating Gun, i.e. whether the
Perforating Gun
fired successfully, partially misfired or totally misfired, and in the case of
a partial
misfire, the quantitative extent of detonation of the gun. The determination
may
include comparison of the best signal estimate to predicted signal based on
modeling
and/or to signal estimates from other detonations. The determination may also
include an application of novel inversion algorithms and further analysis to
best
quantify the extent of detonation. In all of these approaches the
determination relies
upon pre-determined potentials of the perforating gun.
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The process can be performed rapidly and results provided on site so as to
make the result available to the operator soon after the detonation.
BRIEF DESCRIPTION OF THE DRAWINGS
For a more detailed description of the preferred embodiment of the present
invention, reference will now be made to the accompanying drawings, wherein:
Figure 1 is a cut-away view of a rock formation showing a well bore and
system elements as well as a Composite Wavelet received at the surface from
the
detonation of a Perforating Gun.
Figure 2 is a view of a portion of the preferred embodiment as positioned at
or
near the earth's surface.
Figure 3 is a view of the portion of the preferred embodiment with seismic
receivers deployed in a deep borehole.
Figure 4 is a schematic view of the seismic receiver at the surface of the
earth.
Figure 5 is a schematic view of the seismic receiver positioned in a borehole.
Figure 6 is a depiction of the signal processor showing its essential
elements.
Figure 7 is a schematic view of the process controller.
Figure 8 is a schematic view of a section of the Perforating Gun.
Figure 9 is a time-line of the detonation and recording process.
Figure 10 depicts the successive stages of gun detonation and seismic energy
propagation.
Figure 11 illustrates modeled composite wave forms and autocorrelations for
varying Gun Lengths.
Figure 12 shows a basic wavelet and its composite for 6, 24 and 96
milliseconds (msec) Duration
Figure 13 shows successive stages of the inversion of a Composite Wavelet
for varying assumptions of extent of detonation.
Figure 14 contains three graphs that show the input and output of the
inversion process to determine the Duration in the 24 msec case
Figure 15 contains three graphs that show the input and output of the
inversion process to determine the Duration in the 6 msec case
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Figure 16 shows the effect of noise on the inversion process comparing to
Figure 14.
Figure 17 illustrates the autocorrelation method of esfimating Duration.
Figure 18 shows a comparison of Composite Wavelets for a curvilinear
borehole modeled by the time shift method and by the pulse density method.
Figure 19 shows a table of successive steps in the first stage of inversion
and
the second stage of inversion of a modeled Composite Wavelet for a curvilinear
borehole.
Figure 20 graphically illustrates the results of the second stage of inversion
of
a Composite Wavelet modeled using the Pulse Density Method.
Figure 21 illustrates the results comparable to Fig 20 but for a Composite
Wavelet modeled using the Time Shift Method
Figure 22 gives sample equations for successive stages of decomposition of a
Composite Wavelet.
Figure 23 shows a table of values of Duration and Travel Time versus Gun
Segment.
Figure 24 is a diagram of the Perforating Gun divided into Gun Segments and
showing the point of misfire and effective Gun Length.
Figure 25 shows the seismic recording of a successful detonation and of a
total misfire of a Perforating Gun.
BEST MODE FOR CARRYING THE INVENTION
Referring to Fig 1, a number of seismic sensors 100 are shown in position at
or near the earth's surface 160 and connected to a signal processor and
recorder
105. This unit 105 is further linked to the extent of detonation (EOD)
controller 110.
This controller 110 controls all of the equipment that is unique to this
invention.
Together these three subsystems make up the complete EOD system 115. The
remainder of the equipment in Fig 1 comprises items that are normally used in
the
business of drilling, perforating, completing and producing petroleum from
boreholes.
The borehole and borehole equipment 170 are shown connected to wellhead
apparatus 120. A Perforating Gun 140 is shown positioned in the borehole,
ready
for detonation.
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When the Perforating Gun is ready to be detonated, the perforation operator
notifies the seismic observer, who activates the EOD system. The EOD system
then
begins to record seismic data, received by the seismic sensors 100 and then
processed and digitized in the signal processor and recorder 105. The EOD
system
continues to record and store data in memory and on media (such as tape) until
the
seismic energy caused by the explosion of the Perforating Gun has abated.
Seismic ray paths 145 are shown on Fig 1 to indicate the approximate
travel path of seismic waves from the Perforating Gun 140 to the seismic
sensors
100. These ray paths are not perfectly straight lines as shown in Fig 1 but
will be
bent as they pass through layers of earth with differing seismic wave
velocities and
are refracted. The amplitude versus time graph 150, called the Composite
Wavelet,
represents the seismic amplitude received at the seismic sensors 100 and
recorded
and processed digitally. Generally the amplitudes prior to reception of the
energy
from the detonation of the Perforating Gun 140 will be small if seismic noise
level is
low, the early amplitudes of the seismic waves emanating from the detonation
will be
relatively high and they will gradually subside after a few hundred
milliseconds
(msec) to lower levels, eventually dying out after some seconds and leaving
only
seismic noise again.
The seismic noise is defined herein to be the combination of ambient noise,
i.e. seismic waves from uncontrolled external sources, such as caused by wind
and
traffic, and seismic waves resulting from the perforating gun detonation (gun-
generated noise), but other than signal waves, i.e. the direct arrivals
through the
earth from the perforating gun itself. For purpose of determination of the
extent-of
detonation of the perforating gun, signal is defined as these directly
arriving seismic
waves, the Composite Wavelet 150. Thus any other seismic waves caused directly
or indirectly by the perforating gun detonation process are considered to be a
component of seismic noise. Examples of such gun-generated noise components
are seismic waves caused by movement of the equipment in the borehole and at
the
well head, when such movement is caused by the detonation, and seismic waves
traveling from the perforating gun to the sensors by indirect paths that
include
reflection from impedance boundaries (but not reverberations). Reverberations,
defined as short-period multiple reflection energy following the direct
arrival events,
contribute energy to the source wavelet and are considered to be signal for
the
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purpose of extent-of detonation determination. Signal will ordinarily be
compressional
wave energy only, because it will generally be better separated from
gun~enerated
seismic noise than other modes due to its early arrival. However, in
principal, signal
could also be shear wave or other modes of directly arriving seismic energy.
Fig 2 provides further detail of the EOD system 115. The seismic sensors 100
are linked together and connected to the signal processor 105 by a surface
seismic
cable 200. The sensors may be commercially available geophones and/or
hydrophones, hydrophones being suitable if the area is water covered. The
sensors
may be at the ground surface or may be buried to improve coupling and to
reduce
ambient noise. The sensors may also be emplaced in shallow boreholes. The
geophones may be vertical and/or horizontal geophones, i.e. able to sense
vertical or
horizontal motion of the earth. The geophones may be 3-component geophones,
that
sense three orthogonal components of motion. A combination of all four
sensors, one
vertical sensor, two horizontal sensors and a pressure-sensitive sensor or
hydrophone may also be used (called 4C sensor). In water saturated
environments
hydrophones may be used as the sole type of sensor. Any type of transducer or
sensing apparatus capable of sensing variations in pressure or ground motion
is
potentially suitable for the EOD purpose.
