Scholarly article on topic 'Why are Brittleness and Fracability not Equivalent in Designing Hydraulic Fracturing in Tight Shale Gas Reservoirs'

Why are Brittleness and Fracability not Equivalent in Designing Hydraulic Fracturing in Tight Shale Gas Reservoirs Academic research paper on "Materials engineering"

CC BY-NC-ND
0
0
Share paper
Academic journal
Petroleum
OECD Field of science
Keywords
{Brittleness / Fracability / "Rock stiffness" / "Rock strength" / "Formation confinement" / "Horizontal well landing interval"}

Abstract of research paper on Materials engineering, author of scientific article — Mao Bai

Abstract With respect to brittleness, it is about the type of material and its related strength. In comparison with ductile material under load, brittle material has a relatively shorter plastic deformation and responds dominantly by the elastic deformation. With respect to fracability, it is about the rock failure under the ultimate rock strength in either brittle or ductile formation. In comparison, the higher fracable formation should have smaller formation strength than that of the lower fracable formation. In consequence, it is not certain that the brittle formation is easy to fracture than the ductile formation since brittle formation may have greater strength than ductile formation even though the exceptions may exist. More complications arise when evaluating the responses of subsurface formation in great depth to the formation types (e.g. brittle formation or ductile formation). Under this condition, the impact of confinement on the fracability cannot be ignored. In general, the formation subject to higher confinement pressure is more difficult to fracture as the formation strength is greater. Conversely, the formation subject to lower confinement pressure is easy to fracture since the formation strength is smaller. In view of efficient stimulation of tight shale gas reservoirs, it is unclear whether we would choose the brittle interval or the ductile interval to fracture as the strength of either interval is unknown. However, it is apparent that we should choose the formation interval with a higher fracability which is equivalent to the lower formation strength. Under the similar confinements, the lower formation strength may be indicated by the smaller unconfined compressive strength (UCS). As a result, it is advisable that the most fracable interval is the one with lowest UCS. When evaluating the present technology, the formation brittleness should no longer be the associated subject matter as we are unclear about its role to improve the fracability of the tight formation. Disassociating the brittleness with the fracability enables us to focus on identifying the true mechanisms of efficient fracturing of tight shale gas reservoirs. With the objective review and sensible definition of brittleness used in the present petro-physical field to identify the desirable fracturing intervals, the paper presents the ambiguities of using the brittleness to define the formation fracability and points out that the formation brittleness can be unrelated to the formation fracability. As an alternative approach, the paper provides an effective method to define the most fracable formation intervals in designing the hydraulic fracturing in tight shale gas formations.

Academic research paper on topic "Why are Brittleness and Fracability not Equivalent in Designing Hydraulic Fracturing in Tight Shale Gas Reservoirs"

Accepted Manuscript

Why are Brittleness and Fracability not Equivalent in Designing Hydraulic Fracturing in Tight Shale Gas Reservoirs

Mao Bai

PII: S2405-6561(16)00004-3

DOI: 10.1016/j.petlm.2016.01.001

Reference: PETLM 59

To appear in: Petroleum

KcAl ISSN: 2405-5816

№-----1 201503

Vol.1, No.l

Petroleum

Received Date: 22 December 2015

Accepted Date: 7 January 2016

Please cite this article as: M. Bai, Why are Brittleness and Fracability not Equivalent in Designing Hydraulic Fracturing in Tight Shale Gas Reservoirs, Petroleum (2016), doi: 10.1016/j.petlm.2016.01.001.

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Why are Brittleness and Fracability not Equivalent in Designing Hydraulic Fracturing in Tight Shale Gas Reservoirs

Mao Bai

Geomechanics Consultant, Houston, USA Email: mao-bai@excite.com

Abstract

With respect to brittleness, it is about the type of material and its related strength. In comparison with ductile material under load, brittle material has a relatively shorter plastic deformation and responds dominantly by the elastic deformation. With respect to fracability, it is about the rock failure under the ultimate rock strength in either brittle or ductile formation. In comparison, the higher fracable formation should have smaller formation strength than that of the lower fracable formation. In consequence, it is not certain that the brittle formation is easy to fracture than the ductile formation since brittle formation may have greater strength than ductile formation even though the exceptions may exist.

