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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