Note: Descriptions are shown in the official language in which they were submitted.
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MODELING OF INTERACTION OF HYDRAULIC
FRACTURES IN COMPLEX FRACTURE NETWORKS
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims priority to US Provisional Application No.
61/900,479, filed on
November 6, 2013, the entire contents of which is hereby incorporated by
reference herein. This
application is a continuation-in-part of US Patent Application No. 11/356,369,
filed on
November 2, 2012, the entire contents of which is hereby incorporated by
reference herein.
BACKGROUND
[0002] The present disclosure relates generally to methods and systems for
performing wellsite
operations. More particularly, this disclosure is directed to methods and
systems for performing
fracture operations, such as investigating subterranean formations and
characterizing hydraulic
fracture networks in a subterranean formation.
[0003] In order to facilitate the recovery of hydrocarbons from oil and gas
wells, the
subterranean formations surrounding such wells can be hydraulically fractured.
Hydraulic
fracturing may be used to create cracks in subsurface formations to allow oil
or gas to move
toward the well. A formation is fractured by introducing a specially
engineered fluid (referred to
as "fracturing fluid" or "fracturing slurry" herein) at high pressure and high
flow rates into the
formation through one or more wellbores. Hydraulic fractures may extend away
from the
wellbore hundreds of feet in two opposing directions according to the natural
stresses within the
formation. Under certain circumstances, they may form a complex fracture
network. Complex
fracture networks can include induced hydraulic fractures and natural
fractures, which may or
may not intersect, along multiple azimuths, in multiple planes and directions,
and in multiple
regions.
[0004] Current hydraulic fracture monitoring methods and systems may map where
the fractures
occur and the extent of the fractures. Some methods and systems of
microseismic monitoring
may process seismic event locations by mapping seismic arrival times and
polarization
information into three-dimensional space through the use of modeled travel
times and/or ray
paths. These methods and systems can be used to infer hydraulic fracture
propagation over time.
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[0005] Patterns of hydraulic fractures created by the fracturing stimulation
may be complex and
may form a fracture network as indicated by a distribution of associated
microseismic events.
Complex hydraulic fracture networks have been developed to represent the
created hydraulic
fractures. Examples of fracture models are provided in US Patent/Application
Nos. 6101447,
7363162, 7788074, 20080133186, 20100138196, and 20100250215.
SUMMARY
[0006] In at least one aspect, the present disclosure relates to methods of
performing a fracture
operation at a wellsite. The wellsite is positioned about a subterranean
formation having a
wellbore therethrough and a fracture network therein. The fracture network has
natural fractures
therein. The wellsite may be stimulated by injection of an injection fluid
with proppant into the
fracture network. The method involves obtaining wellsite data comprising
natural fracture
parameters of the natural fractures and obtaining a mechanical earth model of
the subterranean
formation and generating a hydraulic fracture growth pattern for the fracture
network over time.
The generating involves extending hydraulic fractures from the wellbore and
into the fracture
network of the subterranean formation to form a hydraulic fracture network
including the natural
fractures and the hydraulic fractures, determining hydraulic fracture
parameters of the hydraulic
fractures after the extending, determining transport parameters for the
proppant passing through
the hydraulic fracture network, and determining fracture dimensions of the
hydraulic fractures
from the determined hydraulic fracture parameters, the determined transport
parameters and the
mechanical earth model. The method also involves performing stress shadowing
on the
hydraulic fractures to determine stress interference between the hydraulic
fractures at different
depths, performing an additional stress shadowing on the hydraulic fractures
to determine stress
interference between the hydraulic fractures at different depths, and
repeating the generating
based on the determined stress interference. The method may also include
analyzing stress
interference between hydraulic fractures to evaluate the height growth of each
fracture.
[0007] The performing stress shadowing may involve performing a first stress
shadowing to
determine interference between the hydraulic fractures and/or performing a
second stress
shadowing to determine interference between the hydraulic fractures at
different depths. The
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performing stress shadowing may involve performing a two dimensional
displacement
discontinuity method and/or performing a three dimensional displacement
discontinuity method.
[0008] If the hydraulic fracture encounters a natural fracture, the method may
also involve
determining the crossing behavior between the hydraulic fractures and an
encountered fracture
based on the determined stress interference, and the repeating may involve
repeating the
generating based on the determined stress interference and the crossing
behavior. The method
may also involve stimulating the wellsite by injection of an injection fluid
with proppant into the
fracture network.
[0009] The method may also involve, if the hydraulic fracture encounters a
natural fracture,
determining the crossing behavior at the encountered natural fracture, and
wherein the repeating
comprises repeating the generating based on the determined stress interference
and the crossing
behavior. The fracture growth pattern may be altered or unaltered by the
crossing behavior. A
fracture pressure of the hydraulic fracture network may be greater than a
stress acting on the
encountered fracture, and the fracture growth pattern may propagate along the
encountered
fracture. The fracture growth pattern may continue to propagate along the
encountered fracture
until an end of the natural fracture is reached. The fracture growth pattern
may change direction
at the end of the natural fracture, and the fracture growth pattern may extend
in a direction
normal to a minimum stress at the end of the natural fracture. The fracture
growth pattern may
propagate normal to a local principal stress according to the stress
shadowing.
[0010] The stress shadowing may involve performing displacement discontinuity
for each of the
hydraulic fractures. The stress shadowing may involve performing stress
shadowing about
multiple wellbores of a wellsite and repeating the generating using the stress
shadowing
performed on the multiple wellbores. The stress shadowing may involve
performing stress
shadowing at multiple stimulation stages in the wellbore.
[0011] The method may also involve validating the fracture growth pattern. The
validating may
involve comparing the fracture growth pattern with at least one simulation of
stimulation of the
fracture network. The method may also involve adjusting the stimulating (e.g.,
pumping rate
and/or fluid viscosity) based on the stress shadowing.
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[0012] The extending may involve extending the hydraulic fractures along a
fracture growth
pattern based on the natural fracture parameters and a minimum stress and a
maximum stress on
the subterranean formation. The determining fracture dimensions may include
one of evaluating
seismic measurements, ant tracking, sonic measurements, geological
measurements and
combinations thereof The wellsite data may include at least one of geological,
petrophysical,
geomechanical, log measurements, completion, historical and combinations
thereof The natural
fracture parameters may be generated by one of observing borehole imaging
logs, estimating
fracture dimensions from wellbore measurements, obtaining microseismic images,
and
combinations thereof
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] Embodiments of the system and method for characterizing wellbore
stresses are
described with reference to the following figures. The same numbers are used
throughout the
figures to reference like features and components.
[0014] Fig. 1.1 is a schematic illustration of a hydraulic fracturing site
depicting a fracture
operation;
[0015] Fig. 1.2 is a schematic illustration of a hydraulic fracture site with
microseismic events
depicted thereon;
[0016] Fig. 2 is a schematic illustration of a 2D fracture;
[0017] Figs. 3.1 and 3.2 are schematic illustrations of a stress shadow
effect;
[0018] Fig. 4 is a schematic illustration comparing 2D DDM and Flac3D for two
parallel straight
fractures;
[0019] Figs. 5.1-5.3 are graphs illustrating 2D DDM and Flac3D of extended
fractures for
stresses in various positions;
[0020] Figs. 6.1-6.2 are graphs depicting propagation paths for two initially
parallel fractures in
isotropic and anisotropic stress fields, respectively;
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[0021] Figs. 7.1-7.2 are graphs depicting propagation paths for two initially
offset fractures in
isotropic and anisotropic stress fields, respectively;
[0022] Fig. 8 is a schematic illustration of transverse parallel fractures
along a horizontal well;
[0023] Fig. 9 is a graph depicting lengths for five parallel fractures;
[0024] Fig. 10 is a schematic diagram depicting UFM fracture geometry and
width for the
parallel fractures of Figure 9;
[0025] Figs. 11.1-11.2 are schematic diagrams depicting fracture geometry for
a high perforation
friction case and a large fracture spacing case, respectively;
[0026] Fig. 12 is a graph depicting microseismic mapping;
[0027] Figs. 13.1-13.4 are schematic diagrams illustrating a simulated
fracture network
compared to the microseismic measurements for stages 1-4, respectively;
[0028] Figs. 14.1-14.4 are schematic diagrams depicting a distributed fracture
network at various
stages;
[0029] Fig. 15 is a flow chart depicting a method of performing a fracture
operation; and
[0030] Figs. 16.1-16.4 are schematic illustrations depicting fracture growth
about a wellbore
during a fracture operation.
[0031] Fig. 17 is a schematic diagram showing a coordinate system attached to
a rectangular 3D
DDM element.
[0032] Figs. 18-20 are schematic diagrams showing two vertical fractures at
different depths and
affecting each fracture's height growth due to stress shadowing.
[0033] Fig. 21 is a flow chart depicting another method of performing a
fracture operation.
DETAILED DESCRIPTION
[0034] The description that follows includes exemplary apparatuses, methods,
techniques, and
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instruction sequences that embody techniques of the inventive subject matter.
However, it is
understood that the described embodiments may be practiced without these
specific details.
[0035] Models have been developed to understand subsurface fracture networks.