Fig 4 shows surface seismic sensors 100 emplaced at the surface in a one-
dimensional array with four geophones per sub-array and 7 sub-arrays
comprising
the total seismic array aperture 410. The geophones in the sub-arrays may be
combined additively, to improve the signal-to-noise ratio, preferably with
individual
time shifts to align the signal prior to combination, or they may be combined
using
other array-processing algorithms. Multiple arrays of various sensor types,
each
consisting of multiple sub-arrays may be utilized. Diversity stacking,
adaptive noise
editing, adaptive filtering, coherency filtering, Weiner filtering, and other
methods
exploiting the multiple sensor sub-arrays and arrays, that sample the signal
waves
and noise waves, may be employed. to improve the signal estimate. If desired,
more
sub-arrays with suitable two-dimensional or three-dimensional geometric design
may
be utilized to provide greater redundancy of channels with desired signal and
noise
characteristics to facilitate the signal-to-noise ratio enhancement through
array
processing. For example the sub-arrays could be emplaced over a rectangular
area
in a two-dimensional array with 7 sub-arrays inline and 7 sub-arrays cross-
line for a
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total of 49 sub-arrays. With appropriate processing a better signal estimate
would
result from this augmentation of the sampling effort. The employment of these
multiple sub-arrays, arrays and processing techniques may be viewed as an
effort to
obtain the best possible representation of the true Composite Wavelet.
However under ideal conditions a single sensor could be used rather than the
more elaborate approach described above, and this would be preferred for cost
reasons. With experience, the practitioner can decide what level of effort
will provide
the desired degree of result quality.
The resultant signal estimate, the best available representation of the ideal
noise-free Composite Wavelet 150, is subjected to analysis and further
mathematical
processing to yield determinations of whether the gun fired or misfired,
whether there
was a partial misfire, and if there was a partial misfire, the quantitative
extent of
detonation of the perforating gun.
The connecting cable 200 may be replaced by a radio linkage to the signal
processor and recorder 105 to provide an equivalent method of transferring the
seismic data. Another equivalent method is to record data at each sensor or
group
of sensors and later transmit or transfer it to the central signal processor
and
recorder 105.
An alternative method of configuring the EOD system 115 is presented in Fig
3. Instead of or in addition to placing the seismic sensors at the surface
they are
positioned in a deep borehole 300. This borehole may either be the same
borehole
170 as contains the Perforating Gun 140 or it may be a different but adjacent
borehole. The downhole seismic sensors 330 may be connected to each other and
up the borehole to the surface and to the signal processor and recorder 105 by
a
downhole cable 320. Alternatively they may store their information for later
retrieval.
In this adaptation the seismic wave recordings may be retrieved from the
downhole
seismic sensors after they are returned to the surface, or information may be
transmitted to the surface by other available methods such as EM or borehole
pressure wave telemetry. Similarly to the application of surface sensor sub-
arrays,
multiple downhole sensors may be combined using a wide range of processing
techniques, as described for surface sensors, to enhance the signal-to-noise
ratio of
the signal estimate. The downhole sensors may not be distributed areally but
instead limited to emplacement along a borehole. However, downhole sensors may
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be deployed in multiple boreholes. As in the case for the surface sensors, the
best
combined signal estimate is subjected to further analysis and processing to
determine the success, partial success, or failure of the detonation and to
quantify
the extent-of-detonation.
Fig 5 shows details of the downhole seismic sensors 330 as they are
deployed for use. Individual geophones are contained in cases that have
locking
arms that may be actuated. These locking arms serve to press the sensor
against
the wall of the borehole or casing to improve the coupling of the sensor to
the earth.
Downhole geophones in this configuration are in conventional use in the
industry.
Alternatively, other types of downhole seismic sensors may be employed such as
hydrophones. Mufti-component geophones may be combined with pressure-
sensitive sensors, just as in the surface sensor method.
Because the seismic sensors may be placed closer to the explosion if a
borehole is used, a means of improving the signal-to-noise ratio of the
seismic data is
available via the downhole method, relative to the surface method. Closer
emplacement provides higher seismic energy levels and more high frequency
signal,
but also simplifies the seismic ray path geometry of the seismic energy
arriving at the
sensors, which is beneficial to the methods of this invention. Another
advantage of
downhole emplacement is that the ambient noise level will generally be much
lower
than at the earth surface. Militating against the downhole sensor emplacement
strategy however is the cost of deploying the sensors. This cost is generally
significantly greater than the cost of surface deployment. A compromise
solution is
to place sensors at a shallow depth in boreholes or to simply bury the sensors
just
below the surface
For both surface and downhole emplacement of sensors, the practitioner
should consider the effect that gun-generated noise may have on the directly
arriving
signal events. Positioning of the sensors at a distance such that gun-
generated
noise events do not arrive simultaneously with signal events may require in
some
cases that a minimum distance from the well head be maintained, or in the case
of
borehole sensors, that a minimum distance from the perforating gun to the
sensors
be maintained. This is because high velocity waves traveling up the borehole
may
interfere, or may excite secondary noise modes at or near the well-head, that
can
interfere with the directly arriving waves that travel through the earth.
Experience will
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provide a guide as to when such conditions will exist. The solution is to
place the
sensors beyond this critical minimum distance.
Fig 6 shows the elements of the signal processor and recorder 105 and Fig 7
shows the EOD controller. Both of these devices are essentially computers of
commercially available types. All of the hardware components are of familiar
type
and commercially available. The software and method of use of the EOD
controller
provide the uniqueness of the system.
Referring to Fig 6, seismic signals are input to the device 105 via cable 100
or
300. These may be analog, as assumed in the present figure, or may be digital
having been digitized at or in proximity to the seismic sensors. In the later
case
commands may be sent from the CPU 640 to the online devices controlling the
sensors. If the seismic signals are brought to the device 105 in analog form
as
electrical voltages in the cable, a pre-amplifier 610 amplifies and conditions
the signal
prior to analog-to-digital conversion in the AID converter 620. Digitized
seismic
amplitudes are stored in memory and may be written to physical media such as
tape
by I/O devices 650. Other standard subsystems of the device 105 include power
supply 680, monitor and keyboard 670 and clock 630. The system elements shown
for the signal processor and recorder 105 are present in integrated form in
commercially available PC-based seismic data acquisition systems such as the
ARAM ARIES system manufactured by Geo-X Systems Ltd.
A second computer system is shown in Fig 7 and is designated as the EOD
controller 110. It is networked or otherwise connected to the signal processor
and
recorder 105 as indicated in the Fig 7 or it may be interfaced solely by the
physical
media recorded by the device 105 and control information provided to device
105 by
the EOD controller 110 via physical media.
The EOD controller 110 includes standard types devices as shown: a CPU
720, memory 740, clock 710, I/O devices 730, monitor and keyboard 750 and
power
supply 760. It is shown as linked to the detonation controller 130. The
detonation
controller may be any means for detonating or controlling the detonation of
the
Perforating Gun 140. It may be contained in a single device located in the
proximity
of the wellhead and in communication with the Perforating Gun assembly in
borehole. Alternatively, the detonation controller 130 may be a cooperative
assembly of numerous devices located at both, the well surface and downhole
e.g.
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physically coupled to the Perforating Gun. The EOD controller may utilize any
type
of physical, electronic or electrical linkage, or it may include a
communication linkage
effected by radio, cell phone or other means. The purpose of the linkage is to
avert
the seismic observer so that he may activate the seismic recording at the
correct time
just prior to the detonation of the Perforating Gun and to allow general
coordination of
well activity and seismic activity.
The signal processor and recorder 105 may be combined with the EOD
controller 110 so that only one computer instead of two are required to carry
out the
required activities, as an alternative and equivalent implementation of the
method.
The Perforating Gun 140 is shown in Fig 8. Essential elements of this include
the electrical wire connected at the top of the gun to the detonator 850; the
detonating cord 860, and a series of shaped charges 855. Each shaped charge
855
is provided with a primer explosive charge 870, a case 875, a liner 880, and a
main
explosive charge 890.
Although only four shaped charges are depicted in Fig 8, normally many more
would be contained in a Perforating Gun of the lengths commonly utilized. The
Perforating Gun sections are manufactured such that total gun assembly lengths
varying from a few feet to many hundreds of feet may be achieved. The shaped
charges will typically be uniformly spaced over the entire length of the
active portion
of the gun assembly with less than 1 ft separation between charges. In
perforating
guns designed to perforate multiple zones with intervening zones to be left un-
perforated, there will be portions of the gun with no shaped charges.
