PETE 302 KFUM Horizontal Well Fracturing Presentation and Research Paper please see the guidelines attached from my instructor !!! i want you to summarize

PETE 302 KFUM Horizontal Well Fracturing Presentation and Research Paper please see the guidelines attached from my instructor !!!

i want you to summarize the papers attached , summarize each paper in 3 pages including the figures , then put them in one word document ,you should separate each summary

you may change the outline used in the paper , yet you should make

the plagiarism should not exceed 10%

the total number of pages should be around 10 pages

here is an easy outline to use

introduction (general)

objectives of each paper

summary of paper 1

summary of paper 2

summary of paper 3

conclusion

references

after you make the summary , make a simple power point slides (7-8) slides , about the papers you have summarized (see the guidelines from my instructor )

I should receive the word document and the power point slides by 26th of april Optimizing Fracture Spacing and
Sequencing in Horizontal-Well Fracturing
Nicolas P. Roussel, SPE, and Mukul M. Sharma, SPE, University of Texas at Austin
Summary
Horizontal wells with multiple fractures are now commonly used
in unconventional (low-permeability) gas reservoirs. The spacing
between perforations and the number and orientation of transverse
fractures all have a major impact on well production.
The opening of propped fractures results in the redistribution
of local Earth stresses. In this paper, the extent of stress reversal
and reorientation has been calculated for fractured horizontal wells
using a 3D numerical model of the stress interference induced by
the creation of one or more propped fractures. The results have
been analyzed for their impact on simultaneous and sequential
fracturing of horizontal wells.
Our results demonstrate that a transverse fracture initiated from
a horizontal well may deviate away from the previous fracture.
The effect of the reservoir’s mechanical properties on the spatial
extent of stress reorientation caused by an opened crack has been
quantified. The paper takes into account the presence of layers
that bound the pay zone but have mechanical properties different
from those of the pay zone. The fracture vertical growth into the
bounding layers is also examined.
It is shown that stress interference, or reorientation, increases
with the number of fractures created and depends on the sequence
of fracturing. Three fracturing sequences are investigated for a
typical field case in the Barnett shale: (a) consecutive fracturing, (b) alternative fracturing, and (c) simultaneous fracturing of
adjacent wells. The numerical calculation of the fracture spacing
required to avoid fracture deviation during propagation, for all
three fracturing techniques, demonstrates the potential advantages
of alternate fracture sequencing and zipper fracs to improve the
performance of stimulation treatments in horizontal wells.
Introduction
For the past few years, most new wells drilled in the Barnett shale
and other shale and tight gas plays have been horizontal wells.
Slickwater fracturing is the primary technique used to hydraulically fracture these wells. The horizontal well is generally fractured
multiple times, one fracture at a time, starting from the toe. More
recently, new stimulation techniques have been investigated to
improve the reservoir volume effectively stimulated (Mayerhofer
et al. 2010). Simultaneous fracturing of two or more parallel adjacent wells, also referred to as simul-fracs or zipper fracs, aims to
generate a more-complex fracture network in the reservoir (Mutalik and Gibson 2008; Waters et al. 2009).
When placing multiple transverse fractures in shales, it is
crucial to minimize the spacing between fractures in order to
achieve commercial production rates and an optimum depletion of
the reservoir (Cipolla et al. 2009), but the spacing of perforation
clusters is limited by the stress perturbation caused by the opening
of propped fractures (Soliman and Boonen 1997). The geometry
and width of fractures are strongly influenced by fracture spacing
and number because of mechanical interactions (Cheng 2009).
The center fractures, subject to the greatest stress interference,
may exhibit a decrease in their width and conductivity. Stress
distributions and fracture mechanics must be well understood and