The models
may consider various factors and/or data, but may not be constrained by
accounting for either the
amount of pumped fluid or mechanical interactions between fractures and
injected fluid and
among the fractures. Constrained models may be provided to give a fundamental
understanding
of involved mechanisms, but may be complex in mathematical description and/or
require
computer processing resources and time in order to provide accurate
simulations of hydraulic
fracture propagation. A constrained model may be configured to perform
simulations to consider
factors, such as interaction between fractures, over time and under desired
conditions.
[0036] An unconventional fracture model (UFM) (or complex model) may be used
to simulate
complex fracture network propagation in a formation with pre-existing natural
fractures.
Multiple fracture branches can propagate simultaneously and intersect/cross
each other. Each
open fracture may exert additional stresses on the surrounding rock and
adjacent fractures, which
may be referred to as "stress shadow" effect. The stress shadow can cause a
restriction of
fracture parameters (e.g., width), which may lead to, for example, a greater
risk of proppant
screenout. The stress shadow can also alter the fracture propagation path and
affect fracture
network patterns. The stress shadow may affect the modeling of the fracture
interaction in a
complex fracture model.
[0037] A method for computing the stress shadow in a complex hydraulic
fracture network is
presented. The method may be performed based on an enhanced 2D Displacement
Discontinuity
Method (2D DDM) with correction for finite fracture height or 3D Displacement
Discontinuity
Method (3D DDM). The computed stress field from 2D DDM may be compared to 3D
numerical
simulation (3D DDM or flac3D) to determine an approximation for the 3D
fracture problem.
This stress shadow calculation may be incorporated in the UFM. The results for
simple cases of
two fractures shows the fractures can either attract or expel each other
depending, for example,
on their initial relative positions, and may be compared with an independent
2D non-planar
hydraulic fracture model. Stress shadowing may also be provided, using for
example 3D DDM,
to take into consideration interaction of fractures at different depths.
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[0038] Additional examples of both planar and complex fractures propagating
from multiple
perforation clusters are presented, showing that fracture interaction may
control the fracture
dimension and propagation pattern. In a formation with small stress
anisotropy, fracture
interaction can lead to dramatic divergence of the fractures as they may tend
to repel each other.
However, even when stress anisotropy is large and fracture turning due to
fracture interaction is
limited, stress shadowing may have an effect on fracture width, which may
affect the injection
rate distribution into multiple perforation clusters, and hence overall
fracture network geometry
and proppant placement.
[0039] Figures 1.1 and 1.2 depict fracture propagation about a wellsite 100.
The wellsite has a
wellbore 104 extending from a wellhead 108 at a surface location and through a
subterranean
formation 102 therebelow. A fracture network 106 extends about the wellbore
104. A pump
system 129 is positioned about the wellhead 108 for passing fluid through
tubing 142.
[0040] The pump system 129 is depicted as being operated by a field operator
127 for recording
maintenance and operational data and/or performing the operation in accordance
with a
prescribed pumping schedule. The pumping system 129 pumps fluid from the
surface to the
wellbore 104 during the fracture operation.
[0041] The pump system 129 may include a water source, such as a plurality of
water tanks 131,
which feed water to a gel hydration unit 133. The gel hydration unit 133
combines water from
the tanks 131 with a gelling agent to form a gel. The gel is then sent to a
blender 135 where it is
mixed with a proppant from a proppant transport 137 to form a fracturing
fluid. The gelling
agent may be used to increase the viscosity of the fracturing fluid, and to
allow the proppant to
be suspended in the fracturing fluid. It may also act as a friction reducing
agent to allow higher
pump rates with less frictional pressure.
[0042] The fracturing fluid is then pumped from the blender 135 to the
treatment trucks 120 with
plunger pumps as shown by solid lines 143. Each treatment truck 120 receives
the fracturing
fluid at a low pressure and discharges it to a common manifold 139 (sometimes
called a missile
trailer or missile) at a high pressure as shown by dashed lines 141. The
missile 139 then directs
the fracturing fluid from the treatment trucks 120 to the wellbore 104 as
shown by solid line 115.
One or more treatment trucks 120 may be used to supply fracturing fluid at a
desired rate.
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[0043] Each treatment truck 120 may be normally operated at any rate, such as
well under its
maximum operating capacity. Operating the treatment trucks 120 under their
operating capacity
may allow for one to fail and the remaining to be run at a higher speed in
order to make up for
the absence of the failed pump. A computerized control system 149 may be
employed to direct
the entire pump system 129 during the fracturing operation.
[0044] Various fluids, such as conventional stimulation fluids with proppants,
may be used to
create fractures. Other fluids, such as viscous gels, "slick water" (which may
have a friction
reducer (polymer) and water) may also be used to hydraulically fracture shale
gas wells. Such
"slick water" may be in the form of a thin fluid (e.g., nearly the same
viscosity as water) and may
be used to create more complex fractures, such as multiple micro-seismic
fractures detectable by
monitoring.
[0045] As also shown in Figures 1.1 and 1.2, the fracture network includes
fractures located at
various positions around the wellbore 104. The various fractures may be
natural fractures 144
present before injection of the fluids, or hydraulic fractures 146 generated
about the formation
102 during injection. Figure 1.2 shows a depiction of the fracture network 106
based on
microseismic events 148 gathered using conventional means.
[0046] Multi-stage stimulation may be the norm for unconventional reservoir
development.
However, an obstacle to optimizing completions in shale reservoirs may involve
a lack of
hydraulic fracture models that can properly simulate complex fracture
propagation often
observed in these formations. A complex fracture network model (or UFM), has
been developed
(see, e.g., Weng, X, Kresse, 0., Wu, R., and Gu, H., Modeling of Hydraulic
Fracture
Propagation in a Naturally Fractured Formation. Paper SPE 140253 presented at
the SPE
Hydraulic Fracturing Conference and Exhibition, Woodlands, Texas, USA, January
24-26
(2011) (hereafter "Weng 2011"); Kresse, 0., Cohen, C., Weng, X, Wu, R., and
Gu, H. 2011
(hereafter "Kresse 2011"). Numerical Modeling of Hydraulic Fracturing in
Naturally Fractured
Formations. 45th US Rock Mechanics/Geomechanics Symposium, San Francisco, CA,
June 26-
29, the entire contents of which are hereby incorporated herein).
[0047] Existing models may be used to simulate fracture propagation, rock
deformation, and
fluid flow in the complex fracture network created during a treatment. The
model may also be
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used to solve the fully coupled problem of fluid flow in the fracture network
and the elastic
deformation of the fractures, which may have similar assumptions and governing
equations as
conventional pseudo-3D fracture models. Transport equations may be solved for
each component
of the fluids and proppants pumped.
[0048] Conventional planar fracture models may model various aspects of the
fracture network.
The provided UFM may also involve the ability to simulate the interaction of
hydraulic fractures
with pre-existing natural fractures, i.e. determine whether a hydraulic
fracture propagates
through or is arrested by a natural fracture when they intersect and
subsequently propagates
along the natural fracture. The branching of the hydraulic fracture at the
intersection with the
natural fracture may give rise to the development of a complex fracture
network.
[0049] A crossing model may be extended from Renshaw and Pollard (see, e.g.,
Renshaw, C. E.
and Pollard, D. D. 1995, An Experimentally Verified Criterion for Propagation
across
Unbounded Frictional Interfaces in Brittle, Linear Elastic Materials. Int. J.
Rock Mech. Mth. Sci.
& Geomech. Abstr., 32: 237-249 (1995) the entire contents of which is hereby
incorporated
herein) interface crossing criterion, to apply to any intersection angle, and
may be developed
(see, e.g., Gu, H. and Weng, X Criterion for Fractures Crossing Frictional
Interfaces at Non-
orthogonal Angles. 44th US Rock symposium, Salt Lake City, Utah, June 27-30,
2010 (hereafter
"Gu and Weng 2010"), the entire contents of which are hereby incorporated by
reference herein)
and validated against experimental data (see, e.g., Gu, H., Weng, X, Lund, J.,
Mack, M.,
Ganguly, U. and Suarez-Rivera R. 2011. Hydraulic Fracture Crossing Natural
Fracture at Non-
Orthogonal Angles, A Criterion, Its Validation and Applications. Paper SPE
139984 presented
at the SPE Hydraulic Fracturing Conference and Exhibition, Woodlands, Texas,
January 24-26
(2011) (hereafter "Gu et al. 2011"), the entire contents of which are hereby
incorporated by
reference herein), and integrated in the UFM.
[0050] To properly simulate the propagation of multiple or complex fractures,
the fracture model
may take into account an interaction among adjacent hydraulic fracture
branches, often referred
to as the "stress shadow" effect. When a single planar hydraulic fracture is
opened under a finite
fluid net pressure, it may exert a stress field on the surrounding rock that
is proportional to the
net pressure.
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[0051] In the limiting case of an infinitely long vertical fracture of a
constant finite height, an
analytical expression of the stress field exerted by the open fracture may be
provided. See, .e.g.,
Warpinski, N.F. and Teufel, L. W., Influence of Geologic Discontinuities on
Hydraulic Fracture
Propagation, JPT, Feb., 209-220 (1987) (hereafter "Warpinski and Teufel") and
Warpinski,
N.R., and Branagan, P.T., Altered-Stress Fracturing. SPE JPT, September, 1989,
990-997
(1989), the entire contents of which are hereby incorporated by reference
herein. The net
pressure (or more precisely, the pressure that produces the given fracture
opening) may exert a
compressive stress in the direction normal to the fracture on top of the
minimum in-situ stress,
which may equal the net pressure at the fracture face, but quickly falls off
with the distance from
the fracture.