More complications arise when evaluating the responses of subsurface formation in great depth to the formation types (e.g. brittle formation or ductile formation). Under this condition, the impact of confinement on the fracability cannot be ignored. In general, the formation subject to higher confinement pressure is more difficult to fracture as the formation strength is greater. Conversely, the formation subject to lower confinement pressure is easy to fracture since the formation strength is smaller.

In view of efficient stimulation of tight shale gas reservoirs, it is unclear whether we would choose the brittle interval or the ductile interval to fracture as the strength of either interval is unknown. However, it is apparent that we should choose the formation interval with a higher fracability which is equivalent to the lower formation strength. Under the similar confinements, the lower formation strength may be indicated by the smaller unconfined compressive strength (UCS). As a result, it is advisable that the most fracable interval is the one with lowest UCS.

When evaluating the present technology, the formation brittleness should no longer be the associated subject matter as we are unclear about its role to improve the fracability of the tight formation. Disassociating the brittleness with the fracability enables us to focus on identifying the true mechanisms of efficient fracturing of tight shale gas reservoirs.

With the objective review and sensible definition of brittleness used in the present petro-physical field to identify the desirable fracturing intervals, the paper presents the ambiguities of using the brittleness to define the formation fracability and points out that the formation brittleness can be unrelated to the formation fracability. As an alternative approach, the paper provides an effective

method to define the most fracable formation intervals in designing the hydraulic fracturing in tight shale gas formations.

Keywords:

Brittleness; fracability; rock stiffness; rock strength; formation confinement; horizontal well landing interval.

1. Introduction

As world conventional hydrocarbon resources have reduced rapidly in recent years, unconventional hydrocarbon resources are gradually taking the central stage in all phases of exploitation from exploration to production. The key parameter that separates the unconventional resources in shale from conventional resources in sandstone is the formation permeability (k) with the common divider of 0.1 md, with k > 0.1 md for conventional reservoirs and k < 0.1 md for unconventional reservoirs (Holditch, 2006). The key method for producing from unconventional shale formations with ultralow permeability is to hydraulically fracture the tight formation with the assistance from connected natural fractures.

Based on fracture mechanics, it appears that a more brittle formation is easier to fracture (Zehnder, 2012). As a result, identifying the brittle zones in unconventional reservoirs to achieve effective fracturing has become the focus of current research. A variety of definitions of brittleness has arisen from various disciplines which promotes the development of empirical relations between formation brittleness and formation mechanical properties, such as the correlation of Young's modulus and Poisson's ratio.

The empirical correlation such as developed by Rickman et al. (2008) is convenient to use as a brittleness index log with reference to other wireline logs to assist in locating the preferred injection intervals. Brittleness is an important property that controls the failure process as discussed by Van Dam et al., (2002). Alassi et al., (2011) pointed out that although rock material is considered brittle in general, many rocks show less brittle and more plastic behavior at high stress conditions. Rock brittleness has been considered an important geomechanics parameter in the pool of petrophysical -geomechanical factors for stimulating unconventional reservoirs (Romanson, et al., 2011).

These empirical methods, however, have their defects of frequently neglecting the true mechanisms of effective fracturing. The controversial debates over the brittleness and fracability even for their respective definitions have intensified in recent years. For example, the negative relationship between Young's modulus and Poisson's ratio may be appropriate for certain materials. The generalization of the relation by associating it with brittleness can be dangerous. Another important but controversial question is whether the brittleness should be related to the rock strength (UCS) instead of to the rock stiffness (Young's modulus). Finally, the brittleness and fracability appear to be simple terms to relate to the stimulation effectiveness. However, the complication of brittleness may largely overshadow its usefulness in achieving the desired fracability, and the effective

fracability could be determined without relating to the brittleness. The purpose of the present paper is to identify the complications of brittleness and to propose an effective method in determining the fracability to stimulate the unconventional tight reservoirs without resourcing to brittleness.