Copyright © 2011 Society of Petroleum Engineers
This paper (SPE 127986) was accepted for presentation at the SPE International Symposium
and Exhibition on Formation Damage Control, Lafayette, Louisiana, USA, 10–12 February
2010, and revised for publication. Original manuscript received 21 November 2009. Revised
manuscript received 08 September 2010. Paper peer approved 29 November 2010.
May 2011 SPE Production & Operations
quantified to avoid screenouts, propagation of longitudinal fractures, or fractures deviating from their orthogonal orientation. The
presence of natural fractures also impacts fracture propagation and
increases fracture-path complexity, depending on their preferential
orientation and on the importance of the net pressure relative to the
horizontal-stress contrast (Olson and Dahi-Taleghani 2009).
Previous studies in the literature on fracture-induced stress
interference mostly focus on the effect of a single fracture (Siebrits
et al. 1998). Using analytical solutions, Soliman and Adams (2004)
calculated the effect of multiple fractures on the expected net pressure and the stress contrast. Both quantities increase substantially
with the number of sequential fractures and a smaller fracture
spacing. The stress field in the horizontal plane and the fracture
geometries were numerically calculated on the basis of a displacement discontinuity method for three transverse fractures assuming
a homogeneous single-layer formation with the bounding layers
not playing any role except to act as barriers to fracture propagation
(Cheng 2009). Microseismic measurements have demonstrated the
existence of mechanical-stress interference between multiple transverse fractures. This is sometimes referred to as the stress-shadow
effect (Fisher et al. 2004). When multiple fractures are propagated
simultaneously, the stress shadow can restrict growth in the middle
section of the wellbore while favoring growth at the heel or at the
toe. Field experience has demonstrated that the optimal cluster
spacing to limit fracture interference must be at least 1.5 to 2 times
the fracture height (Ketter et al. 2008).
3D Model of Stress Interference Around a
Propped-Open Fracture
The results presented here are organized to highlight the important
conclusions that we can reach on the basis of the simulations. The
validity of numerical simulations is verified through comparison
with existing analytical models (Sneddon and Elliot 1946) for simple fracture geometries. The important addition to existing models
consists in the evaluation of the impact of the layers bounding the
pay zone on the width of the fracture, which eventually affects
the stress interference caused by a propped fracture. The identified dimensionless parameters are the fracture aspect ratio (hf /Lf),
the Poisson’s ratio of the pay zone (p), the fracture containment
(hp/hf), and the ratio of Young’s moduli (Eb/Ep). Their effects on the
stress contrast generated by the propped fracture, and consequently
on the spatial extent of the stress-reversal region, are discussed in
the following subsections.
Model Formulation. The geometry of the simulated fracture
is shown in Fig. 1. The model includes the presence of layers
bounding the reservoir, and cases where the fracture is not fully
contained (hf > hp) are accounted for. The layers bounding the pay
zone may have mechanical properties (Eb, b) differing from those
of the pay zone (Ep, p).
The mechanical behavior of the continuous 3D medium is
described mathematically by the equations of equilibrium (Eq. 1),
the definition of strain (Eq. 2), and the constitutive equations (Eq.
3). The algebraic system of 15 equations for 15 unknowns (six
components of stress and strain ε, plus the three components of
the velocity vector v) is solved at each node using an explicit, finitedifference numerical scheme. The Einstein summation convention
applies to indices i, j, and k, which take the values 1, 2, and 3:
ij , j =
dvi
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)
dt
173
Pay zone
Eb , νb
z
x
Ep , νp
hp
Transverse
fractures
y
Lf
hf
Horizontal well
Eb , νb
Bounding layer
Fig. 1—3D model of multiple transverse fractures in a layered reservoir.
dε ij
dt
=
vi , j + v j ,i
2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)
The pay zone is homogeneous, isotropic, and purely elastic.
Hooke’s law relates the components of the strain and stress tensors
(constitutive equation):
2 ⎞