[0052] At a distance beyond one fracture height, the induced stress may be a
small fraction of
the net pressure. Thus, the term "stress shadow" may be used to describe this
increase of stress in
the region surrounding the fracture. If a second hydraulic fracture is created
parallel to an
existing open fracture, and if it falls within the "stress shadow" (i.e. the
distance to the existing
fracture is less than the fracture height), the second fracture may, in
effect, see a closure stress
greater than the original in-situ stress. As a result, a higher pressure may
be needed to propagate
the fracture, and/or the fracture may have a narrower width, as compared to
the corresponding
single fracture.
[0053] One application of the stress shadow study may involve the design and
optimization of
the fracture spacing between multiple fractures propagating simultaneously
from a horizontal
wellbore. In ultra low permeability shale formations, fractures may be closely
spaced for
effective reservoir drainage. However, the stress shadow effect may prevent a
fracture
propagating in close vicinity of other fractures (see, e.g., Fisher, MK., J.R.
Heinze, C.D. Harris,
B.M. Davidson, C.A. Wright, and K.P. Dunn, Optimizing horizontal completion
techniques in the
Barnett Shale using microseismic fracture mapping. SPE 90051 presented at the
SPE Annual
Technical Conference and Exhibition, Houston, 26-29 September 2004, the entire
contents of
which are hereby incorporated by reference herein in its entirety).
[0054] The interference between parallel fractures has been studied in the
past (see, e.g.,
Warpinski and Teufel; Britt, L.K. and Smith, MB., Horizontal Well Completion,
Stimulation
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Optimization, and Risk Mitigation. Paper SPE 125526 presented at the 2009 SPE
Eastern
Regional Meeting, Charleston, September 23-25, 2009; Cheng, Y. 2009. Boundary
Element
Analysis of the Stress Distribution around Multiple Fractures: Implications
for the Spacing of
Perforation Clusters of Hydraulically Fractured Horizontal Wells. Paper SPE
125769 presented
at the 2009 SPE Eastern Regional Meeting, Charleston, September 23-25, 2009;
Meyer, B.R.
and Bazan, L. W., A Discrete Fracture Network Model for Hydraulically Induced
Fractures:
Theory, Parametric and Case Studies. Paper SPE 140514 presented at the SPE
Hydraulic
Fracturing Conference and Exhibition, Woodlands, Texas, USA, January 24-26,
2011; Roussel,
N.P. and Sharma, M.M, Optimizing Fracture Spacing and Sequencing in Horizontal-
Well
Fracturing, SPEPE, May, 2011, pp. 173-184, the entire contents of which are
hereby
incorporated by reference herein). The studies may involve parallel fractures
under static
conditions.
[0055] An effect of stress shadow may be that the fractures in the middle
region of multiple
parallel fractures may have smaller width because of the increased compressive
stresses from
neighboring fractures (see, e.g., Germanovich, L.N., and Astakhov D., Fracture
Closure in
Extension and Mechanical Interaction of Parallel Joints. J. Geophys. Res.,
109, B02208, doi:
10.1029/2002 JB002131 (2004); Olson, J.E., Multi-Fracture Propagation
Modeling:
Applications to Hydraulic Fracturing in Shales and Tight Sands. 42nd US Rock
Mechanics
Symposium and 2nd US-Canada Rock Mechanics Symposium, San Francisco, CA, June
29 ¨
July 2, 2008, the entire contents of which are hereby incorporated by
reference herein). When
multiple fractures are propagating simultaneously, the flow rate distribution
into the fractures
may be a dynamic process and may be affected by the net pressure of the
fractures. The net
pressure may be strongly dependent on fracture width, and hence, the stress
shadow effect on
flow rate distribution and fracture dimensions warrants further study.
[0056] The dynamics of simultaneously propagating multiple fractures may also
depend on the
relative positions of the initial fractures. If the fractures are parallel,
e.g. in the case of multiple
fractures that are orthogonal to a horizontal wellbore, the fractures may
repel each other,
resulting in the fractures curving outward. However, if the multiple fractures
are arranged in an
en echlon pattern, e.g. for fractures initiated from a horizontal wellbore
that is not orthogonal to
the fracture plane, the interaction between the adjacent fractures may be such
that their tips
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attract each other and even connect (see, e.g., Olson, J. E. Fracture
Mechanics Analysis of Joints
and Veins. PhD dissertation, Stanford University, San Francisco, California
(1990); Yew, C.H.,
Mear, ME., Chang, C.C., and Zhang, XC. On Perforating and Fracturing of
Deviated Cased
Wellbores. Paper SPE 26514 presented at SPE 68th Annual Technical Conference
and
Exhibition, Houston, TX, Oct. 3-6 (1993); Weng, X, Fracture Initiation and
Propagation from
Deviated Wellbores. Paper SPE 26597 presented at SPE 68th Annual Technical
Conference and
Exhibition, Houston, TX, Oct. 3-6 (1993), the entire contents of which are
hereby incorporated
by reference herein).
[0057] When a hydraulic fracture intersects a secondary fracture oriented in a
different direction,
it may exert an additional closure stress on the secondary fracture that is
proportional to the net
pressure. This stress may be derived and be taken into account in the fissure
opening pressure
calculation in the analysis of pressure-dependent leakoff in fissured
formation (see, e.g., Nolte,
K., Fracturing Pressure Analysis for nonideal behavior. JPT, Feb. 1991, 210-
218 (SPE 20704)
(1991) (hereafter "Nolte 1991"), the entire contents of which are hereby
incorporated by
reference herein).
[0058] For more complex fractures, a combination of various fracture
interactions as discussed
above may be present. To properly account for these interactions and remain
computationally
efficient so it can be incorporated in the complex fracture network model, a
proper modeling
framework may be constructed. A method based on an enhanced 2D Displacement
Discontinuity
Method (2D DDM) may be used for computing the induced stresses on a given
fracture and in
the rock from the rest of the complex fracture network (see, e.g., Olson,
J.E., Predicting
Fracture Swarms ¨ The Influence of Sub critical Crack Growth and the Crack-Tip
Process Zone
on Joints Spacing in Rock. In The Initiation, Propagation and Arrest of Joints
and Other
Fractures, ed. J.W.Cosgrove and T.Engelder, Geological Soc. Special
Publications, London,
231, 73-87 (2004)(hereafter "Olson 2004"), the entire contents of which are
hereby incorporated
by reference herein). Fracture turning may also be modeled based on the
altered local stress
direction ahead of the propagating fracture tip due to the stress shadow
effect. The simulation
results from the UFM model that incorporates the fracture interaction modeling
are presented.
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UFM Model Description
[0059] To simulate the propagation of a complex fracture network that consists
of many
intersecting fractures, equations governing the underlying physics of the
fracturing process may
be used. The basic governing equations may include, for example, equations
governing fluid
flow in the fracture network, the equation governing the fracture deformation,
and the fracture
propagation/interaction criterion.
[0060] Continuity equation assumes that fluid flow propagates along a fracture
network with the
following mass conservation:
öq a(HflW)
aS at (1)
where q is the local flow rate inside the hydraulic fracture along the
length,(T) is an average
width or opening at the cross-section of the fracture at position s=s(x,y),
Hfl is the height of the
fluid in the fracture, and qL is the leak-off volume rate through the wall of
the hydraulic fracture
into the matrix per unit height (velocity at which fracturing fluid
infiltrates into surrounding
permeable medium) which is expressed through Carter's leak-off model. The
fracture tips
propagate as a sharp front, and the length of the hydraulic fracture at any
given time t is defined
as 1(t).
[0061] The properties of driving fluid may be defined by power-law exponent n'
(fluid behavior
index) and consistency index K'. The fluid flow could be laminar, turbulent or
Darcy flow
through a proppant pack, and may be described correspondingly by different
laws. For the
general case of 1D laminar flow of power-law fluid in any given fracture
branch, the Poiseuille
law (see, e.g., Nolte, 1991) may be used:
n'-1
OP 1
¨ =¨a0 _________________ q q
as W2n'+1 Hfl H fl (2)
where
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2n'+1
,
2K' 14n'+2 n
n
1 f I 141(Z) '
ao = , n,=; 0(11')= i dz
0(0 n' ) H ji H ji w i
(3)
Here w(z) represents fracture width as a function of depth at current position
s, a is coefficient, n'
is power law exponent (fluid consistency index), (I) is shape function, and dz
is the integration
increment along the height of the fracture in the formula.
[0062] Fracture width may be related to fluid pressure through the elasticity
equation. The elastic
properties of the rock (which may be considered as homogeneous, isotropic,
linear elastic
material) may be defined by Young's modulus E and Poisson's ratio v . For a
vertical fracture in
a layered medium with variable minimum horizontal stress h(x, y, z) and fluid
pressure p, the
width profile (w) can be determined from an analytical solution given as:
w(x, y, z) = w(p(x, y), H, z) (4)
where W is the fracture width at a point with spatial coordinates x, y, z
(coordinates of the center
of fracture element); p(x,y) is the fluid pressure, H is the fracture element
height, and z is the
vertical coordinate along fracture element at point (x,y).