Normal practice is to have the detonator 850 positioned at the upper end of
the gun assembly as shown so that detonation is initiated at the upper end. In
this
case the detonation will progress from the detonator along the detonating cord
860 to
successively lower points along the detonating cord until the detonation
ceases.
Each primer explosive charge 870 will be caused to detonate by the detonating
cord
as the detonation front reaches it, unless a misfire occurs. The detonation of
the
primer explosive charge 870 will cause the main explosive charge 890 of its
shaped
charge 855 to detonate.
If the detonation front progresses along the gun without interruption as
intended, each successive shaped charge will be detonated in turn, until the
last
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shaped charge, furthest from the detonator 850, explodes, completing the
detonation
process.
If the detonator 850 fails to detonate when the operator attempts to detonate
it, a 'total misfire' of the Perforating Gun occurs. If the detonator
detonates, but a
misfire interrupts the progression of the detonation front along the
detonating cord
before the last shaped charge is detonated, a 'partial misfire' occurs. If all
shaped
charges detonate including the furthest shaped charge from the detonator, a
'complete firing' or 'successful firing' occurs.
Several types of Perforating Gun assemblies are available in the industry and
various methods of firing Perforating Guns are provided by the industry
practitioners.
The method of this invention is not limited to any particular type of
Perforating Gun
assembly or method of detonation, but can work effectively so long as the
detonation
is initiated at one point at either the top or bottom of the gun and
progresses along
the gun from that point.
Fig 8 indicates three critical parameters of the Perforating Gun: these are
the
position deemed the "top of the gun" 800, the "bottom of the gun" 810" and the
"Gun
Length" 820. The "top of the gun" is defined as the position of the center of
the
uppermost shaped charge along the borehole axis. The "bottom of the gun" is
the
position of the center of the lowermost shaped charge within the borehole.
Both of
these positions are defined in terms of X, Y and Z coordinates of three-
dimensional
space with the Perforating Gun positioned ready for detonation. The "Gun
Length" is
the distance along the borehole axis between the "top of the gun" and "bottom
of the
gun".
Similarly, the position of the seismic receiver is given by the coordinates in
three dimensions of the geometric center of the seismic sensor array aperture
420.
Fig 9 shows the sequence of steps that take place when the perforation
operator notifies the seismic observer of his intent to commence detonation at
a
specified time. The seismic observer activates the EOD system 115 (Fig 1) at
time
to, having already deployed the seismic sensors and tested all of the
subsystems.
Prior to the earliest possible time of the detonation commencement t3 he
causes the
signal processor and recorder 105 to begin to record seismic data, and the
recording
continues from this time t~ onward to ts. The perforation operator takes
action at time
t2 to initiate the detonation process as required by the particular type of
perforation
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system and according to the schedule that has been communicated to the seismic
observer. Sometime later (at t4) the detonation commences, i.e. the detonator
850
detonates. The amount of delay between initiation of the detonation process
and the
instant of detonation commencement is variable depending on the type of firing
system and control system used. In any case the seismic recording process must
be
initiated prior to detonation and continue some time after the detonation of
the
Perforating Gun ceases at ts.
A unique feature of the method of this invention is that it is not a
requirement
that the time of detonation be known in order for the determination of the
extent of
detonation to succeed. Therefore no provision need be made to measure,
determine
or otherwise know that particular instant of time, the moment of detonation.
This
aspect simplifies the field implementation of the recording process because
there
does not have to be an electronic or electrical linkup between the detonation
controller 130 and the EOD system 115.
However if there is a link befinreen the gun firing system and the seismic
recording system, or if both systems are equipped with or have access to
accurate
synchronized clocks or to external time signals such as from GPS satellites,
so that
the instant of detonation is known precisely, a secondary benefit may befall
the
practitioner. The knowledge of exact firing time allows the use of the
perforating gun
seismic recording as a single shot VSP (Vertical Seismic Profile) survey.
Seismic
surveys in the area may be calibrated with and tied to the detonation
recording and
further, to well geology, using this information and methods familiar to those
skilled in
the art. Referring to Fig. 1, if the Detonation Controller 130 controls an
electrical firing
system from the surface, it can be readily linked to the Process Controller
110. This
would facilitate the use of the recorded data for this secondary purpose.
The amount of additional time that must be recorded depends on the distance
between the seismic sensors and the Perforating Gun, the seismic velocity and
other
factors. Normally at least 20 seconds of data would be recorded after the
latest
expected time of detonation. Only the first few hundred msec of data including
the
first arrivals and their immediate aftermath are useful to the inversion
process of this
invention, however additional evidence of the detonation and even the extent
of
detonation of the Perforating Gun may be gleaned from data at times later than
this.
An example of this would be seismic energy caused by later movement of the
gases
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in the borehole, the gases having been generated by the explosion. Such
seismic
energy may arrive by diverse non-direct paths to the seismic sensors and can
be
useful in ascertaining that the detonation did in fact occur.
S Fig 10 illustrates in a cross-sectional view of the Perforating Gun 140 in
the
surrounding earth in four successive stages of detonation and seismic
emanation
from the gun. At ta, as in the prior figure, detonation commences, at the top
of the
gun. Sometime later, at t4.5 the detonation front 1030 has progressed 50% of
the way
along the gun to a position midway along the borehole axis between the top and
the
bottom of the gun. At time t5 the detonation front 1030 has just initiated the
detonation of the bottom-most shaped charge in the Perforating Gun. The
detonation
front 1030 travels along the axis of the Perforating Gun and the nearly co-
located
axis of the borehole itself, at a constant velocity Vd .
This detonation velocity Vd is a characteristic of the particular design of
the
type of Perfora~ng Gun chosen by the operator. It will have been measured in
the
laboratory and is a known quantity. A typical value for Vd is 10 ft per msec.
This is
less than half of the velocity of detonation of the detonating cord 860 that
carries the
detonation front 1030. This reduction in velocity is due to the helical
configuration of
the detonating cord within the Perforating Gun as it descends from shaped
charge to
shaped charge, the shaped charges being located with orientations from 0 to
360
degrees around the Perforating Gun axis. Because the cord typically takes this
indirect path along the gun axis the length of cord required may be more than
twice
the length of the Perforating Gun. This results in the significant lowering of
the
effective detonation velocity as measured along the gun axis, Vd , from the
absolute
detonation velocity along the cord itself, for typical Perforating Guns.
Certain Perforating Guns, however, do not have this type of helical detonating
cord configuration and have instead a more or less straight detonating cord
along the
Perforating Gun axis, either for the whole length of the gun or just for
certain portions
of the gun. These Perforating Gun designs will of course exhibit an effective
detonation velocity that approaches the value of the absolute detonation
velocity of
the detonating cord itself, e.g. greater than 20 ft per msec.
Fig 10 also depicts the seismic wavelet associated with the seismic energy
that propagates from the exploding gun toward the earth surface. The seismic
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waves, of course, propagate in all directions, but only the upward traveling
waves are
considered here. Wave A in Fig 10 is the leading edge of the leading wave
1000, i.e.
the first seismic energy in the seismic wavelet that travels upward from the
first
shaped charge to explode. It progresses upward at a velocity Vr that is the
compressional wave velocity (p wave velocity) of the rock through which it
travels
and will typically be the first energy from the detonation to be received by
the seismic
sensor array.
