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1. INTRODUCTION

Hydraulic fracturing is a widely us

stimulation of unconventional rese

commercial production. As fracture

important aspect of well completion

reservoirs to unlock the hydroca

permeability formations, basic in

fractures such as the direction of fraand the impact of natural fractures on

propagation as well as the rate of p

critical points while fracturing. Al

fractures usually open in the directio

principal stress and propagate perp

direction, but its been proven to be

initially thought [1]. Hydraulic fractu

the presence of natural fractures is sub

from fracture propagation in reservoi

fractures due to interaction between p

fractures and the advancing hydraul

field observations of fracturing treat

fractured reservoirs do not always sup

the commonly accepted fracture pro

[2]. Experimental studies as welexperiments [3, 4, 5, 6, 7] and the mi

ARMA 12-129

Hydraulic Fracture Pro

Natural fractures

Keshavarzi, R.

Young Researchers Club, Science and

Mohammadi, S. and Bayesteh, H.

School of Civil Engineering, Universit

Copyright 2012 ARMA, American Rock Mecha

This paper was prepared for presentation at2012.

This paper was selected for presentation at ththe paper by a minimum of two technical revie

members. Electronic reproduction, distributiois prohibited. Permission to reproduce in priabstract must contain conspicuous acknowled

ABSTRACT:Recovering hydraobarbonfracture stimulation treatments to make p

and the advancing hydraulic fracture is a k

possible to recover hydrocarbons from the

hydraulic fracture path caused by natural

another hand, the activation of natural fra

the reservoir and potentially improve the p

developed to investigate the hydraulic fra

The results indicate that hydraulic fracture

intersection. Also, it is clearly observed th

the in-situ horizontal differential stress and

d technology in

rvoirs to obtain

stimulation is an

in unconventional

bon from low-

formation about

cture propagationhydraulic fracture

roduction are the

though hydraulic

of the minimum

endicular to this

ore complex than

re propagation in

tantially different

s without natural

e-existing natural

ic fracture. Also,

ment in naturally

ort the concept of

agation behavior

l as mine-backroseismic studies

recorded during hydrau

indicate the creation o

geometry. Meanwhile, a

complex pattern is still la

patterns have significant

the fracturing treatmentproppant might not be abl

the fracture network [1

hydraulic and natural

premature screen-out. Re

growing interest in the

hydraulic fracturing pr

increase. So, the indust

activation of natural fractreservoirs to create a net

reservoir and improve th

shales, however, the strhydraulic fracture propa

activation of natural

treatments. Hence, unde

hydraulic fractures throimportant issue during

reservoirs where without

recover hydrocarbons fromain issues during hy

agation in Unconventional R

Research Branch, Islamic Azad University, Tehr

y of Tehran, Tehran, Iran

nics Association

the 46thUS Rock Mechanics / Geomechanics Symposium

symposium by an ARMA Technical Program Committee bawers. The material, as presented, does not necessarily refle

, or storage of any part of this paper for commercial purposnt is restricted to an abstract of not more than 300 words;ement of where and by whom the paper was presented.

from unconventional reservoirs is always a challen

oduction economic. Meanwhile, the interaction bet

y challenge especially in unconventional reservoirs,

se reservoirs. During hydraulic fracture propagation,

ractures, increases the possibility of premature scree

tures commonly found in shale reservoirs can create

roduction. In this study, an eXtended Finite Element

ture propagation and interaction with a natural frac

diversion as well as natural fracture activation takes

at hydraulic and natural fracture behaviors after inte

the orientation of the natural fractures.

lic fracture treatments [8,9]

a complex fracture pattern

thorough understanding of this

king whereas complex fracture

onsequences for the design of

and the conventionally usede to be transported to the tip of

0, 11] due to interaction of

fracture which can lead to

cent years, have witnessed the

role of natural fractures in

ocess and the productivity

ry has focused more on the

ures commonly found in shaleork of connectivity within the

e rate of production. In most

ess anisotropy can affect theation behavior as well as the

fractures during stimulation

rstanding the propagation of

ugh natural fractures is antimulation of unconventional

fractures, it is not possible to

these reservoirs. One of thedraulic and natural fracture

servoirs: The Role of

an, Iran.

held in Chicago, IL, USA, 24-27 June

ed on a technical and critical review oft any position of ARMA, its officers, or

s without the written consent of ARMAillustrations may not be copied. The

e since it requires cost-effective

een pre-existing natural fractures

ecause without fractures, it is not

any diversion or abrupt change in

out which leads to job failure. In

a network of connectivity within

Method (XFEM) model has been

ure in unconventional reservoirs.