[0063] Because the height of the fractures may vary, the set of governing
equations may also
include the height growth calculation as described, for example, in Kresse
2011.
[0064] In addition to equations described above, the global volume balance
condition may be
satisfied:
t L(t) t L(t)
J Q(t)dt = f H(s,t)-17(s,t)ds + f f f 2gLdsdtdhi
0 0 H 0 0
L (5)
where gL is fluid leakoff velocity, Q(t) is time dependent injection rate,
H(s,t) height of the
fracture at spacial point s(x,y) and at the time t, ds is length increment for
integration along
fracture length, dt is time increment, dlit is increment of leakoff height, HL
is leakoff height, an so
is a spurt loss coefficient. Equation (5) provides that the total volume of
fluid pumped during
time t is equal to the volume of fluid in the fracture network and the volume
leaked from the
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fracture up to time t. Here L(t) represents the total length of the HFN at the
time t and So is the
spurt loss coefficient. The boundary conditions may require the flow rate, net
pressure and
fracture width to be zero at all fracture tips.
[0065] The system of Eq. 1 ¨ 5, together with initial and boundary conditions,
may be used to
represent a set of governing equations. Combining these equations and
discretizing the fracture
network into small elements may lead to a nonlinear system of equations in
terms of fluid
pressure p in each element, simplified as f(p) = 0, which may be solved by
using a damped
Newton-Raphson method.
[0066] Fracture interaction may be taken into account to model hydraulic
fracture propagation in
naturally fractured reservoirs. This includes, for example, the interaction
between hydraulic
fractures and natural fractures, as well as interaction between hydraulic
fractures. For the
interaction between hydraulic and natural fractures a semi-analytical crossing
criterion may be
implemented in the UFM using, for example, the approach described in Gu and
Weng 2010, and
Gu et al. 2011.
Modeling of Stress Shadow
[0067] For parallel fractures, the stress shadow can be represented by the
superposition of
stresses from neighboring fractures. Figure 2 is a schematic depiction of a 2D
fracture 200 about
a coordinate system having an x-axis and a y-axis. Various points along the 2D
fractures, such
as a first end at h/2, a second end at ¨h/2 and a midpoint are extended to an
observation point
(x,y). Each line L extends at angles 01, 02 from the points along the 2D
fracture to the
observation point.
[0068] The stress field around a 2D fracture with internal pressure p can be
calculated using, for
example, the techniques as described in Warpinski and Teufel. The stress that
affects fracture
width is cr,õ and can be calculated from:
L 0
1
o-x = p[l ¨0+2) cos, (0 ¨ ¨ ¨ L ¨3 sinesin (2 (01 + 02))1 (6)
vLiL2 2 l (1,11,2) 2
where
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0 = arctan(¨=
Y)
ei= arctan --. k )
(
1+ y
02 = arctan (.._) (7)
1-y
and where ax is stress in the x direction, p is internal pressure, and .k, )7,
L, L1, L2 are the
coordinates and distances in Figure 2 normalized by the fracture half-height
h/2. Since as. varies
in the y-direction as well as in the x-direction, an averaged stress over the
fracture height may be
used in the stress shadow calculation.
[0069] The analytical equation given above can be used to compute the average
effective stress
of one fracture on an adjacent parallel fracture and can be included in the
effective closure stress
on that fracture.
[0070] For more complex fracture networks, the fractures may orient in
different directions and
intersect each other. Figure 3.1 shows a complex fracture network 300
depicting stress shadow
effects. The fracture network 300 includes hydraulic fractures 303 extending
from a wellbore
304 and interacting with other fractures 305 in the fracture network 300.
[0071] A more general approach may be used to compute the effective stress on
any given
fracture branch from the rest of the fracture network. In UFM, the mechanical
interactions
between fractures may be modeled based on an enhanced 2D Displacement
Discontinuity
Method (DDM) (Olson 2004) for computing the induced stresses (see, e.g.,
Figure 3.2).
[0072] In a 2D, plane-strain, displacement discontinuity solution, (see, e.g.,
Crouch, Si. and
Starfield, A.M., Boundary Element Methods in Solid Mechanics, George Allen &
Unwin Ltd,
London. Fisher, MK. (1983)(hereafter Crouch and Starfleld 1983), the entire
contents of which
are hereby incorporated by reference) may be used to describe the normal and
shear stresses (o.
and us) acting on one fracture element induced by the opening and shearing
displacement
discontinuities (D. and Ds) from all fracture elements. To account for the 3D
effect due to finite
fracture height, Olson 2004 may be used to provide a 3D correction factor to
the influence
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coefficients CY in combination with the modified elasticity equations of 2D
DDM as follows:
ai = LAijCDsj +LAijCij
nn n
s = LAijCi j +LAijCsnDnj (8)
ss s
where A is a matrix of influence coefficients described in eq. (9), N is a
total number of
elements in the network whose interaction is considered, i is the element
considered, and j=1, N
are other elements in the network whose influence on the stresses on element i
are calculated;
and where CY are the 2D, plane-strain elastic influence coefficients. These
expressions can be
found in Crouch and Starfield 1983.
[0073] Elem i and j of Figure 3.2 schematically depict the variables i and j
in equation (8).
Discontinuities Ds and Dn applied to Elem j are also depicted in Figure 3.2.
Dn may be the same
as the fracture width, and the shear stress s may be 0 as depicted.
Displacement discontinuity
from Elem j creates a stress on Elem i as depicted by as and an.
[0074] The 3D correction factor suggested by Olson 2004 may be presented as
follows:
dfl
Ail =1 r __________________________
(.2.- hla)2y/2 (9)
where h is the fracture height, du is the distance between elements i and j, a
and f3 are fitting
parameters. Eq. 9 shows that the 3D correction factor may lead to decaying of
interaction
between any two fracture elements when the distance increases.
[0075] In the UFM model, at each time step, the additional induced stresses
due to the stress
shadow effects may be computed. It may be assumed that at any time, fracture
width equals the
normal displacement discontinuities (Do) and shear stress at the fracture
surface is zero, i.e.,
= wi, asz = O. Substituting these two conditions into Eq. 8, the shear
displacement discontinuities
(Ds) and normal stress induced on each fracture element (an) may be found.
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[0076] The effects of the stress shadow induced stresses on the fracture
network propagation
pattern may be described in two folds. First, during pressure and width
iteration, the original in-
situ stresses at each fracture element may be modified by adding the
additional normal stress due
to the stress shadow effect. This may directly affect the fracture pressure
and width distribution
which may result in a change on the fracture growth. Second, by including the
stress shadow
induced stresses (normal and shear stresses), the local stress fields ahead of
the propagating tips
may also be altered which may cause the local principal stress direction to
deviate from the
original in-situ stress direction. This altered local principal stress
direction may result in the
fracture turning from its original propagation plane and may further affect
the fracture network
propagation pattern.
3D Displacement Discontinuity Method (3D DDM)
[0077] In addition to the enhanced 2D DDM method described herein, a method
based on 3D
DDM can be used for various applications. For a given hydraulic fracture
network that is
discretized into connected small rectangular elements, any given rectangular
element may be
subjected to displacement discontinuity between two faces of the rectangular
element
represented by Dx, Dy, and Dz, and the induced stresses in the rock at any
point (x, y, z) can be
computed using the 3D DDM solution presented herein.
[0078] Figure 17 shows a schematic diagram 1700 of a local x,y,z coordinate
system for a
rectangular element 1740 in an x-y plane. This figure depicts a fracture plane
about the
coordinate axis. The induced displacement and stress field can be expressed
as:
u , = [2(1 ¨ =')f _ ¨ zr.1D ¨ ¨
(10)
U. = ¨ zf D (1 ¨ ¨ ¨ R1¨ 2t,) f s. _
(11)
= [(1¨ 211)1, ¨ +[(I ¨ 2-v) f ¨ zf _]D. [2i ¨v)./. ¨ zr
- (12)
= 2G [21,2 ¨ zr P [211. ¨ + (1¨ ¨ zi la}
A
µ'sv
(13)
= 2G{ 2f',.¨[ [21 ¨7fD,+[f (1¨ 20.1. ¨
,s
(14)
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Or_ = 2G{¨zf D, ¨ zf _JD zf,
, 7 -
(15)
r = 2G{[( )j. f ¨ +[(1 ¨ ¨ ]).5 ¨ [O. ¨ 21.1.)f zr _]D,1
, - - (16)
= 2G t ¨Dfx, 1fr,. ¨ z_f ¨
, (17)
r = 2 G [c f _ ip _ rt 7/- ]D _ 71
;Z: _ (18)
Where a and b are the half lengths of the edges of the rectangle, the induced
displacement and
stress field can be expressed as follows:
1
_________________ 11 [(x ¨ (y ¨77)' 2 1-12 4-di7 4' a,177 h
(19)
where A is the area of the rectangle, (x,y,z) is the coordinate system
originated at the element,
(440) are coordinates at point P, and v is Poisson's ratio.