ij = 2Gε ij + ⎜ K − G ⎟ ε kkij ,

3 ⎠
where, K =
⎧S xx = Sh max

⎨S yy = Sh min .
⎪S = S
v
⎩ zz
. . . . . . . . . . . . . . . . . . . . . . . (3)
E
E
and G =
.
3 (1 − 2 v )
2 (1 + v )
Displacement is allowed along the faces of the fracture where a
constant stress, equal to the net pressure pnet plus the minimum in-situ
horizontal stress Shmin, is imposed. It must be noted that the constantstress boundary condition on the fracture face is equal to the pressure
required to maintain a fracture width w0, which differs from the
Net extension
pressure
=pf –Shmin
pressure during fracture propagation. To avoid an impact on the stress
distribution around the hydraulic fracture, the far-field boundaries are
placed at a distance from the fracture equal to at least three times the
fracture half-length Lf . A constant-stress boundary condition normal
to the “block” faces is applied at outside boundaries. In-situ stresses
are initialized before the opening of the fracture:
After the first fracture is created, its geometry is fixed (no
displacement is allowed). We assume that compression of the proppant placed inside previous fractures is negligible as a subsequent
fracture is opened. Subsequent transverse fractures are modeled
using similar boundary conditions (Fig. 2). It is observed that the
net pressure required to achieve a specified fracture width increases
with each additional fracture.
1
Semi-infinite 2D fracture
0.9
z
0.8
ΔSxx /pnet, ΔSyy /pnet
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (4)
0.7
0.6
Syy
y
x
Sxx
2hf
ΔSxx numerical
ΔSyy numerical
ΔSxx analytical
0.5
ΔSyy analytical
0.4
0.3
0.2
0.1
Additional stress normal and
parallel to the fracture plane
2
4
x/hf
Dimensionless distance
normal to the fracture
8
Fig. 2—Comparisons of analytical (Sneddon and Elliot 1946) and numerical additional stresses along a normal (y = z = 0) to a
semi-infinite fracture (v = 0.2).
174
May 2011 SPE Production & Operations
1
Penny-shaped fracture
0.8
z
2hf
Syy
x
0.6
ΔSxx /pnet, ΔSyy /pnet
y
Sxx
ΔSxx numerical
ΔSyy numerical
ΔSxx analytical
0.4
ΔSyy analytical
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
4
–0.2
x/hf
Fig. 3—Comparisons of analytical (Sneddon and Elliot 1946) and numerical additional stresses along a normal (y = z = 0) to a
penny-shaped fracture.
Model Validation. Sneddon and Elliot (1946) derived analytical
expressions of the additional normal and shear stresses vs. the
distance normal to the fracture for two geometries: semi-infinite
(Fig. 2) and penny-shaped fractures (Fig. 3).
The results of the 3D numerical model were compared to analytical solutions by plotting the additional stress in the direction
parallel (Syy) and perpendicular (Sxx) to the fracture as a function
of the net extension pressure (pnet). The net extension pressure is
the stress remaining as the fracture closes on the proppant minus
the minimum horizontal stress. In the present study, net pressure is
assumed to be constant along the fracture (uniform proppant distribution). Stress distributions are plotted vs. the distance normal to
the fracture face (x) normalized by the fracture half-height (hf).
Figs. 2 and 3 show that the additional stress in the horizontal
plane is always higher in the direction perpendicular to the fracture
than in the direction parallel to the fracture. As is true initially, the
Fracture
Direction of
maximum stress
points towards
the fracture
direction of maximum horizontal stress is parallel to the crack,
and the stresses are reoriented in the vicinity of the fracture. The
numerical results agree well with the analytical solution, indicating
that the numerical results are correct for this simple case.
The additional stress normal to the fracture (Sxx) decreases
monotonically with distance away from the fracture. For the case of
the penny-shaped fracture (Fig. 3), Syy becomes negative at some
distance normal to the fracture and then passes through a minimum.