places even several stages before

section are strongly controlled by

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interaction is whether the induced hydraulic fracture

crosses the natural fracture or turns into it and opens the

natural fracture and how the natural fracture can be

activated by the propagating hydraulic fracture before

and after intersection. In this way, several experimental

studies have been done [4, 5, 6] to account for the

interaction between hydraulic and natural fracture butthey have just given a general viewpoint due to

experiments results and they dont give any physical

explanation for the behaviors observed. In this study a

new approach for hydraulic fracture propagation and

intersection with natural fracture has been introduced

based on the eXtended Finite Element Method (XFEM).

2. DIFFERENT SCENARIOS FOR HYDRAULICAND NATURAL FRACTURE INTERACTION

Mainly, there are several scenarios for hydraulic and

natural fracture interaction which can be devided intotwo main groups: crossing and opening. In crossing, the

propagating hydraulic fracture intersects the pre-existingnatural fracture and crosses it without any significant

change in its direction (Fig. 1).

Fig. 1. Propagating hydraulic fracture crosses the natural

fracture and keeps moving without any significant change in

its path.

In the second scenario, the advancing hydraulic fracture

will turn into the natural fracture and opens it (Fig. 2).

Fig. 2. Hydraulic fracture opens the natural fracture and

propagates along the natural fracture.

While the hydraulic fracture is propagating along the

natural fracture plane, it may extend to natural fracture

tip and propagate from the tip or it may cross the natural

fracture in a weak point somewhere along the natural

fracture. In addition, if the length of natural fracture is

high enough or shear slippage takes place, the risk of

hydraulic fracture arrest will increase. Althoughbasically induced hydraulic fracture may cross or open

the pre-existing natural fracture but a comprehensive

viewpoint about the interaction between hydraulic and

natural fractures hasnt yet been fully demonstrated

while getting a basic point of view about the physical

mechanisms of hydraulic and natural fractures

interaction seems to be so influential during stimulation

in naturally fractured reservoirs. One of the behaviors

which takes place during hydraulic fracturing in

naturally fractured reservoirs and has been seldom

discussed, is debonding of sealed natural fracture in the

near-tip region of a propagating hydraulic fracture beforefractures intersection (Fig. 3)[12].

Fig.3. Schematic view of natural fracture debonding prior to

intersection.

Debonding of natural fracture prior to intersection with

hydraulic fracture is due to tensile stress exerted ahead

of hydraulic fracture tip and if this stress is large enough,

it debonds the sealed natural fracture. Debonding is a

phenomenon which will activate the natural fracture

since the debonded natural fracture can be reopened by

the hydraulic fracture much easier than the bondednatural fracture. In other words, as debonding takes

place, weak paths will be activated and the creation of

network of connectivity within the reservoir to improve

the productivity will be facilitated. In unconventional

reservoirs, especially in shale, the pre-existing natural

fractures characterization is in such a way that they act

as weak planes which can be activated while fracturing

[13].

Hydraulic fracture

Natural fracture

Debonded zone

Natural fracture

Hydraulic fracture

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3. EXTENDED FINITE ELEMENT METHOD

eXtended Finite Element Method (XFEM) was

developed in 1999 [14] to help the shortcomings of the

conventional finite element method and has been used tomodel the propagation of various discontinuities such as

cracks and fractures[15]. XFEM allows therepresentation of discontinuities independently of the

mesh which leads toavoiding the remeshing in each stepof the fracture propagation as well as being able to

consider arbitrary varying geometry of fractures [12].

The idea of XFEM is that a part of the displacement

field is approximated by a discontinuous displacementenrichment, hence the displacement field is

approximated by the sum of the regular displacement

field, which is the displacement without any

discontinuities, and the enrichment displacement field

(Eq.(1))[16]:

(1)

Where uh, u

FE and u

ENR are approximated displacement

field, conventional (continuous) and enriched(discontinuous) parts of the displacement approximation,

respectively. General form of approximated

displacement by XFEM can be rewritten as below [16]:

(2)

where uj is the vector of regular degrees of nodal

freedom in the finite element method, N is a shape

function, akis the added set of degrees of freedom to the

standard finite element model and (x) is the

discontinuous enrichment function defined for the set of

nodes that the discontinuity has in its influence domain.