[0079] For any given observation point P(x,y,z) in the 3D space, the induced
stress at the point P
(x,y,z) with production rate Q(440) may be computed by superposing the
stresses from all
fracture elements, and by applying a coordinate transform. Example techniques
involving 3D
DDM are provided in Crouch, S.L. and Starfield, A.M. (1990), Boundary Element
Methods in
Solid Mechanics, Unwin Hyman, London, the entire contents of which are hereby
incorporated
by reference herein.
[0080] Interaction among multiple propagating hydraulic fractures, or the
herein referenced
stress shadow effect, can influence the fracture height growth for fractures
propagating in the
same layer or different layers in depth, which may have implications on the
success of a fracture
treatment.
[0081] In at least one embodiment of the hydraulic fracture model described
herein, the model
may additionally integrate the 3D DDM for computing the induced 3D stress
field surrounding
the propagating hydraulic fractures, and may incorporate the induced stress
change along the
vertical depth into a fracture height calculation of the fracture model.
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[0082] For example, for two parallel fractures 1811.1, 1811.2, as illustrated
in the schematic
diagram 1800 of Fig. 18, the height growth may be promoted or suppressed
depending on the
relative fracture height. For fractures initiated from different depths, the
presence of the adjacent
fracture can help prevent one fracture from growing into the layer occupied by
the other fracture
due to the vertical stress shadowing effect. For example, due to interaction
between the fractures
1811.1, 1811.2 at different depths, fracture 1811.1 may grow in an upward
direction and fracture
1811.2 may grow in a downward direction as indicated by the arrows.
Validation of Stress Shadow Model
[0083] Validation of the UFM model for the cases of bi-wing fractures may be
performed using,
for example, Weng 2011 or Kresse 2011. Validation may also be performed using
the stress
shadow modeling approach. By way of example, the results may be compared using
2D DDM to
Flac 3D as provided in Itasca Consulting Group Inc., 2002, FLAC3D (Fast
Lagrangian Analysis
of Continua in 3 Dimensions), Version 2.1, Minneapolis: ICG (2002) (hereafter
"Itasca, 2002").
Comparison of Enhanced 2D DDM to Flac3D
[0084] The 3D correction factors suggested by Olson 2004 contain two empirical
constants, a
and f3. The values of a and f3 may be calibrated by comparing stresses
obtained from numerical
solutions (enhanced 2D DDM) to the analytical solution for a plane-strain
fracture with infinite
length and finite height. The model may further be validated by comparing the
2D DDM results
to a full three dimensional numerical solutions, utilizing, for example,
FLAC3D, for two parallel
straight fractures with finite lengths and heights.
[0085] The validation problem is shown in Figure 4. Figure 4 depicts a
schematic diagram 400
comparing enhanced 2D DDM to Flac3D for two parallel straight fractures. As
shown in Figure
400, two parallel fractures 407.1, 407.2 are subject to stresses ax, ay along
an x, y coordinate
axis. The fractures have length 2Lxf, and pressure of the fracture pi, p2,
respectively. The
fractures are a distance s apart.
[0086] The fracture in Flac3D may be simulated as two surfaces at the same
location but with
un-attached grid points. Constant internal fluid pressure may be applied as
the normal stress on
the grids. Fractures may also be subject to remote stresses, ax and ay. Two
fractures may have
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the same length and height with the ratio of height/half-length = 0.3.
[0087] Stresses along x-axis (y = 0) and y-axis (x = 0) may be compared. Two
closely spaced
fractures (slh = 0.5) may be simulated as shown in the comparison of Figures
5.1-5.3. These
figures provide a comparison of extended 2D DDM to Flac3D: Stresses along x-
axis (y = 0) and
y-axis (x = 0).
[0088] These figures include graphs 500.1, 500.2, 500.3, respectively,
illustrating 2D DDM and
Flac3D of extended fractures for ay along the y-axis, ax along the y-axis, and
ay along the x-
axis, respectively. Figure 5.1 plots ay/p (y-axis) versus normalized distance
from fracture (x-
axis) using 2D DDM and Flac3D. Figure 5.2 plots ax/p (y-axis) versus
normalized distance from
fracture (x-axis) using 2D DDM and Flac3D. Figure 5.3 plots ay/p (y-axis)
versus normalized
distance from fracture (x-axis) using 2D DDM and Flac3D. The location Lf of
the fracture tip is
depicted along line x/h.
[0089] As shown in Figures 5.1-5.3, the stresses simulated from enhanced 2D
DDM approach
with 3D correction factor match pretty well to those from the full 3D
simulator results, which
indicates that the correction factor allows capture the 3D effect from the
fracture height on the
stress field.
Comparison to CSIRO model
[0090] The UFM model that incorporates the enchanced 2DDM approach may be
validated
against full 2D DDM simulator by CSIRO (see, e.g., Zhang, X, Jeffrey, R. G.,
and Thiercelin, M.
2007. Deflection and Propagation of Fluid-Driven Fractures at Frictional
Bedding Interfaces: A
Numerical Investigation. Journal of Structural Geology, 29: 396-410,
(hereafter "Zhang 2007")
the entire contents of which is hereby incorporated by reference in its
entirety). This approach
may be used, for example, in the limiting case of very large fracture height
where 2D DDM
approaches do not consider 3D effects of the fractures height.
[0091] The comparison of influence of two closely propagating fractures on
each other's
propagation paths may be employed. The propagation of two hydraulic fractures
initiated parallel
to each other (propagating along local max stress direction) may be simulated
for configurations,
such as: 1) initiation points on top of each other and offset from each other
for isotropic, and 2)
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anisotropic far field stresses. The fracture propagation path and pressure
inside of each fracture
may be compared for UFM and CSIRO code for the input data given in Table 1.
Injection rate 0.106m3/s 40 bbl/min
Stress anisotropy 0.9MPa 130 psi
Young's modulus 3 x 10^10Pa 4.35e+6 psi
Poisson's ratio 0.35 0.35
Fluid viscosity 0.001pa-s 1 cp
Fluid Specific 1.0 1.0
Gravity
Min horizontal stress 46.7MPa 6773 psi
Max horizontal 47.6MPa 6903 psi
stress
Fracture toughness 1MPa-m 5 1000 psi/in0*5
Fracture height 120m 394 ft
Table 1 Input data for validation against CSIRO model
[0092] When two fractures are initiated parallel to each other with initiation
points separated by
dx = 0, dy = 33 ft (10.1 m) (max horizontal stress field is oriented in x-
direction), they may turn
away from each other due to the stress shadow effect.
[0093] The propagation paths for isotropic and anisotropic stress fields are
shown in Figures 6.1
and 6.2. These figures are graphs 600.1, 600.2 depicting propagation paths for
two initially
parallel fractures 609.1, 609.2 in isotropic and anisotropic stress fields,
respectively. The
fractures 609.1 and 609.2 are initially parallel near the injection points
615.1, 615.2, but diverge
as they extend away therefrom. Comparing with isotropic case, the curvatures
of the fractures in
the case of stress anisotropy are depicted as being smaller. This may be due
to the competition
between the stress shadow effect which tends to turn fractures away from each
other, and far¨
field stresses which pushes fractures to propagate in the direction of maximum
horizontal stress
(x-direction). The influence of far-field stress becomes dominant as the
distance between the
fractures increases, in which case the fractures may tend to propagate
parallel to maximum
horizontal stress direction.
[0094] Figures 7.1 and 7.2 depict graphs 700.1, 7002 showing a pair of
fractures initiated from
two different injection points 711.1, 711.2, respectively. These figures show
a comparison for
the case when fractures are initiated from points separated by a distance dx =
dy = (10.1m) for an
isotropic and anisotropic stress field, respectively. In these figures, the
fractures 709.1, 709.2
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tend to propagate towards each other. Examples of similar type of behavior
have been observed
in lab experiments (see, e.g., Zhang 2007).
[0095] As indicated above, the enchanced 2D DDM approach implemented in UFM
model may
be able to capture the 3D effects of finite fracture height on fracture
interaction and propagation
pattern, while being computationally efficient. A good estimation of the
stress field for a
network of vertical hydraulic fractures and fracture propagation direction
(pattern) may be
provided.
Example cases
Case #1 Parallel fractures in horizontal wells
[0096] Figure 8 is a schematic plot 800 of parallel transverse fractures
811.1, 811.2, 811.3
propagating simultaneously from multiple perforation clusters 815.1, 815.2,
815.3, respectively,
about a horizontal wellbore 804. Each of the fractures 811.1, 811.2, 811.3
provides a different
flow rate qi, q2, q3 that is part of the total flow qt at a pressure po.
[0097] When the formation condition and the perforations are the same for all
the fractures, the
fractures may have about the same dimensions if the friction pressure in the
wellbore between
the perforation clusters is proportionally small. This may be assumed where
the fractures are
separated far enough and the stress shadow effects are negligible. When the
spacing between the
fractures is within the region of stress shadow influence, the fractures may
be affected in width,
and in other fracture dimension. To illustrate this, a simple example of five
parallel fractures may
be considered.
[0098] In this example, the fractures are assumed to have a constant height of
100 ft (30.5 m).
The spacing between the fractures is 65 ft (19.8m). Other input parameters are
given in Table 2.