2. Review of Current Brittleness Approach

Based on the laboratory ultrasonic measurements to derive the relationship between dynamic Young's modulus and Poisson's ratio, Rickman et al. (2008) proposed the following equation to evaluate the brittleness:

B = — (E - 28v +10.2)

where E is Young's modulus and v is Poisson's ratio, both are derived from the correlations of sonic velocity logs. It can be easily proved that

Br = 0 when E = 1 (mpsi) and v = 0.4

Br = 70 when E = 6.1604 (mpsi) and v = 0.2343

where mpsi = psi x10 ; 1 mpsi = 6.8947573 GPa.

The data from Eq. (1) can be illustrated by the dotted pink line in Fig. 1.

YMS C/PR C

0.10 0.13

~016 019

0.22 0.25 0.28 PR C

Fig. 1. Linear relationship between Young's modulus and Poisson's ratio from Eq. (1) (YMS_C unit is mpsi ^ psi x106 and 1 mpsi = 6.8947573 GPa; Rickman et al., 2008).

The relationship between Young's modulus and Poisson's ratio to interpret formation brittleness proposed by Rickman et al. (2008) in Eq. (1) has been widely used in the petrophysical domain as an indispensable geomechanical component in stimulating unconventional tight reservoirs. The workflow has been established by the practitioners in oil/gas industry to plot the brittleness index log along the perforated interval in order to identify the desired fracturing intervals.

However, Rickman et al.'s proposal raised much opposition from the geomechanics domain. The main debate is about the definition of brittleness. Using the proportion between elastic deformation and plastic deformation as well as the maximum stress (xmax) and residual stress (xres) as reference points, as shown in Fig. 2, Holt et al. (2011) proposed the following equation to calculate the brittleness:

Br = — (2)

where eel is the elastic strain and st is the total strain:

— =—el + —pl (3)

where spl is the plastic strain.

Fig. 2. Relation between stress and strain to determine the elastic strain (sei) and plastic strain (epi)

(Holt et al. 2011).

For three types of clay-rich shale (H Shale - clay 30~85%; S Shale - clay 47%; W Shale clay 44%), Holt et al. (2011) related brittleness defined in Eq. (2) to the effective confining stress as shown in

Fig. 3. The apparent reversed relation between brittleness and effective confining stress exists for all shales, especially for H Shale. In other words, greater brittleness refers to smaller confining stress.

1 ■ • • ' . >

*—■* o,s ■ *

CD X 111 •a c 0,6 - *

in <r> tl C 0,4 - - H m *

C m 0,2 - M • Mi hale ■SsM« ■fylfchali!

U 1 1 I

0 5 10 15

Effective confining stress [MPa]

Fig. 3. Relation between brittleness defined in Eq. (2) and effective confining stress (Holt et al.,

2011).

Holt et al. (2011) attempted to reproduce the result from Rickman et al. (2008) using laboratory ultrasonic tests under the same hydrostatic loading conditions to generate the P wave and S wave velocities. The brittleness by Rickman et al. (2008) should in principle represent brittleness under the conditions where wave velocities are measured. Since wave speeds increase with increasing stress and P-wave velocity normally increases faster than S-wave velocity, one would expect the brittleness by Rickman et al. (2008) to increase rather than decrease with increasing stress such as confining stress. Holt et al. (2011) performed the laboratory ultrasonic tests under hydrostatic stress condition to clay-rich North Sea F Shale and confirmed the positive correlation between brittleness and confining stress, as shown in Fig. 4. It is understood that the in-situ confining stress represents the lateral stress or often horizontal stress that can be determined if the stress path is known. In general, the in-situ stress under the hydrostatic condition (stress path = 1) is extremely rare. For this reason, the result in Fig. 4 should not be considered as a general guide to the derivation of brittleness.

Miskimins (2012) collected the correlations between Young's modulus and Poisson's ratio from various depths of different parts of Woodford shale intervals, and showed in Fig. 5 that a positive trend between Young's modulus and Poisson's ratio indeed exists. The trend in Fig. 5 is apparently contradictory to the trend by Rickman et al. (2008) in Fig. 1 (Note: "Y" axis in Miskimins' case is in a reversed order from "Y" axis in Rickman et al's case).