At time t4,5 the Wave A 1000 will have reached a position well above the top
of
the gun as shown. At this lime the detonation front 1030 has reached a
position
midway along the Perforating Gun. As each shaped charge explodes new seismic
energy is emitted. A quasi-continuous series of seismic wavelets, one from
each
shaped charge, are intermingled as they progress upward. The figure shows the
leading edge of the leading wave from the shaped charge midway along the gun
beginning to form at time t4.5
At time t5 Wave A and following waves have progressed further upward and
the detonation front has progressed further downward and just caused the
bottom-
most shaped charge to explode. Wave B begins to emanate upward at this
instant,
representing the leading edge of the trailing wavelet. No further wavelets are
initiated as the explosive material in the Perforating Gun is now totally
spent.
A short time later at time t5.5 the Wave B has progressed upward to a point
somewhere above the bottom of the gun and Wave C, defined as the trailing edge
of
the trailing wavelet has progressed a short way up from the bottom of the gun.
All of
the waves between A and C continue upward, eventually reach the seismic
sensors
and are recorded as a Composite Wavelet.
This Composite Wavelet 1100 may be viewed as the summation of a set of
individual Basic Wavelets 1210, one from each segment of the Perforating Gun,
with
each successive wavelet delayed by a small amount of time relative to the
prior
wavelet. For a downward propagating detonation and simple geometry, the amount
of the delay is the sum of the time for the detonation to propagate down the
gun to
the next segment plus the seismic travel time from the lower segment to the
upper
segment.
A Gun Segment 2410 may be defined as an arbitrarily small length of the live
portion of the Perforating Gun containing one or more, but an integral number,
of
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shaped charges.. Using this definition, any Perforating Gun may be divided
into a
series of equally-powered Gun Segments (with the possible exception of the
last
segment). Each of the Gun Segments would generate the same Basic Wavelet 1210
under identical conditions of detonation. Figure 24 shows the Perforating Gun
divided
into a set of Gun Segments 2410.
In a constant-velocity host rock environment the Gun Segments 2410 would
generate a series of upward-traveling seismic wavelets of identical form.
These
wavelets in addition to being of identical form would be separated in time
upon
departure from the vicinity of the gun and upon arrival at the seismic
receiver by
equal increments of time. This suggests a method of modeling the Composite
Wavelet 1100 which is used in Fig 11 and subsequent figures, to model
Composite
Wavelets given an arbitrary Basic Wavelet 1210, i.e. the wavelet from one
segment
of the Perforating Gun.
Fig 11 shows Composite Wavelets from five different lengths of Perforating
Gun varying from 13 ft to 320 ft. The autocorrelation of each Composite
Wavelet
appears on the right side of the figure. As the length of the Perforating Gun
increases the appearance gradually changes from that of a fairly simple
wavelet to a
two-part wavelet with a predominately positive first half and a predominately
negative
second half. In fact the second half appears to be the same as the first half
but with
opposite polarity. This is the exact case. The first half of the Composite
Wavelet of a
long perforating gun may be either negative or positive, depending on the
initial
polarity of the Basic Wavelet, but will always be of opposite polarity to the
second
half. The 320 ft gun is also found to have a time delay between the first half
and the
second half exactly equal to the modeled time between the "leading edge of the
leading wave" and the "leading edge of the trailing wave" (see Fig. 10). The
autocorrelation also exhibits a strong negative side lobe peaking at this time
relative
to the zero-lag peak.
Fig 12 provides three examples of Composite Wavelets 1210 of varying
Duration: 6, 24 and 96 msec. Also shown is the Basic Wavelet 1210, which was
summed to yield the Composite Wavelet. The Basic Wavelet is the wavelet from
one
segment of the Perforating Gun. Duration is defined as the time interval
between the
"leading edge of the leading wave" and the "leading edge of the trailing wave"
and
may be computed- in the case of simple vertical geometry- by adding the time
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interval between the detonation of the first Gun Segment and the detonation of
the
last Gun Segment to the seismic travel time between the position of the last
detonating Gun Segment and the position of the first Gun Segment.
The Duration for a given detonation of a given Perforating Gun is a function
of
the position of the seismic sensor array. For a vertical borehole and uniform
geology
the maximum Duration value would be observed at the wellhead. In this case if
the
sensor array is positioned away from the well head the Duration is reduced
eventually to zero at very great distances away from the well head. For non-
vertical
boreholes, the Duration will be maximized at some set of positions away from
the
well-head. Because the determination of EOD is benefited if the Duration can
be
observed at maximum value, the practitioner should consider this when deciding
the
location of the sensor array. Ray-path modeling can guide this decision. A
compromise between maximizing Duration and achieving best signal-to-noise
ratio
may be required in some cases.
Again referring to Fig 12, the 6 msec and 24 msec Duration Composite
Wavelets do not show separation into a first half on one polarity and a second
half of
opposite polarity. This is due to the fact that the Basic Wavelet is too tong
relative to
the Duration to allow this appearance, causing the two parts to overlap.
However the
96 msec Duration Composite Wavelet does show this clear separation into two
opposite polarity halves. The time interval between the leading peak 1220 and
its
negative counterpart, the following trough 1230, is precisely 96 msec, the
exact value
of the Duration.
This suggests a method of determining extent of detonation at least for long
Perforating Guns, that is, guns that are long enough to have good separation
between the leading (first polarity) and trailing (second polarity that is
opposite to first
polarity) halves of the Composite Wavelet. Unfortunately many Perforating Guns
are
not long enough for this to occur. But when the Perforating Gun is
sufficiently long to
provide this separation in its Composite Wavelet, the extent of detonation can
be
estimated this way, providing the geometry and positions of the gun and
seismic
receiver are known, ray path geometry can be modeled, and detonation and
seismic
velocities are known. The time separation between first and second halves of
the
Composite Wavelet may be measured directly or preferably with aid of the
autocorrelation. This time is equated to the sum of detonation propagation
time and
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the differential seismic travel time to the receiver for the first Gun Segment
and the
last Gun Segment. The position of the last Gun Segment that is assumed to
actually
have detonated is varied in the calculations to achieve the best equivalence.
If this
best equivalence is not obtained when calculating for the last physical Gun
Segment
in the Perforating Gun, a partial misfire is thereby determined to have
occurred.
A total misfire can also be conveniently determined using an autocorrelation
meths or by direct observation of the seismic recording. If the
autocorrelation of the
seismic data received after the gun is expected to have fired does not
indicate a
significantly higher level then during a period of known quiescence, total
misfire is
likely to have occurred. Further evidence of a total misfire is the absence of
first
energy on the seismic recording with its predictable delay time from one
seismic sub-
array to the next and its typical waveform and energy pattern as can be
determined
by one experienced in seismic methods.
Figure 25a depicts a seismic recording made with the EOD system 115 with a
typical Surface Seismic Receiver 210 as detailed in Figure 4. In this
recording the
Perforating Gun has detonated and fired successfully. A characteristic seismic
energy pattern appears with successive arrival times as predictable from ray
trace
modeling from nearest to furthest seismic sensor sub-array from the
Perforating Gun.
The seismic energy stands above the level of the seismic noise energy.
Measurement of like wavelet peak and trough times can be used together with
the
ray-path-modeling predicted travel times from the top of the gun to each
seismic sub-
array to determine whether the origination of the seismic energy was at the
location
of the Perforating Gun. While patterns of coherent seismic events may appear
on
the seismic noise recording they do 'not exhibit the arrival time pattern of
the energy
from the location of the Perforating Gun. Neither do they show the wavelet
shape
characteristic of a long Perforating Gun with a first half of one polarity and
a second
half of opposite polarity . Finally, the amplitude levels of the typical
seismic noise do
not reach the amplitude levels of the characteristic energy from the
detonation of the
Perforating Gun. All of these criteria can be used to verify that the observed
seismic
energy is in fact from the Perforating Gun detonation.
Figure 25b shows the seismic recording made during a time period in which a
Perforating Gun was expected to fire. The characteristic seismic energy
pattern from
the Perforating Gun is not evident. Only the amplitudes and energy patterns
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indicative of seismic noise are discemable. From the evidence of the recording
in
Figure 25b a conclusion can be made that the Perforating Gun did not fire.