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Young's modulus6
6.6x10 psi=4.55e+10Pa
Poisson's ratio 0.35
Rate 12.2 bbl/min=0.032m3/s
Viscosity 300 cp=0.3Pa-s
Height 100 ft=30.5m
Leakoff coefficient 3 .9 x 10-2 Mis 1/2
Stress anisotropy 200 psi=1.4Mpa
Fracture spacing 65 ft=19.8m
No. of perfs per frac 100
Table 2 Input parameters for Case #1
For this simple case, a conventional Perkins-Kern-Nordgren (PKN) model (see,
e.g., Mack, M. G.
and Warpinski, N.R., Mechanics of Hydraulic Fracturing. Chapter 6, Reservoir
Stimulation, 3rd
Ed., eds. Econom ides, M.J. and Nolte, K. G. John Wiley & Sons (2000)) for
multiple fractures
may be modified by incorporating the stress shadow calculation as given from
Eq. 6. The
increase in closure stress may be approximated by averaging the computed
stress from Eq. 6 over
the entire fracture. Note that this simplistic PKN model may not simulate the
fracture turning due
to the stress shadow effect. The results from this simple model may be
compared to the results
from the UFM model that incorporates point-by-point stress shadow calculation
along the entire
fracture paths as well as fracture turning.
[0099] Figure 9 shows the simulation results of fracture lengths of the five
fractures, computed
from both models. Fig. 9 is a graph 900 depicting length (y-axis) versus time
(t) of five parallel
fractures during injection. Lines 917.1-917.5 are generated from the UFM
model. Lines 919.1-
919.5 are generated from the simplistic PKN model.
[0100] The fracture geometry and width contour from the UFM model for the five
fractures of
Figure 9 are shown in Figure 10. Figure 10 is a schematic diagram 1000
depicting fractures
1021.1-1021.5 about a wellbore 1004.
[0101] Fracture 1021.3 is the middle one of the five fractures, and fractures
1021.1 and 1021.5
are the outmost ones. Since fractures 1021.2, 1021.3, and 1021.4 have smaller
width than that of
the outer ones due to the stress shadow effect, they may have larger flow
resistance, receive less
flow rate, and have shorter length. Therefore, the stress shadow effects may
be fracture width
and also fracture length under dynamic conditions.
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[0102] The effect of stress shadow on fracture geometry may be influenced by
many parameters.
To illustrate the effect of some of these parameters, the computed fracture
lengths for the cases
with varying fracture spacing, perforation friction, and stress anisotropy are
shown in Table 3.
[0103] Figures 11.1 and 11.2 shows the fracture geometry predicted by the UFM
for the case of
large perforation friction and the case of large fracture spacing (e.g., about
120 ft (36.6 m)).
Figures 11.1 and 11.2 are schematic diagrams 1100.1 and 1100.2 depicting five
fractures 1123.1-
1123.5 about a wellbore 1104. When the perforation friction is large, a large
diversion force that
uniformly distributes the flow rate into all perforation clusters may be
provided. Consequently,
the stress shadow may be overcome and the resulting fracture lengths may
become
approximately equal as shown in Figure 11.1. When fracture spacing is large,
the effect of the
stress shadow may dissipate, and fractures may have approximately the same
dimensions as
shown in Figure 11.2.
Frac Base case 120 ft spacing No.
of perfs = 2 Anisotropy = 50 psi
(36.6 m) (345000Pa)
1 133 113 105 111
2 93 104 104 95
3 83 96 104 99
4 93 104 100 95
123 113 109 102
Table 3 Influence of various parameters on fracture geometry
Case #2 Complex fractures
[0104] In an example of Figure 12, the UFM model may be used to simulate a 4-
stage hydraulic
fracture treatment in a horizontal well in a shale formation. See, e.g.,
Cipolla, C., Weng, X,
Mack, M., Ganguly, U., Kresse, 0., Gu, H., Cohen, C. and Wu, R., Integrating
Microseismic
Mapping and Complex Fracture Modeling to Characterize Fracture Complexity.
Paper SPE
140185 presented at the SPE Hydraulic Fracturing Conference and Exhibition,
Woodlands,
Texas, USA, January 24-26, 2011, (hereinafter "Cipolla 2011") the entire
contents of which are
hereby incorporated by reference in their entirety. The well may be cased and
cemented, and
each stage pumped through three or four perforation clusters. Each of the four
stages may consist
of approximately 25,000 bbls (4000 m3) of fluid and 440,000 lbs (2e+6kg) of
proppant.
Extensive data may be available on the well, including advanced sonic logs
that provide an
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estimate of minimum and maximum horizontal stress. Microseismic mapping data
may be
available for all stages. See, e.g., Daniels, J., Waters, G., LeCalvez, J.,
Lassek, J., and Bentley,
D., Contacting More of the Barnett Shale Through an Integration of Real-Time
Microseismic
Monitoring, Petrophysics, and Hydraulic Fracture Design. Paper SPE 110562
presented at the
2007 SPE Annual Technical Conference and Exhibition, Anaheim, California, USA,
October 12-
14, 2007. This example is shown in Figure 12. Fig. 12 is a graph depicting
microseismic
mapping of microseismic events 1223 at various stages about a wellbore 1204.
[0105] The stress anisotropy from the advanced sonic log, indicates a higher
stress anisotropy in
the toe section of the well compared to the heel. An advanced 3D seismic
interpretation may
indicate that the dominant natural fracture trend changes from NE-SW in the
toe section to NW-
SE in heel portion of the lateral. See, e.g., Rich, J.P. and Ammerman, M,
Unconventional
Geophysics for Unconventional Plays. Paper SPE 131779 presented at the
Unconventional Gas
Conference, Pittsburgh, Pennsylvania, USA, February 23-25, 2010, the entire
contents of which
is hereby incorporated by reference herein in its entirety.
[0106] Simulation results may be based on the UFM model without incorporating
the full stress
shadow calculation (see, e.g., Cipolla 2011), including shear stress and
fracture turning (see, e.g.,
Weng 2011). The simulation may be updated with the full stress model as
provided herein.
Figures 13.1-13.4 show a plan view of a simulated fracture network 1306 about
a wellbore 1304
for all four stages, respectively, and their comparison to the microseismic
measurements 1323.1-
1323.4, respectively.
[0107] From simulation results in Figures 13.1-13.4, it can be seen that for
Stages 1 and 2, the
closely spaced fractures did not diverge significantly. This may be because of
the high stress
anisotropy in the toe section of the wellbore. For Stage 3 and 4, where stress
anisotropy is lower,
more fracture divergence can be seen as a result of the stress shadow effect.
Case #3 Multi-stage example
[0108] Case #3 is an example showing how stress shadow from previous stages
can influence the
propagation pattern of hydraulic fracture networks for next treatment stages,
resulting in
changing of total picture of generated hydraulic fracture network for the four
stage treatment
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case.
[0109] This case includes four hydraulic fracture treatment stages. The well
is cased and
cemented. Stages 1 and 2 are pumped through three perforated clusters, and
Stages 3 and 4 are
pumped through four perforated clusters. The rock fabric is isotropic. The
input parameters are
listed in Table 4 below. The top view of total hydraulic fracture network
without and with
accounting for stress shadow from previous stages is shown in Figures 13.1-
13.4.
Young's modulus 4.5x106psi=3.1e+10Pa
Poisson's ratio 0.35
Rate 30.9 bpm=0.082m3/s
Viscosity 0.5 cp=0.0005pa-s
Height 330 ft=101m
Pumping time 70 min
Table 4 Input parameters for Case #3
[0110] Figures 14.1-14.4 are schematic diagrams 1400.1-1400.4 depicting a
fracture network
1429 at various stages during a fracture operation. Figure 14.1 shows a
discrete fracture network
(DFN) 1429 before treatment. Figure 14.2 depicts a simulated DFN 1429 after a
first treatment
stage. The DFN 1429 has propagated hydraulic fractures (HFN) 1431 extending
therefrom due
to the first treatment stage. Figure 14.3 shows the DFN depicting a simulated
HFN 1431.1-
1431.4 propagated during four stages, respectively, but without accounting for
previous stage
effects. Figure 14.4 shows the DFN depicting HFN 1431.1, 1431.2'-1431.4'
propagated during
four stages, but with accounting for the fractures, stress shadows and HFN
from previous stages.
[0111] When stages are generated separately, they may not see each other as
indicated in Figure
14.3. When stress shadow and HFN from previous stages are taken into account
as in Figure 14.4
the propagation pattern may change. The hydraulic fractures 1431.1 generated
for the first stage
is the same for both case scenarios as shown in Figures 14.3 and 14.4. The
second stage 1431.2
propagation pattern may be influenced by the first stage through stress
shadow, as well as
through new DFN (including HFN 1431.1 from Stage 1), resulting in the changing
of
propagation patterns to HFN 1431.2'. The HFN 1431.1' may start to follow HFN
1431.1 created
at stage 1 while intercounting it. The third stage 1431.3 may follow a
hydraulic fracture created
during second stage treatment 1431.2, 1431.2', and may not propagate too far
due to stress
shadow effect from Stage 2 as indicated by 1431.3 versus 1431.3'. Stage 4
(1431.4) may tend to
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turn away from stage three when it could, but may follow HFN 1431.3' from
previous stages
when encounters it and be depicted as HFN 1431.4' in Figure 14.4.