Fig. 4. Relation between brittleness defined in Eq. (1) and effective confining stress based on the ultrasonic measurements under hydrostatic loading (Holt et al., 2011).

♦ Middle Woodford ♦ Upper of Lower Woodford ♦ Upper Woodford a Lower of Lower Woodford

2.60E+07 2.40E+07 2.20E+07 2.00E+07 3 1.80E+07

1.60E+07 1.40E+07 1.20E+07 1-O0E+07

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Fig. 5. Positive correlation between Young's modulus and Poisson's ratio for Woodford cases

(Miskimins, 2012).

Zhang and Bentley (2005) proposed that the fractures in the rock and their saturation status would affect the relation between Young's modulus and Poisson's ratio significantly. For the case with the fractures being dominated in the rock without saturated fluid, Fig. 6 indicates that Young's modulus has a positive relation with Poisson's ratio, similar to the case shown in Fig. 5. The rock is dry and under the effective pressure of 10 MPa. Zhang and Bentley argued that greater Poisson's ratio corresponds to larger Young's modulus while the higher Poisson's ratio is the result of fewer cracks, which leads to the larger Young modulus.

If the fractures are still pervasive but the rock is water saturated, then the relationship between Young's modulus and Poisson's ratio is reversed, as shown in Fig. 7 (Zhang and Bentley, 2005). The greater Poisson's ratio is related to the smaller Young's modulus. The fewer cracks are conversely the result of high pressure.

■o 45

1 35 30

250 0.05 0.1 0.15

Poisson's ratio (1 OMPa)

o Rock solid:

o Bulk modulus: 39 GP3

She3r modulus: 41 GPa

o Poisson's ratio: 0.1108

o o 8 °

^ o- .

* o ° 8

O / 0 o

o oo « o

Fig. 6. Poisson's ratio is positively related to Young's modulus in fractured dry rock (Zhang and

Bentley, 2005).

If the deformable rock is not heavily fractured and if the rock is water saturated, the reverse relation between Young's modulus and Poisson's ratio with certain degree of smearing is observed (Fig. 8).

Altindag (2003) defined the brittleness as a property of materials that rupture or fracture with little or no plastic deformation. Altindag believed that brittleness measures the relative preference of a material to two competing mechanical responses: deformation and fracture in the process of ductile-brittle transition.

O o Matrix property: Young's modulus: 39 GPa

% Shear modulus: 41 GPa

Poisson's ratio: 0.1108

8 otl $ „ o o

O <b°i k IV Oq o o *o °° o o

ra ÛL

| 5S E

o 9>°

_ » o

Matrix property: Young's modulus: 39 GPa Shear modulus: 41 GPa Poisson's ratio: 0.1108

0 16 0.18 0.2 0.22 0.24 Poisson s ratio (10MPa)

Fig. 7. Poisson's ratio is negatively related to Young's modulus in fractured wet rock (Zhang and

Bentley, 2005).

0.2 0.25

Poisson's ratio (10MPa)

Fig. 8. The relationship between Young's modulus and Poisson's ratio is in reserve mode when the deformable rock contains fewer fractures but fractures are water saturated (Zhang and Bentley,

2005).

The equations calculating brittleness are largely empirical. The following criterion of brittleness has been used widely (Walsh and Brace, 1964; Niwa and Kobayashi, 1974; Chiu and Johnson, 1983; Inyang, 1991; and Kahraman, 2002):

where ac is the unconfined compressive strength (UCS) and at is the tensile strength.

Br in Eq. (4) is a dimensionless number. It means that if the rock strength under no confinement (i.e., UCS) is significant, the rock is brittle. If no information about the tensile strength of the rock is

available, it can be assumed to be 1/10th of UCS. Instead of the simple ratio in Eq. (4), Altindag (2003) proposed the alternative brittleness as follows:

Using the average area concept to calculate the brittleness shown in Eq. (5), Altindag (2003) considered the brittleness definition in Eq. (5) as a better one because it showed a strong correlation to the specific energy with the improved application in describing cutting efficiency.