Only in
the case of very high relative seismic noise levels-sufficiently high to
obscure the
energy from the Perforating Gun- could this conclusion be incorrect.
Experience
can provide a guideline as to what level of seismic noise could obscure the
seismic
energy of a particular Perforating Gun as detected by a given seismic sensor
array.
Thus direct observation and analysis of the seismic energy patterns recorded
by the
EOD system 115 can be used to determine with a high degree of certainty the
occurrence of a total misfire.
Independently of wavelet shape, the amplitude of the Composite Wavelet that
is observed from the detonation of a perforating gun can also give an
indication of
the length of gun that actually detonated. Various measures of amplitude
including,
for example, maximum peak amplitude, rms amplitude, average absolute amplitude
and average power may be used to compare a particular observed Composite
Wavelet to other Composite Wavelets. Referring to Fig. 11, the Composite
Wavelets
for the various gun lengths exhibit a progressive increase from shortest
perforating
gun to longest perforating gun (left side of figure labeled Gun Signatures.)
These
wavelets were modeled to simulate the wavelets that would be observed under
identical physical conditions including geology, type of perforating gun,
position of top
of gun, and type and position of seismic receiver. If another perforating gun
Composite Wavelet for these same conditions, but a different gun length were
modeled, it could be readily compared to the six wavelets and its effective
perforating
gun length computed, interpolating between shorter and longer guns. A
quantitative
estimate of the length of gun that detonated to produce the new Composite
Wavelet
could be thus obtained. Of course, wavelet shape as well as amplitude could be
used together to improve the estimate.
In the case of real observed Composite Wavelets the same procedure could
be applied if comparison wavelets were available. The comparison wavelets
would
preferably have been obtained from identical gun type, at similar depth, under
similar
geologic conditions-it would not be possible to have identical conditions as
in the
model study above. If perforating gun detonations were routinely recorded in a
given
geologic environment, such as within a geologic basin or within an oil field,
a set of
wavelets could be made available for comparison and computation of effective
gun
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length and extent-of detonation as described above for the models. Simple
correction
factors for varying depths, type of perforating gun and other variables can be
applied
to improve the accuracy of the determination. As in the model case, both
wavelet
shape and amplitude can be used separately and in combination to improve the
accuracy of the extent-of detonation computation.
Another method of determining the extent-of detonation of a perforating gun is
next disclosed. This method relies on inversion of the Composite Wavelet
instead of
the previously described observations, comparisons and computations. Like the
methods previously described, the inversion method also relies upon
predetermined
potentials of the Perforating Gun, based on physical conditions, computations,
theoretical predictions and/or actual observations of Composite Wavelets. It
can be
used independently or together with the other methods to give independent
quantitative determinations of the extent-of detonation.
This inversion method of determining extent of detonation can work effectively
when the Perforating Gun is detonated in a portion of a borehole that is
neither
perfectly linear nor perfectly vertical. In many cases the borehole will not
be vertical-
Perforating Guns are often used in horizontal boreholes or boreholes that
represent
less extreme cases of non-verticality but are none the less non-vertical.
Furthermore, the borehole axis is not necessarily a straight line; it may be
curved in
two or three dimensions. A borehole that is curved in three dimensions is
called
herein a curvilinear borehole or a 3D borehole.
One of the assumptions made in constructing the Composite Wavelets of Fig
11 and Fig 12 is that the seismic velocity in the vicinity of the Perforafing
Gun is
constant. This assumption might be good for many cases involving relatively
short
guns, but it would be desirable to have a method that would not rely on such
an
assumption. To be generally applicable and able to deal with medium length and
longer Perforating Guns, a method of determining extent of detonation must be
able
to handle the case of variable seismic velocity in the rock surrounding the
Perforating
Gun .
Such a method combining all of these desirable and essential features has
been invented and demonstrated to work using model data; and is the subject of
the
remainder of this Preferred Embodiment section.
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A two-stage inversion process has been invented that is applied to the
Composite Wavelet that is recorded when the Perforating Gun is detonated. The
first
stage (Stage 1) of the inversion ideally yields an output wavelet (Stage 1
Wavelet)
that is equivalent to the convolution of the Basic Wavelet with a positive
unity spike at
time zero (+1) followed by a negative unity spike (-1) at a time equal to the
Duration
of the Composite Wavelet. Or stated another way, the Stage 1 Wavelet is the
sum of
a positive Basic Wavelet starting at time zero (t=0) and a negative Basic
Wavelet
delayed by the time of the Duration (t=Duration).
This ideal output occurs in the Stage 1 inversion process only under one
crucial condition. That condition is that the process is given the correct
value of
Duration to use. But the practitioner does not know this value, because this
is the
whole objective of the exercise, to learn the actual value of Duration.
Therefore a
series of Stage 1 inversions must be performed, assuming every possible value
of
Duration. The maximum possible Duration corresponds to the detonation of the
entire Perforating Gun. The minimum Duration corresponds to the firing of only
the
very first Gun Segment. The Duration range from maximum to minimum Duration is
sampled at a suitably small interval, for example an interval equivalent to
the
Duration increment caused by adding a single Gun Segment .to the Perforating
Gun.
When the correct actual value of Duration is used in the Stage 1 inversion
process, the ideal output results. For longer guns the Stage 1 output will be
similar in
appearance to a Composite Wavelet from a longer gun. The second half will be a
polarity-reversed repetition of the first half; however, unlike the Composite
Wavelet,
the first half will not be predominately of one polarity (the first polarity)
and neither will
the second half be predominately of one polarity (opposite to the first
polarity). Each
half will have a zero mean, i.e. will be oscillatory around zero amplitude.
For short and medium-length guns, the first half will be overlapped with the
second half, making it difficult to observe the positive and negative Basic
Wavelet
components of the Stage 1 Wavelet. For longer guns it is possible to discern
the
probable correct value of Duration by comparing Stage 1 Wavelets over the
range of
assumed Duration values. For short and medium length guns this is not
possible.
The second stage of the inversion process (Stage 2) is applied to the Stage 1
Wavelet and yields an output that is a single Basic Wavelet starting at time
zero
(t=0), free of all other information. This resolves the problem of
interpreting the
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correct value of Duration for all lengths of Perforating Guns, including short
and
medium length guns.
The Stage 2 inversion assumes the same value of Duration that was assumed
in the Stage 1 inversion and thus the two stages are consistent in this
regard. Thus
S the output wavelets from the finro stages may be displayed on a one-for-one
basis, as
in Fig 13. On the left are shown five Stage 1 wavelets, each for a different
assumed
value of Duration, from 11 msec to 15 msec at 1 msec intervals. On the right
are the
corresponding Stage 2 wavelets.
In the example of Fig 13, the value of Duration used to model the Composite
Wavelet that was input to the inversion process is 13 msec. By careful
observation
one can discern that the Stage 1 wavelet for the 13 msec inversion 1310 is the
most
perfect repetition of positive front half followed by a polarity-reversed
second half.
However, each of the five gives a reasonably good representation of this
appearance, and it would be somewhat challenging to determine the correct
Duration
from this evidence alone.
On the right of Fig 13 the Stage 2 inversion wavelets are displayed. The
Stage 2 wavelet for a Duration assumption of 13 msec 1320, clearly shows the
minimum energy of the five. Its initial wavelet is followed by a quiescent
tail whereas
for other values of Duration, the tail continues to oscillate, even increasing
in
amplitude for Durations of 11 and 15 msec. The Stage 2 wavelets are compared
mathematically and visually by the user to determine the correct value of
Duration for
the detonation that occurred. The correct value, Duration = 13 cosec, is
chosen.