[0112] A method for computing the stress shadow in a complex hydraulic
fracture network is
presented. The method may involve an enhanced 2D or 3D Displacement
Discontinuity Method
with correction for finite fracture height. The method may be used to
approximate the interaction
between different fracture branches in a complex fracture network for the
fundamentally 3D
fracture problem. This stress shadow calculation may be incorporated in the
UFM, a complex
fracture network model. The results for simple cases of two fractures show the
fractures can
either attract or expel each other depending on their initial relative
positions, and compare
favorably with an independent 2D non-planar hydraulic fracture model.
[0113] Simulations of multiple parallel fractures from a horizontal well may
be used to confirm
the behavior of the two outmost fractures that may be more dominant, while the
inner fractures
have reduced fracture length and width due to the stress shadow effect. This
behavior may also
depend on other parameters, such as perforation friction and fracture spacing.
When fracture
spacing is greater than fracture height, the stress shadow effect may diminish
and there may be
insignificant differences among the multiple fractures. When perforation
friction is large,
sufficient diversion to distribute the flow equally among the perforation
clusters may be
provided, and the fracture dimensions may become approximately equal despite
the stress
shadow effect.
[0114] When complex fractures are created, if the formation has a small stress
anisotropy,
fracture interaction can lead to dramatic divergence of the fractures where
they tend to repel each
other. On the other hand, for large stress anisotropy, there may be limited
fracture divergence
where the stress anisotropy offsets the effect of fracture turning due to the
stress shadow, and the
fracture may be forced to go in the direction of maximum stress. Regardless of
the amount of
fracture divergence, the stress shadowing may have an effect on fracture
width, which may affect
the injection rate distribution into multiple perforation clusters, and
overall fracture network
footprint and proppant placement.
[0115] Figure 15 is a flow chart depicting a method 1500 of performing a
fracture operation at a
wellsite, such as the wellsite 100 of Figure 1.1. The wellsite is positioned
about a subterranean
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formation having a wellbore therethrough and a fracture network therein. The
fracture network
has natural fractures as shown in Figures 1.1 and 1.2. The method (1500) may
involve (1580)
performing a stimulation operation by stimulating the wellsite by injection of
an injection fluid
with proppant into the fracture network to form a hydraulic fracture network.
In some cases, the
stimulation may be performed at the wellsite or by simulation.
[0116] The method involves (1582) obtaining wellsite data and a mechanical
earth model of the
subterranean formation. The wellsite data may include any data about the
wellsite that may be
useful to the simulation, such as natural fracture parameters of the natural
fractures, images of
the fracture network, etc. The natural fracture parameters may include, for
example, density
orientation, distribution, and mechanical properties (e.g., coefficients of
friction, cohesion,
fracture toughness, etc.) The fracture parameters may be obtained from direct
observations of
borehole imaging logs, estimated from 3D seismic, ant tracking, sonic wave
anisotropy,
geological layer curvature, microseismic events or images, etc. Examples of
techniques for
obtaining fracture parameters are provided in PCT/US2012/48871 and
US2008/0183451, the
entire contents of which are hereby incorporated by reference herein in their
entirety.
[0117] Images may be obtained by, for example, observing borehole imaging
logs, estimating
fracture dimensions from wellbore measurements, obtaining microseismic images,
and/or the
like. The fracture dimensions may be estimated by evaluating seismic
measurements, ant
tracking, sonic measurements, geological measurements, and/or the like. Other
wellsite data
may also be generated from various sources, such as wellsite measurements,
historical data,
assumptions, etc. Such data may involve, for example, completion, geological
structure,
petrophysical, geomechanical, log measurement and other forms of data. The
mechanical earth
model may be obtained using conventional techniques.
[0118] The method (1500) also involves (1584) generating a hydraulic fracture
growth pattern
over time, such as during the stimulation operation. Figures 16.1-16.4 depict
an example of
(1584) generating a hydraulic fracture growth pattern. As shown in Figure
16.1, in its initial
state, a fracture network 1606.1 with natural fractures 1623 is positioned
about a subterranean
formation 1602 with a wellbore 1604 therethrough. As proppant is injected into
the subterranean
formation 1602 from the wellbore 1604, pressure from the proppant creates
hydraulic fractures
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1691 about the wellbore 1604. The hydraulic fractures 1691 extend into the
subterranean
formation along L1 and L2 (Figure 16.2), and encounter other fractures in the
fracture network
1606.1 over time as indicated in Figures 16.2-16.3. The points of contact with
the other fractures
are intersections 1625.
[0119] The generating (1584) may involve (1586) extending hydraulic fractures
from the
wellbore and into the fracture network of the subterranean formation to form a
hydraulic fracture
network including the natural fractures and the hydraulic fractures as shown
in Figure 16.2. The
fracture growth pattern is based on the natural fracture parameters and a
minimum stress and a
maximum stress on the subterranean formation. The generating may also involve
(1588)
determining hydraulic fracture parameters (e.g., pressure p, width w, flow
rate q, etc.) of the
hydraulic fractures, (1590) determining transport parameters for the proppant
passing through the
hydraulic fracture network, and (1592) determining fracture dimensions (e.g.,
height) of the
hydraulic fractures from, for example, the determined hydraulic fracture
parameters, the
determined transport parameters and the mechanical earth model. The hydraulic
fracture
parameters may be determined after the extending. The determining (1592) may
also be
performed by from the proppant transport parameters, wellsite parameters and
other items.
[0120] The generating (1584) may involve modeling rock properties based on a
mechanical earth
model as described, for example, in Koutsabeloulis and Zhang, 3D Reservoir
Geomechanics
Modeling in Oil/Gas Field Production, SPE Paper 126095, 2009 SPE Saudi Arabia
Section
Technical Symposium and Exhibition held in Al Khobar, Saudi Arabia, 9-11 May,
2009. The
generating may also involve modeling the fracture operation by using the
wellsite data, fracture
parameters and/or images as inputs modeling software, such as UFM, to generate
successive
images of induced hydraulic fractures in the fracture network.
[0121] The method (1500) also involves (1594) performing stress shadowing on
the hydraulic
fractures to determine stress interference between the hydraulic fractures (or
with other
fractures), and (1598) repeating the generating (1584) based on the stress
shadowing and/or the
determined stress interference between the hydraulic fractures. The repeating
may be performed
to account for fracture interference that may affect fracture growth. Stress
shadowing may
involve performing, for example, a 2D or 3D DDM for each of the hydraulic
fractures and
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updating the fracture growth pattern over time. The fracture growth pattern
may propagate
normal to a local principal stress direction according to stress shadowing.
The fracture growth
pattern may involve influences of the natural and hydraulic fractures over the
fracture network
(see Fig. 16.3).
[0122] Stress shadowing may be performed for multiple wellbores of the
wellsite. The stress
shadowing from the various wellbores may be combined to determine the
interaction of fractures
as determined from each of the wellbores. The generating may be repeated for
each of the stress
shadowings performed for one or more of the multiple wellbores. The generating
may also be
repeated for stress shadowing performed where stimulation is provided from
multiple wellbores.
Multiple simulations may also be performed on the same wellbore with various
combinations of
data, and compared as desired. Historical or other data may also be input into
the generating to
provide multiple sources of information for consideration in the ultimate
results.
[0123] The method also involves (1596) determining crossing behavior between
the hydraulic
fractures and an encountered fracture if the hydraulic fracture encounters
another fracture, and
(1598) repeating the generating (1584) based on the crossing behavior if the
hydraulic fracture
encounters a fracture (see, e.g., Figure 16.3). Crossing behavior may be
determined using, for
example, the techniques of PCT/U52012/059774, the entire contents of which is
hereby
incorporated herein in its entirety.
[0124] The determining crossing behavior may involve performing stress
shadowing.
Depending on downhole conditions, the fracture growth pattern may be unaltered
or altered
when the hydraulic fracture encounters the fracture. When a fracture pressure
is greater than a
stress acting on the encountered fracture, the fracture growth pattern may
propagate along the
encountered fracture. The fracture growth pattern may continue propagation
along the
encountered fracture until the end of the natural fracture is reached. The
fracture growth pattern
may change direction at the end of the natural fracture, with the fracture
growth pattern
extending in a direction normal to a minimum stress at the end of the natural
fracture as shown in
Figure 16.4. As shown in Figure 16.4, the hydraulic fracture extends on a new
path 1627
according to the local stresses al and a2.
[0125] Optionally, the method (1500) may also involve (1599) validating the
fracture growth
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pattern. The validation may be performed by comparing the resulting growth
pattern with other
data, such as microseismic images as shown, for example, in Figures 7.1 and
7.2.
[0126] The method may be performed in any order and repeated as desired. For
example, the
generating (1584) - (1599) may be repeated over time, for example, by
iteration as the fracture
network changes. The generating (1584) may be performed to update the iterated
simulation
performed during the generating to account for the interaction and effects of
multiple fractures as
the fracture network is stimulated over time.
[0127] The method 1500 may be used for a variety of wellsite conditions having
perforations
and fractures, such as fractures 811.1-811.3 as depicted in Figure 8. In the
example of Figure 8,
the fractures 811.1-811.3 may be positioned at about the same depth in the
formation. In some
cases, the fractures may be at different depths as shown, for example, in
Figures 18-20.