With respect to the influence of mineralogy on brittleness of the shale, Rickman et al. (2008) claimed that shale is brittle if it is quartz rich or carbonate rich. Conversely, the shale is ductile if it is clay rich, as depicted in Fig. 9.

100 90 80 70 60 50 40 30 20 10

Quartz

1: Brittle quartz rich 2: Brittle carbonate 3,4: Ductile, hard to frac

Carbonate

OftUnon

n lltwwfc

■ LHjcx

p... • <916

Fig. 9. Brittle shale is either quartz rich or carbonate rich, otherwise it is ductile (Rickman et al.,

2008).

Jarvie (2007) proposed the relation between brittleness and shale mineralogy as follows:

_ . 7 Quartz

Brittlenes s =-—-

Quartz + Carbonate + Clay

Jarvie assumed that the content of quartz dictates the brittleness of the shale. Buller et al. (2010) proposed the equation to calculate the Fracindex (i.e., fracability) as:

Fracindex = tV (7)

where Br is the brittleness defined by Rickman et al. (2008) in Eq.(1), while TIV is the transverse interval velocity and:

TIV --stow (8)

DTSfast V '

where DTSsiow is the slow sonic shear travel time and DTSfast is the fast sonic shear travel time, respectively.

Hucka and Das (1974) proposed a simple method to calculate the brittleness using the single factor of internal friction angle as follows:

Br - sin j (0 <j> 90) (9)

where 9 is internal friction angle. From Eq. (9), it is seen that the larger the friction angle, the greater the brittleness.

Referring to the unconfined compressive strength and tensile strength, Hucka and Das (1974) presented another equation of brittleness:

Br - C+S (10)

C0 +ST

where C0 is the unconfined compressive strength (UCS) and aT is tensile strength. Baron et al. (1962) presented the brittleness using the energy terms as follows: W

Br -(11) rW

where Wel is the elastic energy while Wtot is the total energy.

Using peak shear strength (rmax) and residual shear strength (rres), Bishop (1967) defined the brittleness as:

t —t

D _ max res /1

Br ---(12)

Hajiabdolmajid and Kaiser (2003) proposed the brittleness in the following equation:

Br = (13)

where sp* is the plastic strain at failure while ss* is the specific strain beyond failure.

Employing the stress as primary variable, Ingram and Urai (1999) defined the brittleness in the following equation:

Br = (SvmaL)b (14)

where av,max is the maximum previous experienced effective vertical stress, av is the current effective vertical stress, and b is the empirical constant.

Using the static data from rock mechanical testing (Sone and Zoback, 2013), Yang et al. (2013) observed that the brittleness defined by Holt et al. (2011) in Eq. (2) showed the reversed relationship with the confinement pressure, as observed by Holt et al. (2011). On the other hand, the brittleness defined by Eq. (2) did not show an apparent relationship to Young's modulus and Poisson's ratio, according to the report by Yang et al. (2013).

With reference to various definitions of brittleness as described above, sensible ones are those related to rock strength (e.g., tensile, shear or compressive strength) and rock failure (e.g., permanent failure or plastic deformation). Other non-strength or non-failure related definitions of brittleness have been suggested but may have not been physically verified.

From the data of a well in Gulf of Mexico (GOM, data from the published domain), Fig.10 shows the cross plot between Young's modulus and Poisson's ratio for sandstone and shale. The blue dots represent values from the upper overburden shale formation while the red dots represent values from the reservoir sandstone section. The green dots represent the lower shale formation.

The approximated negative linear section between Young's modulus and Poisson's ratio is from Section 1 of the shallow shale (Section 1, blue dots). Conversely, Sandstone (red dots) in Section 2 shows an approximately positive linear relationship between Young's modulus and Poisson's ratio. For the deep shale (Section 3, green dots), the relationship between Young's modulus and Poisson's ratio becomes unclear. It appears that the data from the deep shale are clustered at the intersection between the shallow shale and sandstone sections and further are overshadowed by the two strong linear relationships.