4. NUMERICAL PROCEDURE AND RESULTS

For simplicity, it is assumed that rock is a homogeneous

isotropic material and the fractures are propagating in an

elastic medium under plane strain and quasi-static

conditions by a constant and uniform net pressure

throughout the hydraulic fracture system. Also, forfracture propagation an energy based criterion has been

considered which is energy release rate, G. Energy

release rate has been calculated by the J integral using

the domain integral approach [17] whereas J integral is

equivalent to the definition of the fracture energy release

rate, G, for linear elastic medium. If the energy releaserate, G, is greater than a critical value, Gc, the fracture

will advance. At the point where hydraulic and natural

fracture intersect with eachother, G, is calculated for

both opening and crossing directions and the one that

has a higher value will show the hydraulic fracture

behavior after intersection. Also for any diversion

occurred as hydraulic fracture propagating toward the

natural fracture, the fracture propagation angle in eachstep can be calculated as below [17]:

+

= 8

4

12tan

2

1-

II

I

II

Ic

K

K

K

K

Where c is the fracture growth angle in the local

fracture-tip coordinate system. KI and KII are opening

and shearing mode stress intensity factors, respectively.

If KII= 0 then c= 0 (pure mode I) and if K II> 0, the

fracture growth angle c< 0, and if KII< 0, then c> 0.In addition, the fracturing fluid pressure is included in

the model by putting force tractions on the necessary

degrees of freedom along the fracture. To detect the

debonded zone along the natural fracture, in each step of

fracture propagation, stresses are detected along the

natural fracture and wherever the stress becomes tensile,

its been considered as a debonded zone. So, a 2D

XFEM model has been developed to investigate the

hydraulic fracture propagation behavior in the presence

of a natural fracture. In the first step, to verify the

developed XFEM code Blantons experiments [4] havebeen taken into account. For this purpose, Blantons

experiments have been modeled through a 2D XFEM

model and the results have been compared (Table 1)

which shows a good agreement.

Table 1. Comparing XFEM model results with Blanton

Experimens.

Naturalfracture

orientation(o)

Horizontalstresses

(psi)

Horizotaldifferential

stress(psi)

Type of interaction

Max min Max- minBlanton

Experimens

[4]

XFEM

model

30 2755 1450 1305 opening opening

30 2900 725 2175 arrest opening

60 1740 1450 290 opening opening

60 2900 725 2175 crossing crossing

90 2030 725 1305 crossing crossing

As shown in Table 1, at low angle of approach opening

and at high angle of approach crossing is observed. At

medium angle of approach, opening and crossing bothare abserved depending on the differences betweenhorizontal stresses (horizontal differential stress).

(3)

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Table 1, indicates that in Blantons experiments at 30o

natural fracture orientation and high horizontal

differential stress, hydraulic fracture will be arrested in

the natural fracture while this is just the initial

interaction between the induced fracture and the natural

fracture, however, in reality with continued pumping of

the fluid, the hydraulic fracture may cross or open thenatural fracture that in this case due to the XFEM result,

the hydraulic fracture opens the natural fracture.

Experimental studies have just considered a few steps

before hydraulic and natural fracture intersection in

small blocks and they give just a general viewpoint

about hydraulic and natural fracture interaction while

this issue should be investigated in a reservoir scale

conditions. So, a reservoir-scale model has been

developed through a 2D XFEM approach in such a way

that the hydraulic fracture is propagating towards a

natural fracture which is 10m far from the wellbore with

the orientation of the 30o, 60o, 90o. Maximum horizontalstress varies from 1159.4 to 2898.5 psi and minimumhorizontal stress and fracturing fluid pressure are 500 psi

and 2898.5 psi, respectively. Also Youngs modulus,

Poissons ratio and fracture toughness of the reservoirrock are 4*106 psi, 0.25 and 0.75 MPa.m1/2respectively.