Comparison of Stress Reorientation Because of Poroelastic and
Mechanical Effects. Stress reorientation around fractured wells can
occur because of the fracture opening and because of poroelastic
effects. Because the production or injection of fluids is minimal, poroelastic effects can be neglected in the fracturing of horizontal wells.
However, in other cases where significant volumes of fluids have been
produced from a well, poroelastic effects can be dominant.
Direction of
maximum stress
oriented along the
fracture plane
In-situ
stress state
Isotropic point
Stress reversal
region
Fig. 4—Comparison of stress reorientation because of (a) mechanical effects and (b) poroelastic effects (direction of maximum
horizontal stress).
May 2011 SPE Production & Operations
175
0.8
hf /Lf =1 (penny-shaped)
0.7
hf /Lf =1 (penny-shaped)
hf /Lf =0.7
0.6
hf /Lf =0.9
hf /Lf =0.5
0.5
hf /Lf =0.9
ΔSyy /pnet
ΔSxx /pnet
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
hf /Lf =0.3
hf /Lf =0 (semi-infinite)
hf /Lf =0.7
hf /Lf =0.5
0.4
hf /Lf =0.3
0.3
hf /Lf =0 (semi-infinite)
0.2
0.1
0
0
1
2
x /hf
3
4
–0.1
0
1
2
3
4
x /hf
Fig. 5—Effect of fracture aspect ratio (hf /Lf) on the stress perturbation.
The structure of stress reorientation around a single fracture
because of poroelastic effects has been well described in the literature (Siebrits et al. 1998; Singh et al. 2008; Roussel and Sharma
2010). In the vicinity of the fracture, the direction of maximum horizontal stress is rotated 90° from its in-situ direction (for producing
wells). Stress reorientation is not just limited to the stress-reversal
region. The stress distribution resulting from the mechanical opening of a fracture differs from that because of poroelastic stresses.
It was shown that outside the stress reversal region, the direction
of maximum horizontal stress points toward the fracture (radial
orientation), while it is oriented in the orthoradial direction in the
case of poroelastic effects (Roussel and Sharma 2010) (Fig. 4).
The extent of the stress-reversal region (L)
is not limited to
f
0.58 Lf , which has been shown numerically by Siebrits et al. (1998)
to be the highest possible value of Lf because of poroelastic effects.
It may even extend to a distance larger than the fracture half-length
(Lf). How far the stress-reversal region extends in the reservoir
depends mainly on fracture width and height and on the Young’s
modulus in the pay zone. The reoriented-stress region (outside the
stress-reversal region) is confined to the vicinity of the fracture,
contrary to poroelastic stress reorientation, which can be observed
far inside the reservoir.
Effect of Fracture Dimensions. The additional stresses in the
parallel and normal directions are plotted vs. the dimensionless
distance x/hf normal to the fracture in Fig. 5. Both components
increase as the fracture length increases compared to its height.
The quantity of practical interest, though, is the difference between
the additional stress in the direction perpendicular to and in the
direction parallel to the fracture (Fig. 6). This difference represents
the stress contrast that is generated by the opening of the fracture,
or the generated stress contrast (GSC):
GSC = S⊥ − S / / = S xx − S yy . . . . . . . . . . . . . . . . . . . . . . (5)
In most situations, the creation of the fracture generates large
additional stresses perpendicular to the fracture face. This alters the
stress contrast and may cause the direction of maximum stress to
rotate 90° in the vicinity of the fracture. The stress contrast generated by the open crack decreases with distance from the fracture
(Fig. 6). At some distance from the fracture, this stress contrast
becomes smaller than the in-situ stress contrast and the direction
of maximum stress is oriented as initially.
The areal extent of the stress-reversal region is directly proportional to the fracture height because the distance to the fracture is