This chosen value of Duration must then be converted to the value of the
length of Perforating Gun that actually detonated. This is done using the
known
values of detonation velocity, seismic velocity and locations of the receiver
and
Perforating Gun, and modeling the seismic ray paths to determine the seismic
travel
times. The first step in this process is to build a Duration Table as
illustrated in Fig
23, containing values of travel time from the center of each Gun Segment to
seismic
receiver and the corresponding values of Duration. These values of Duration
are as
would be observed if the gun misfired after that Gun Segment 2410. The point
of the
misfire 2440 and the Effective Gun Length 2430 are shown on Fig 24.
If Vertical Seismic Profiling (VSP) observations of travel time are available,
they may be used to build the Duration Table. If VSP observations are not
available,
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the values of travel time are preferably obtained by ray tracing, using all
available
information pertaining to the space-time variant seismic velocity field in the
vicinity of
the borehole. In a simplified variation of the method the user may assume
straight
ray path travel which under some conditions, e.g. when velocity is nearly
invariant, is
a sufficiently accurate way to model the ray paths.
Knowing the effective velocity of detonation of the Perforating Gun, Vd , the
following relationship is applied:
Duration=( Ll Vd) + DT Equation 1
Where:
L is the Effective Gun Length 2430 i.e. the length of the gun that
detonates down to the point of the misfire, or bottom of the gun if there is
no
misfire,
Vd is the effective detonation velocity, and
DT is the difference in seismic travel time (to the receiver) for the first
Gun Segment and the last Gun Segment to fire.
Having already determined the chosen actual value of Duration as previously
described, or by using the more general 3D borehole method described
subsequently to determine Duration, the practitioner finds in the Table (Fig
23) the
value of travel time that corresponds to this value of Duration, interpolating
between
values in the table if necessary. Alternately, a specific ray tracing may be
performed
that exactly corresponds to this value of Duration.
In either of these two cases, this value of travel time from the last Gun
Segment and the travel time for the first Gun Segment are differenced to
compute
DT, and the equation rearranged to compute L (~ signifies multiplication).
L=(Duration - DT) =Vd Equation 2
This value, L, is the primary measure of the extent of detonation of the
Perforating Gun, and the objective of all of the preceding and following
described
processes of this invention. A related measure of the extent of detonation is
the
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percentage of the total gun that actually detonated, found by dividing L by
the total
Gun Length and multiplying by 100.
In summary, the length of the Perforating Gun that actually detonated is equal
to the determined value of Duration less the differential seismic travel time
between
the first Gun Segment and the last Gun Segment that detonated and that
quantity
multiplied by the effective detonation velocity Vd of the Perforating Gun.
Because the result is dependent on differential travel time rather than total
travel time the result is not dependent on highly accurate modeling of the
intervening
geology between the top of the gun and the receiver. Only the modeling of ray
paths
in the vicinity of the gun itself must be done accurately. This modeling is
easily and
accurately performed if the seismic velocity field in the vicinity of the
Perforating Gun
has been measured using conventional well logging techniques, as are well
known in
the industry, and has been extrapolated using structural geologic maps as are
typically available for an oil field.
If a VSP seismic survey has previously been performed for the well
undergoing perforation the total seismic travel times will have been
accurately
measured for multiple positions along the borehole, for travel between the
borehole
and selected surface locations. In this case it is recommended that a subset
of the
surface locations be re-occupied for the EOD receiver locations, so that the
accuracy of the ray path modeling may be verified, or adjusted to agree with
observed times, for the total travel path. Modeling parameters may be adjusted
until
a good match is achieved between the modeled travel times and the VSP observed
travel times. Alternatively the modeled times may be simply replaced by the
VSP
observed travel times.
Fig 14 shows results for a different example, a case where the gun is
relatively
short so that the two halves of the Composite Wavelet and of the Stage 1
Wavelet
are heavily overlapped. The top graph of Fig 14 shows the Composite Wavelet
1100, the Stage 1 wavelet 1310 and Stage 2 wavelet 1320 estimated for
Duration=24msec. The middle graph shows the Stage 2 wavelets 1320 for three
differing assumed Durations, 23, 24, and 25 msec. The bottom graph is a plot
of the
RMS amplitude of the tail energy of the Stage 2 wavelets. In this example, the
value
of Duration to build the model was 24 msec. The Stage 2 wavelets have nearly
identical first cycles but are highly divergent for later times. The Stage 2
wavelet for
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Duration=24msec becomes quiescent after a few oscillations but the neighboring
wavelets are highly oscillatory, exhibiting distorted unstable tail energy.
The RMS
Amplitude graph shows a very distinct minimum 1410 at the correct value of
Duration=24 msec. Thus the process is very well able to find both
mathematically
(by power computation) and by visual evidence (wavelet shape) the correct
value of
Duration. By virtue of this finding, the length of the Perforating Gun that
actually
detonated can be readily calculated as previously described.
Fig 15 shows a similar modeled example, in which a much smaller value of
Duration was assumed, 6 msec. This case is more challenging to the method,
because of the extreme overlap in the Composite Wavelet and Stage 1 wavelet,
i.e.
the gun is very short. The three graphs of Fig 14 corresppnd to the three
graphs of
Fig 13. Less difference is observed among the three Stage 2 wavelets in the
middle
graph. The Duration=6 wavelet from Stage 2 is more stable and exhibits less
high-
frequency distortion than its neighbors, but the difference is less pronounced
than in
the previous case. The RMS Amplitude graph shows a minimum 1410 at 6 cosec but
it is not as well resolved as previously. Thus the method works, but not as
powerfully
and with not as much resolution for the very short Duration Perforating Gun.
In
general one can expect the medium and longer Perforating Gun wavelets to be
better resolved through this process than the wavelets from short guns. This
translates to a better resolution of extent of detonation for the longer guns.
Optimal
location of the seismic receiver increases the Duration of the Composite
Wavelet for
a given detonation and should be considered as a method of increasing
resolution by
the practiitioner.
In Fig 16 the effect of seismic noise on the inversion process is studied. In
practical cases there will be some amount of seismic noise remaining in the
final
estimate of the true Composite Wavelet. The model used for Fig 14 was modified
by
the addition of random noise and again processed through the two stages of
inversion. Noise appears together with signal in the Stage 1 wavelet 1310 and
Stage
2 wavelets 1320. The RMS Amplitude graph shows a minimum at 23 cosec instead
of 24 cosec, the correct value of Duration. Thus the noise has caused a small
error in
the Duration calculated by the process. Curve-fitting to the RMS Amplitude
values
can reduce the effect of the noise and allow the correct value, 24 cosec, to
be
calculated in this case.
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Seismic noise may be reduced using well-designed arrays and sub-arrays of
seismic receivers, positioning receivers in closer proximity to the
Perforating Gun,
positioning receivers at sufficiently great distance to avoid gun-generated
noise
interfering with signal and by using signal processing methods as previously
described to reduce the effects of seismic noise and enhance the signal
estimate.
The inversion method may be performed in the manner next described. The
inversion method is applied to the final estimate of the true Composite
Wavelet
defined previously. The basis of the method is the assumption that the
Composite
Wavelet is the sum of Basic Wavelets from a series of Gun Segments, the
Perforating Gun being arbitrarily divided into a series of these uniform
segments,
each containing an identical or at least substantially similar set of
explosive
components, with the possible exception of the last gun segment.
First considering a simple model in which the Perforating Gun is vertical, the
rock is of constant seismic velocity, and the receiver is vertically above the
Perforating Gun, it can be easily seen that the Composite Wavelet is a sum of
Basic
Wavelets with each Basic Wavelet delayed slightly relative to the one from the
previous Gun Segment. The first sample of the Composite Wavelet is simply
equal to
the first sample of the Basic Wavelet. Knowing this, the second sample of the
Basic
Wavelet can be computed by subtracting the first value of the Basic Wavelet
from the
second value of the Composite Wavelet. Now the first two samples in the Basic
Wavelet are known. The process can be continued for the whole Composite
Wavelet
until an assumed value of Duration is reached and then discontinued. The
result will
be a pure Basic Wavelet followed by a negative copy of the Basic Wavelet
starting at
the time of the Duration of the Composite Wavelet if the assumed value of
Duration
was correct.