For the shallow shale section, the negative linear relationship between Young's modulus and Poisson's ratio can be represented in Fig. 11. The trend is consistent with the one proposed by Rickman et al. (2008) shown in Fig. 1 (note: 1 mpsi = 6.8947573 GPa). For sandstone section, the positive linear relationship between Young's modulus and Poisson's ratio is depicted in Fig. 12. It

may be speculated that the relation between Young's modulus and Poisson's ratio proposed by Rickman et al. (2008) may be relevant only to the shallow shale formations.

Jin et al. (2014) provided a comprehensive listing of current brittleness definitions and methods, which can be viewed in Table 1.

1 Shale 1

■ • • > , , * w • . V ••

I ■ ¡.."ifR . ■

I--.: »7.J

■ \ VAVw^'l'V'h'l — 2 Sandstone

Poisson's Ratio

Fig. 10. Cross plot between Young's modulus and Poisson's ratio showing negative relation in the upper shale and positive relation in reservoir sands. The data from the lower shale has little impact in

the relationship chart.

Poisson's Ratio

Fig. 11. Negative linear relation between Young's modulus and Poisson's ratio for the shallow shale

section in Fig. 10.

• • * V. \ *• • . **. .

* * Y * * * * *v . *

" * f ** * r s V. -i* v* • .- * v • *

~ . -- \ . * • .' E =663.9 17 v - 133.7575

* * • •• '

0.2 0.25 0.3 0.35 9.4

Poisson's Ratio

Fig. 12. Positive linear relation between Young's modulus and Poisson's ratio for the sandstone

section in Fig. 10.

Table 1 Brittleness definition in current literature (Jin et al., 2012)

Formulae Variables Methods References

Br1=(Hm-H)/K H-hardness, Hm-micro hardness, K-bulk modulus Hardness test Honda and Sanada, 1956

Br2=qOc q-percent of debris, Decompressive strength Impact test Protodyakonov, 1962

Br3=8ux (100%) sux-unrecoverable axial strain Stress-strain test Andreev, 1995

Br4=(8p-8r)/8p sp-peak strain, sr-residual strain As above Hajiabdolmajid and Kaiser, 2003

Br5=(Tp-Tr)/Tp Tp-peak shear stress, Tr-residual shear stress As above Bishop, 1967

Br6=8r/8t Sf-recoverable strain, st-total strain As above Hucka and Das, 1974

Br7=Wr/Wt Wr-recoverable strain energy, Wt-total strain energy As above As above

Br8=öc/öten Decompressive strength, oten-tensile strength UCS and Brazilian tests As above

Br9=( Oc-Oten)/( Öc+Gten) As above As above As above

Br10=( GcGten)/2 As above As above Altindag, 2003

Br11=( GcGten)°'5/2 As above As above As above

Br12=H/KIC H-hardness, KIC-fracture toughness Hardness and fracture toughness tests Lawn and Marshall, 1979

Br13=c/d c-crack length, d-indent size Indentation test Sehgal et al., 1995

Br14=Pinc/Pdec Pmc-increment force, Pdec-decrement force As above Copur et al., 2003

Br15=Fmax/P Fmax-max. force, P-related penetration As above Yagiz, 2009

Br16=H*E* Kic2 H-hardness, E-Young's modulus, KIC- Hardness, stress- Quinn and Quinn,

fracture toughness strain, and fracture toughness tests 1997

Br17=450+9/2 9-internal friction angle Mohr-Coulomb analysis Hucka and Das, 1974

Br18=sin9 As above As above As above

Br19=(En+Vn)/2 En-normalized Young's modulus, vn-normalized Poisson's ratio Sonic logging data analysis Rickman et al., 2008

Br20=Wqtz/Wt Wqtz-weight of quartz, Wt-total mineral weight Mineralogy or XRD analysis Jarvie et al., 2007

Br21=(Wqtz+Wdol)/Wt As above, alsoWdol-weight of dolomite As above Wang and Gale, 2009

Br22=(WgFM+Wcarb)/Wt WQFM-weight of quartz, feldspar and mica; Wcarb-weight of carbonates, Wt-total mineral weight As above Jin et al., 2014

3. Brittleness and Ductility are Related to Rock Strength

The definitions of stiffness and strength can be confusing. A material may be stiff and strong, but this statement cannot be generalized because some stiff materials may also be weak. From the point of view of rock mechanical testing, strength refers to a load carrying capability, which is related to the material failure, while stiffness refers to a deflection capability, which is related to a material property.