normalized by the fracture half-height in our analysis. Fig. 6 also
shows that as the fracture length increases, the GSC is higher. For
instance, assuming that the in-situ stress contrast is equal to 0.2 pnet,
the maximum distance of stress reversal Lf is increased by 36% for a
semi-infinite fracture compared to a penny-shaped fracture (Fig. 6).
Effect of Poisson’s Ratio in the Pay Zone. The effect of the
Poisson’s ratio in the pay zone on the stress reorientation around
the fracture depends on the fracture geometry. In the limiting case
(ΔSxx −ΔSyy)/pnet
1
0.9
hf /Lf =1 (penny-shaped)
0.8
hf /Lf =0.9
0.7
hf /Lf =0.7
0.6
hf /Lf =0.5
hf /Lf =0.3
0.5
hf /Lf =0 (semi-infinite)
0.4
if Sh=0.2 pnet
0.3
0.2
0.1
x isotropic, penny-shaped=1.8 hf
0
0
1
2
x /hf
3
x isotropic, semi-infinite=2.45 hf
4
(36% increase)
Fig. 6—Effect of fracture aspect ratio (hf /Lf) on the GSC.
176
May 2011 SPE Production & Operations
(ΔSxx −ΔSyy)/pnet
1
0.9
ν=0.1
0.8
ν=0.2
ν=0.3
0.7
Semi-infinite
fracture
ν=0.4
0.6
Penny-shaped fracture
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
3
3.5
4
y /hf
Fig. 7—Effect of Poisson’s ratio in the pay zone on the GSC for semi-infinite and penny-shaped fractures.
of a penny-shaped fracture (hf = Lf), stresses are independent of
the Poisson’s ratio (Sneddon and Elliot 1946), and so is the GSC.
In the more general case where the fracture length differs from the
fracture height, Poisson’s ratio will play a role.
It is shown in Fig. 7 that an opened crack generates more stress
contrast in a rock with a low Poisson’s ratio. A low Poisson’s ratio
implies that the deformation in the direction parallel to the fracture
is small compared to the deformation in the direction normal to the
fracture. When p = 0, all the deformation occurs along the in-situ
direction of minimum horizontal stress (εyy = 0), thus maximizing
the stress contrast generated.
w0 =
0
1
2
x /hf
3
)p
net
h f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (6)
Effect of Fracture Containment. The bounding layers’ mechanical properties do not affect the extent of stress reorientation if the
fracture is fully contained. In the Barnett shale, fractures are generally well contained in the pay zone even though “out-of-zone”
growth has been measured in the field (Maxwell et al. 2002). From
the relationship between fracture width and Young’s modulus (Eq.
6), it can be deduced that the further the fracture penetrates into the
bounding layers, the more the stress reorientation will be affected
by their mechanical properties. For instance, in the case where the
Young’s modulus is higher in the layers bounding the pay zone, the
maximum width of the crack, and consequently the GSC, decreases
as the fracture height increases (Figs. 9 and 10).
Application of the Model to Multiple
Hydraulic Fractures in Horizontal Wells
The quantification of the extent of the stress-reversal region around
a propped-open fracture is critical in the design of multiple hydraulic fractures in horizontal wells. In low-permeability reservoirs
such as shales where the slow depletion allows for short spacing
(ΔSxx −ΔSyy)/pnet
(ΔSxx −ΔSyy)/pnet
hp /hf =0.5
hp /hf =0.75
hp /hf =1
hp /hf =1.5
hp /hf =2
Monolayer solution
E
The effect of the Poisson’s ratio in the bounding layers was
also analyzed (Fig. 10). It is shown that the GSC is independent
of this value, and it depends only on the Poisson’s ratio inside
the pay zone.
Effect of the Bounding Layers’ Mechanical Properties. Models
of stress interference available in the literature (Sneddon and Elliot
1946; Cheng 2009) assume homogeneous mechanical properties
and do not model layered rocks accurately. The rocks bounding gas
reservoirs often have mechanical properties different from those of
the reservoir and can play an important role in stress reorientation.
Fig. 8 shows that the GSC decreases if the Young’s modulus of
the bounding layers is highe…
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