[0128] Figures 18-20 show various example schematic plots 1800, 1900, 2000 of
parallel
transverse fractures 1811.1, 1811.2 propagating simultaneously from multiple
perforation
clusters 1815.1, 1815.2, respectively, about an inclined wellbore 1804 in
formation 1802. Each
of the fractures 1811.1, 1811.2 traverses strata 1817.1, 1817.2, 1817.3,
1817.4, 1817.5, 1817.6 at
various depths D1-D6, respectively, along formation 1802. The formation 1802
may have one or
more strata of various makeup, such as shale, sand, rock, etc. The formation
1802 has an overall
stress af, and each strata 1817.1-1817.6 has a corresponding stress f1 -f6,
respectively.
[0129] Figures 18 and 19 may be generating using the stress-shadowing as
described above. In
the example of Figure 18, the fracture 1811.1 extends through strata 1817.2-
1817.4 and fracture
1811.2 extends through strata 1817.3-1817.5. In the example of Figure 19, the
fracture 1811.2'
extends through strata 1817.2-1817.5. As shown by Figure 19, the fractures may
have a given
vertical length and extend a given distance through one or more strata and
receive the
corresponding stress effects therefrom.
[0130] In the example of Fig. 19, the fractures 1811.1, 1811.2' are taken
without considering the
effects of stress shadowing. In this case, height growth of the fractures
1811.1 and 1811.2' is
influenced by the vertical in-situ stress distribution of the stresses af of
the corresponding strata
around the fractures. Fracture 1811.1 has a vertical length Li above the
perforation cluster
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1815.1 and a vertical length L2 below the perforation cluster 1815.1. Fracture
1811.2' has a
vertical length L3 above the perforation cluster 1815.2 and a vertical length
L4 below the
perforation cluster 1815.2.
[0131] Figure 20 may be generated by stress shadowing using 3D DDM as
described above. In
the example of Figure 20, the fracture 1811.1' extends through strata 1817.1-
1817.4 and fracture
1811.2" extends through strata 1817.3-1817.6. Fig. 20 shows a cross section of
the fractures of
Figure 19 once the effect of vertical stress shadowing is taken into
consideration. The fracture
1811.1 grows more upward and fracture 1811.2 grows more downward due to the
stress
shadowing.
[0132] In this case, height growth of the fractures is influenced by the
vertical in-situ stress
distribution plus the stress shadow of the adjacent fractures. Fracture
1811.1' has an extended
vertical length Li' above the perforation cluster 1815.1 and a reduced
vertical length L2' below
the perforation cluster 1815.1. Fracture 1811.2" has a reduced vertical length
L3' above the
perforation cluster 1815.2 and an extended vertical length L4' below the
perforation cluster
1815.2. The growth shown in Figure 20 reflects the divergent growth due to
interaction of the
fractures as schematically depicted by the arrows of Figure 18.
[0133] As in Figures 19-20, where fractures are at different depths and
subject to different
stresses, the height growth of the fractures may vary depending on the
relative fracture height.
The fractures are initiated from different formations, and the presence of the
adjacent fracture
can help prevent one fracture from growing into the layer of strata occupied
by another fracture
due to the vertical stress shadowing effect.
[0134] The stress shadowing described herein may take into consideration
interaction between
the fractures at the same or different depths. For example in Figure 8, the
middle fracture may
be compressed by the fractures on either side thereof and become smaller and
narrower as
described with respect to Figure 10. The UFM model provided herein may be used
to describe
such interaction. In another example, as shown in Figures 18-20, the two
fractures may
compress each other and drive the fractures apart. In this example, fracture
1811.1 extends
upward and the fracture on the right grows downward due to the slant of the
wellbore.
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[0135] Figure 21 depicts another version of the method 2100 that may take into
consideration the
effects of the fractures at various depths. The method 2100 may take into
consideration stress
interference between hydraulic fractures to evaluate the height growth of each
fracture whether
at the same or different depths. The method 2100 may be used to perform a
fracture operation at
a wellsite having a wellbore with a fracture network thereabout as shown, for
example, in
Figures 18-20. In this version, the method 2100 may be performed according to
part or all of the
method 1500 as previously described with respect to Figure 15, except with an
additional stress
shadowing 2195, a modified determining 1596', and a modified repeating 1598'.
[0136] The additional stress shadowing 2195 may be performed based on vertical
growth of the
hydraulic fractures to take into consideration the effects of hydraulic
fractures at different depths.
The additional stress shadowing 2195 may be performed using 3D DDM when the
fractures are
at different depths (see, e.g., Figs. 18-20). The additional stress shadowing
2195 may be
performed after the performing 1594 and before the modified determining 1596'.
In some cases,
the additional stress shadowing 2195 may be performed simultaneously with the
performing
stress shadowing 1594. For example, where the performing 1594 is done using 3D
DDM, the
depth may be taken into consideration without the additional stress shadowing
2195. In some
cases, the performing 1594 may be done using another technique, such as 2D
DDM, and the
depth of the fractures may be taken into consideration with the additional
stress shadowing 2195
using 3D DDM. The 3D DDM may take into consideration the influence of adjacent
fractures
and associated vertical stresses, and generate an adjusted vertical growth
and/or length.
[0137] The determining 1596' and the repeating 1598' may be modified to take
into
consideration the additional 2195 stress shadowing, if performed. The modified
determining
1596' involves, determining the crossing behavior between the hydraulic
fracture and the
encountered fracture based on the performing 1594 and the additional stress
shadowing 2195.
The modified repeating 1598' involves repeating the fracture growth pattern
based on the 1594
determining stress interference, the 2195 additional stress shadowing, and the
1596' determining
crossing behavior.
[0138] An additional adjusting 2197 may be performed based on the stress
shadowing 1594
and/or 2195. For example, the fracture growth may be offset by adjusting at
least one
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stimulation parameter, such as pumping pressures, fluid viscosity, etc.,
during injection (or
fracturing). The fracture growth may be simulated using the UFM model modified
for the
adjusted pumping parameters.
[0139] One or more portions of the method, such as the performing the
stimulation operation
1580 may be repeated based on part or all of 1594-1599. For example, based on
the stress
shadowing 1594 and/or 2195, and/or the resulting fracture growth, the
stimulation may be
adjusted to achieve the desired fracture growth (see, e.g., Figure 20). The
stimulating may be
modified, for example, by adjusting pumping pressures, fluid viscosities
and/or other injection
parameters to achieve the desired wellsite operation and/or a desired fracture
growth.
[0140] Various combinations of part or all of the methods of Figures 15 and/or
21 may be
performed in various orders.
[0141] Although the present disclosure has been described with reference to
exemplary
embodiments and implementations thereof, the present disclosure is not to be
limited by or to
such exemplary embodiments and/or implementations. Rather, the systems and
methods of the
present disclosure are susceptible to various modifications, variations and/or
enhancements
without departing from the spirit or scope of the present disclosure.
Accordingly, the present
disclosure expressly encompasses all such modifications, variations and
enhancements within its
scope.
[0142] It should be noted that in the development of any such actual
embodiment, or numerous
implementation, specific decisions may be made to achieve the developer's
specific goals, such
as compliance with system related and business related constraints, which will
vary from one
implementation to another. Moreover, it will be appreciated that such a
development effort might
be complex and time consuming but would nevertheless be a routine undertaking
for those of
ordinary skill in the art having the benefit of this disclosure. In addition,
the embodiments
used/disclosed herein can also include some components other than those cited.
[0143] In the description, each numerical value should be read once as
modified by the term
"about" (unless already expressly so modified), and then read again as not so
modified unless
otherwise indicated in context. Also, in the description, it should be
understood that any range
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listed or described as being useful, suitable, or the like, is intended that
values within the range,
including the end points, is to be considered as having been stated. For
example, "a range of
from 1 to 10" is to be read as indicating possible numbers along the continuum
between about 1
and about 10. Thus, even if specific data points within the range, or even no
data points within
the range, are explicitly identified or refer to a few specific ones, it is to
be understood that
inventors appreciate and understand that any and all data points within the
range are to be
considered to have been specified, and that inventors possessed knowledge of
the entire range
and all points within the range.
[0144] The statements made herein merely provide information related to the
present disclosure
and may not constitute prior art, and may describe some embodiments
illustrating the invention.
All references cited herein are incorporated by reference into the current
application in their
entirety.
[0145] Although a few example embodiments have been described in detail above,
those skilled
in the art will readily appreciate that many modifications are possible in the
example
embodiments without materially departing from the system and method for
performing wellbore
stimulation operations. Accordingly, all such modifications are intended to be
included within
the scope of this disclosure as defined in the following claims. In the
claims, means-plus-
function clauses are intended to cover the structures described herein as
performing the recited
function and a structural equivalents and equivalent structures. Thus,
although a nail and a screw
may not be structural equivalents in that a nail employs a cylindrical surface
to secure wooden
parts together, whereas a screw employs a helical surface, in the environment
of fastening
wooden parts, a nail and a screw may be equivalent structures. It is the
express intention of the
applicant not to invoke 35 U.S.C. 112, paragraph 6 for any limitations of
any of the claims
herein, except for those in which the claim expressly uses the words 'means
for' together with an
associated function.
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