Each possible value of Duration will be tried through this same process and
the results compared. The outputs of the first stage of the inversion are
called Stage
1 Wavelets. These Stage 1 Wavelets will also become the inputs to the Stage 2
inversion; the Stage 2 inversion will use the same assumed value of Durafion
as was
used to obtain that particular Stage 1 result.
No assumptions have been made as to the shape or length of the Basic
Wavelet to obtain the Stage 1 Wavelet nor will any be made in performing the
Stage
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2 inversion. Thus this invention does not require a priori knowledge of
wavelet
characteristics.
The foregoing process is the Stage 1 of the inversion method as appropriate
for the simple case of straight vertical borehole and constant seismic
velocity. It
works by virtue of the fact that the first sample of the first Basic Wavelet
is un-
obscured. This allows a successive stripping away of overlying information to
eventually reveal the Basic Wavelet summed with a delayed polarity-reversed
version of itself, if the Duration assumption was correct. If this assumption
was
incorrect, the output will have a larger RMS amplitude and asymmetry compared
to
the result obtained when the correct assumption was made.
The Stage 2 inversion process is applied to the Stage 1 result, and if the
Duration assumption is correct will yield the simple and pure Basic Wavelet.
Otherwise the symptoms of incorrect Duration assumption including higher RMS
Amplitude and unstable or high frequency tail amplitudes will be observed.
The Stage 2 inversion is very simple and is accomplished by subtracting
sample by sample the early amplitudes of the Stage 1 inversion from the later
Stage
1 amplitudes with a delay equal to the assumed Duration. The process continues
from the first modified amplitude, at a time equal to the Duration, to a time
substantially greater than the predicted total time of the Basic Wavelet. In
the Stage
2 inversion after time equals twice the Duration the already-corrected Stage 2
value
(rather than the corresponding Stage 1 amplitude) is used to subtract from the
next
Stage 1 value; thus the Stage 2 inversion iterates once for times greater than
twice
the Duration.
The definition of the portion of the Perforating Gun that constitutes one Gun
Segment 2410 is conveniently done by choosing the portion of gun that will
have its
Basic Wavelet separated from those of adjacent Gun Segments by one unit time
sample. The size of the Gun Segment chosen should be suitably small relative
to the
bandwidth of the seismic signal received and recorded. For example if 1 msec
recording sample period is suitable for the seismic signal, then the Gun
Segment
size should be chosen such that adjacent Basic Wavelets 1320 within the
Composite
Wavelet 1100 are separated by 1 msec or less. For a detonation velocity of
10,000
fps and a seismic velocity of 8000 fps, the Gun Segment would be 4.44 ft to
conform
to 1 msec sampling. This result is obtained by determining the Duration of the
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Composite Wavelet for an assumed Gun Length as described earlier, and dividing
the Gun Length by the Duration. The Gun Segment Length may be set at a shorter
interval to make it contain an integral and invariant number of shaped charges
for
every Gun Segment in the Perforating Gun to avoid issues of variable number of
shaped charges in various Gun Segments.
Next, the more general case of inversion of a Composite Wavelet from a
curvilinear borehole in rock of variable seismic velocity is described
In this case the ray paths and the corresponding seismic travel times from the
center of each of the Gun Segments to the receiver are first calculated. This
may be
done using various modeling methods in use within the industry. Preferably
three-
dimensional earth models, derived from all available sources of subsurface
information, e.g. from drilling, well logging and prior seismic surveys, will
be used,
together with the coordinates of the Gun Segments and the receiver. The
detonation
velocity for the Perforating Gun is also used, as obtained from prior testing
of an
identical Perforating Gun. The seismic travel time for each Gun Segment is
added to
its detonation delay, relative to the first Gun Segment at time zero (t=0) to
give the
Arrival Time at the receiver for each Gun Segment.
This array of Arrival Times is used to calculate a quantity defined as Pulse
Density. Pulse Density is simply the number of pulses arriving at the receiver
per
unit of time relative to the number of pulses arriving in the first sample of
the
Composite Wavelet. If, for example, the first sample in the Composite Wavelet
results from the Basic Wavelet first arrival of the first Gun Segment only,
and a later
sample of the Composite Wavelet is the sum of first arrivals from two Gun
Segments
(due to hole curvature, ray path geometry, etc.) that later sample is said to
have a
Pulse Density of two (2). This convention is arbitrary but it makes possible a
convenient adaptation of the previously described inversion method to account
for
the general case. It also takes advantage the equivalence between sampling
density
and amplitude of a function. This equivalence enables the replacement (in the
representation of a combined sampled function) of a pair of simultaneous equal
sampled values with a single sampled value of twice the amplitude. Using this
relationship the Composite Wavelet can be represented by one sample per unit
time
by accounting for multiple coincident Basic Wavelets originating within one
time
sample- by modifying amplitude with the Pulse Density.
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A series of Pulse Density values are derived, one per unit time increment,
which is equal to the number of Basic Wavelets having the same Arrival Time at
the
receiver for that time increment of sampled Arrival Time. The Arrival Times
fully
account for borehole curvature in 3 dimensions and the space-time variant
seismic
velocity field between the Perforating Gun and the receiver, being based on
ray path
calculations or VSP observations, as well as the time delay incurred for
propagation
of the detonation front along the Perforating Gun. For perforating guns with
non-
uniform charge distribution and/or with variable detonation velocity along the
axis of
the gun, the Arrival Times can be calculated accordingly and thereby allow the
Pulse
Density to account for these factors. Perforating guns of this type are
commonly
used when multiple zones are to be perforated with intervening zones to be
left un-
perforated. Such guns may be constructed such that they exhibit variable
detonation
velocity along the gun axis.
Amplitudes of the Basic Wavelets are affected by spherical divergence loss,
absorption and transmission losses during their travel from the originating
Gun
Segments to the receiver. These losses are different for each Gun Segment due
to
varying distance of travel and differing absorption and transmission losses
due to
passage through differing rock. These loss mechanisms may not cause
significant
variation among the Basic Wavelets for relatively short Perforating Guns that
are far
from the receiver, however for longer guns and shorter travel paths, the
differences
are significant and must be accounted for in the inversion process.
The spherical divergence, absorption and transmission losses expected to be
incurred may be calculated through a seismic modeling process using techniques
familiar to those skilled in seismic processing and modeling. Alternatively
they may
be measured directly from seismic recordings made in a VSP survey. These
losses,
one value per Gun Segment, may conveniently be multiplied by the Pulse Density
values to compute Modified Pulse Density values. These values are then
normalized
by dividing each Gun Segment's Modified Pulse Density value by the value for
the
first Gun Segment. This normalizing method ensures that the complete inversion
process, including Stage 1 and Stage 2, is a true amplitude process. The
normalization is effected by dividing the initial Modified Pulse Density, for
the first
Gun Segment, into each of the Modified Pulse Density values. These Normalized
Modified Pulse Density Values are termed 'Weights'.
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In the Stage 1 inversion process of the invention, using the Normalized
Modified Pulse Density Values as is next described, the effects of amplitude
losses
due to the listed causes, will be fully accommodated and therefore cause no
errors in
the calculation of the Stage 1 Wavelet.
To prepare for the Stage 1 Inversion, the normalized Modified Pulse Density
values are converted to what is termed Adjustment Factors as follows:
~; _ [(MPD); -1] * (-1 ) Equation 3
Where:
[i; is the it" Adjustment Factor and
(MPD), is the it" Normalized Modified Pulse Density.