The results indicate that natural fracture debonding and

activation takes place several meters before intersection

with the advancing hydraulic fracture (Fig. 4). As it canbe clearly observed in Fig. 4, natural fracture debonding

for low angles of approach takes palce sooner than

medium and high angles of approach. Meanwhile, as

soon as debonding of natural fracture gets started, thepropagating hydraulic fracture is diverted from its

original path; hence the hydraulic fracture doesnt

intersect with the pre-existing natural fracture in a

straight line which is illustrated in Fig. 5 for low to high

angles of approach. To investigate the hydraulic and

natural fracture interaction in detail, Fig.6 depicts the

hydraulic fracture behavior from the beginning of

debonding for low angle of approach. As it can be seenin Fig. 6, debonding and activation of natural fracture

induced by the propagating hydraulic fracture gets

started around 5m far from the natural fracture and some

part of the natural fracture that has been debonded in the

previous steps may become closed in the next steps of

hydraulic fracture propagation due to stresses exerted by

the advancing hydraulic fracture. In addition, Fig. 6

illustrates how the length and the position of the

debonded zone can affect the hydraulic fracture

propagation behavior. Also, if enough attention is paid to

the debonded zone at the intersection point (as shown in

Fig. 6) one can easily conclude that the at low angles ofapproach, the debonded zone is in such a way thathydraulic fracture will be diverted into natural fracture

and natural fracture will be activated and opened by the

growing hydraulic fracture. The stress maps can befound in Fig. 7 that can clearly demonstrate the stress

exerted ahead of hydraulic fracture tip to the natural

fracture which makes it debonded and activated. To

understand the role of horizontal differential stress onhydraulic fracture diversion before intersecting with

natural fracture, a natural fracture with the orientation of

60ohas been considered and horizontal differential stress

varies from 434.7 to 2173.9 psi (Fig. 8). As shown inFig. 8, any increase in horizontal differential stress can

result in hydraulic fracture diversion decrease.

Fig. 4. Initial step of debonding (highlighted in green) and activation of natural fracture as hydraulic fracture is advancing

toward it, in a reservoir scale XFEM model for a natural fracture with orientation of 30o(horizontal differential

stress=2173.9 psi), 60o(horizontal differential stress=1159.4 psi), 90

o(horizontal differential stress=2173.9 psi).

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Fig. 5. Hydraulic fracture diversion before intersecting with the pre-existing natural fracture in a reservoir scale XFEM

model for a natural fracture with orientation of 30

o

(horizontal differential stress=2173.9 psi), 60

o

(horizontal differentialstress=1159.4 psi), 90

o(horizontal differential stress=2173.9 psi).

Fig. 6. Hydraulic fracture and natural fracture behaviors as hydraulic fracture is propagating toward the pre-existing natural

fracture and intersects with it (natural fracture with orientation of 30o(horizontal differential stress=2173.9 psi)). The upper

images show the debonded zone in each step and the images below them are the numerical deformed configurations

(magnified by 20).

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Fig. 8. Comparing the diversion of hydraulic fracture before intersecting with a 60ooriented natural fracture in a different

horizontal differential stresses and specific fracturing pressure. Horizontal differential stress =2173.9 psi, 1152.4 psi and

434.78 psi for the left, middle and right images respectively at 2898.5 psi fracturing pressure.

Fig. 7. Stress maps (magnified by 20) for hydraulic and natural fracture behaviors as hydraulic fracture is propagating

toward the pre-existing natural fracture and intersects with it (natural fracture with orientation of 30o(horizontal differential

stress=2173.9 psi)).

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5. CONCLUSIONS

Fracture stimulation is required to make the production

of unconventional resources economically viable and

more efficient. Meanwhile, the behavior of the hydraulic

fracture in vicinity of a pre-existing natural fracture as

well as natural fracture activation is of concern ineffective reservoir stimulation and production processes.

Therefore, a new 2D XFEM approach was developed to

deal with hydraulic and natural fracture interaction and

demonstrated the role of the influential parameters on

this mechanism. A new mechanism called debonding of

natural fracture due to interaction with the propagating

hydraulic fracture was successfully demonstrated which

can be a key factor to explain almost all of the behaviors

observed during hydraulic and natural fracture

interaction. It was shown that hydraulic fracture

diversion as well as natural fracture activation begins

several stages before intersection which is controlled bythe length and the position of the debonded zone alongthe natural fracture prior to intersection, natural fracture

orientation and horizontal differential stress. It was

clearly observed that at high angles of approach,

hydraulic fracture diversion and natural fracture

activation is less than low angles of approach. Also, in a

constant fracturing pressure and angle of approach,

increasing the horizontal differential stress leads todecrease in hydraulic fracture diversion. The

observations suggest more focus on hydraulic fracture

diversion and natural fracture activation even before

intersection, prior to fracturing job to prevent any failurecaused by any change or diversion in hydraulic fracture

path and optimize the treatment outcome.

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