The general expression for the Stage 1 inversion calculation for a point along
the solution diagonal 1900 of Fig 19 is
Equation 4
Y"", _ ['A(n-1 )'" - 'A(n-1 )'n.~J + (io ~ Xo + E3~ ~ X~ + (32 ~ X2 + ...
... + (i".~ ~ 'A(n-1 )'a + ~ "-2 t'A(n-1 )'2 + ~ ".~ _ 'A(n-1 )'~
Where:
n is the index of the point on the solution diagonal 1900 and also of the
output sample of the Stage 1 Wavelet;
m is the assumed Duration in units of time;
'A(n-1)' is A, the first column in the solution matrix when n=2; B, the
second column for n=3, etc.
A" is the value in the solution matrix in column A, row n.
~o~ ~~, a2 ~ ... , [i"-~ are the Adjustment Factors;
A1 , B~ , C~ ... contain the Composite Wavelet; and:
Xo = 'A(n-1)'" + 'A(n-1)'"a" +'A(n-1)'"_2m +...continuing until (n-i~m)
goes negative
X~ _ 'A(n-1)'"_~ + 'A(n-1)'n~m+~~ +'A(n-1)'n~zm+~~ +... continuing until n-
i*m +1 ) goes negative;
CA 02474911 2004-07-30
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X2 = 'A(n-1 )'".2 + 'A(n-1 )'".gym+2~ +'A(n-1 )'".~2m+2) +...continuing until
n-
i=m +2) goes negative;
and so on continuing the Xi series until the initial term subscript becomes
negative.
Summarizing Equation 4, Y"m is the n~' amplitude of the Stage 1 Wavelet for
an assumed Duration of m time units.
Equation 4 is used to calculate amplitude values of the Stage 1 Wavelet
progressively, starting with the second value and continuing to the final
value. The
position of the final value is set arbitrarily but so as to include the entire
significant
portion of the Stage 1 Wavelet. The first amplitude value of the Stage 1
Wavelet is
always set exactly equal to the first amplitude value of the Basic Wavelet,
A1.
This is done because the initial value is not obscured by later arrivals and
because the initial Adjustment Factor is always zero, because of the
normalization
process previously described. It can be seen that it is essential that the
initial value of
the Composite Wavelet must remain unmodified if the process is to preserve
true
amplitudes, because this value is also the initial value of the un-obscured
Basic
Wavelet.
The solution diagonal 1900 is computed progressively from first point (upper
left) to last point (lower right). Values in the matrix at times later than
the solution
point are calculated by subtracting from the prior value, the prior solution
value at the
solution diagonal.
Figure 22a shows examples of the equations that apply for typical points
along the solution diagonal for a case in which the Duration has been assumed
to be
3 time units (m=3). The illustrated calculations along the diagonal are all
based on
expansion of the general Equation 4 from n=2 to n=7. For higher values of n
the
calculations would proceed in the same manner, with increasing numbers of
terms.
Figure 22b shows examples of the equations that apply for points in the matrix
away from the solution diagonal. Of particular importance are the calculations
in the
cells below the solution diagonal 1900. Note that as each successive value of
the
Stage 1 Wavelet is completed it is next subtracted from all values in the
previous
partial solution. This in effect gradually strips away overlying information
to reveal
the sought Stage 1 Wavelet, point by point. The right hand column contains the
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same values as have emerged along the solution diagonal, which comprise the
Stage 1 Wavelet.
Using Equation 4 and the other relationships previously described for
implementing the solution matrix, any curvilinear borehole in a variable
seismic
velocity medium may be inverted to reveal the Stage 1 wavelet as previously
described for the simpler cases.
No revision to the previously described process is required for the Stage 2
inversion to accommodate the general case of the three-dimensional borehole.
To demonstrate the application of the generalized method to model data, Fig
18 shows two Composite Wavelets for a curvilinear borehole, calculated using
two
different methods. The Pulse Density Method yields Composite Wavelet 1800 and
a
simple time-shift method yields Composite Wavelet 1810. Small differences are
observed in the two wavelets and these are due to small errors in the
interpolation
method used (linear) rather than to any flaw in the Pulse Density general
method.
These Composite Wavelets were processed through the generalized inversion
process based on Equation 4.
The results of Stage 1 of the generalized inversion are shown in Fig 19a 19b
and 19c. The solution emerges along the solution diagonal 1900. In Fig 19c the
final
Stage 1 result appears 1910. The Stage 2 result 1920 appears to the right.
These
results are graphed in Fig 20. The Stage 2 result 1920 perfectly reproduces
the
model wavelet used to build the Composite Wavelet that was input to the
inversion
process. The correct value of Duration, 13 msec, yields the lowest RMS
Amplitude
value 1410 as observed on the graph, confirming the choice one would make from
comparing the Basic Wavelets calculated for assumed Duration values of 12, 13
and
14 msec.
The calculations of Fig 19 and the results shown in Fig 20 are obtained from
the input Composite Wavelet 1800 formed using the Pulse Density method to
simulate the wavelet that would be recorded in the real case. Fig 21 shows the
inversion results from the time-shift Composite Wavelet 1810 and using the
same
generalized inversion method as illustrated in Fig 19 and Fig 20.
The resultant Basic Wavelet 2120 shows nearly identical form to Basic
Wavelet 1920, but with small tail amplitudes instead of zeroes. A sharp
minimum in
RMS Amplitude is in evidence at the correct Duration, 13 msec. Thus the
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generalized inversion method works well on the Composite Wavelet generated
using
a difFerent set of assumptions than the inversion method itself.
An alternate r~thod of performing the inversion processing is to bypass the
Stage 1 inversion step and perform the Stage 2 inversion on the best estimate
of the
true Composite Wavelet. The Stage 2 result by itself yields a stable decaying
wavelet at the correct Duration, with the difference that the output is not a
single
Basic Wavelet but the summation of a series of Basic Wavelets over the
Duration.
The output of the Stage 2 inversion can be subjected to visual and
mathematical
analysis as previously described to find the best estimate of Duration and
extent-of
detonation of the perforating gun. An advantage of this approach is that the
Stage 2
inversion may be more robust in the presence of seismic noise than is the
Stage 1
inversion. Both approaches may be tried and compared in practice.
Further, in this alternative approach, the Stage 1 inversion may be applied to
the Stage 2 output. Thus the order of the stages may be reversed. In the ideal
noise-free case the interpreted results would be identical.
Yet another viable model-based method of determining the extent-of
detonation is to compute synthetic Composite Wavelets such as illustrated in
Fig.11
and to compute best fit to the real Composite Wavelet estimate. An assumed
Basic
Wavelet can be summed repetitively with appropriate time delays for the
physical
environment and position of the perforating gun. The assumed Basic Wavelet may
be judiciously chosen from actual recorded prior detonations under similar
conditions, obtained from inversion according to the present invention from
prior
detonations, or otherwise provided. Various assumptions of extent-of-
detonafion can
be used to compute corresponding synthetic Composite Wavelets. The synthetic
Composite Wavelets are then compared to the real Composite Wavelet (best
estimate of true Composite Wavelet). The method of comparison can be variously
chosen ranging from visual comparison, differencing, power calculations, Least-
Mean-Square Error (LSME) fit measurement, spectral fit and other methods.
Other mathematical methods of performing the generalized inversion may be
substituted by those skilled in the mathematical arts.
While preferred embodiments of this invention have been shown and
described, modifications thereof can be made by one skilled in the art without
departing from the spirit or teaching of this invention. The embodiments
described
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herein are exemplary only and are not limiting. Many variations and
modifications of
the system and apparatus are possible and are within the scope of the
invention.
Accordingly, the scope of protection is not limited to the embodiments
described
herein, but is only limited by the clairr~ that follow, the scope of which
shall include all
equivalents of the subject matter of the claims.
34