The definition of stiffness is the ability of a material to resist the non-permanent (or elastic) deformation. For example, Young's modulus (E), also known as the elastic modulus, is a measure of the stiffness of an elastic material or a material at the elastic stage [see stress (o) - strain (s) relationship in Fig. 13]. There is no indication of material failure from Young's modulus (E) alone

Brittleness, on the other hand, is the ability of a material to resist permanent (or inelastic) deformation. Permanent deformation represents material failure. When the material changes from the elastic stage to the plastic stage, the material is subjected to failure or the material is in dilation. For brittle failure, however, the period of plastic deformation is short and brief. If the period of plastic deformation is long, the material is subjected to ductile failure. As shown in Fig.14, the difference between brittle material and ductile material is the duration of the ability to resist the permanent deformation (plastic strain) or ultimate load. It is noted that brittleness is independent of Young's modulus.

The bottom line is that elasticity and plasticity are related to rock mechanical properties while brittleness and ductility are related to the rock mechanical strength at failure. In other words, brittle rock failure implies that rock is still largely elastic but may be partially plastic. By the same token, ductile rock failure indicates that rock is largely plastic but may be partially elastic. Elastic - brittle and plastic - ductile are often used as equivalent terms in literature. However, the subtle but important differences among them must be recognized.

(Fig. 13).

Fig. 13. A stiffer material has a greater Young's modulus E.

Brittle vs . ductile deformation

CO co CD Yield / 'S " s brittle --ductile

-4—• CO point / / / / f / Ductile: can accommodate permanent strain without losing the ability to resist load

/ / t / / / brittle Brittle: its ability to resist load decreases with permanent strain

strain

Fig. 14. Material failure in brittle mode and ductile mode.

As in Fig. 15 (Ticona, 2000), brittle rock failure can occur with both low strength and low modulus (stiffness) as well as with high strength and high modulus .

Similarly, the ductile rock failure can occur with both low stiffness and low strength rock as well as with high stiffness and high strength rock, as shown in Fig. 16 (Ticona, 2000).

Strain Strain -»»

Fig.15. Brittle rock failure for low stiffness and low strength rock as well as for high stiffness

and high strength rock (Ticona, 2000).

Lower Strength Higher Strength

Lower Modulus Higher Modulus

Fig.16. Ductile rock failure for low stiffness and low strength rock as well as for high stiffness

and high strength rock (Ticona, 2000).

The comparison between the brittle failure in Fig. 15 and ductile failure in Fig. 16 points out an important difference between these two failures, that is, the deformation, or strain, from brittle failure is much smaller than that from ductile failure. This difference was recognized by MPE (1996) for different materials (alloys, ceramics and polymers) as shown in Fig. 17.

Therefore, there is no definite rule that more brittle rock is stiffer and stronger while more ductile rock is softer and weaker. As demonstrated by Hudson and Harrison (1997), the rock stiffness and strength vary with different rocks regardless of whether it is brittle failure or ductile failure (Fig. 18).

Fig.17. Strain from ductile failure is much greater than strain from brittle failure (MPE, 1996).

High sti ffnes, strength Very brittle (basait)

Low stt ffries Low strength Brittle (chalk)

Medium stifTnes JV1 ccltmil strength Medium brittleness ( limestone Ï

Low stiffnes Low strength Ductile <rock salt)

Fig. 18. Stiffness, strength, brittleness and ductility can have different combinations for different

rocks (Hudson and Harrison, 1997).

As illustrated in Fig. 19 (Wickham, 2012), brittle failure is dominated by the elastic deformation with a small portion of plastic deformation from the rock mechanical testing. The opposite is true for ductile failure which is dominated by plastic deformation.

Strain [%)

Fig. 19. Brittle failure and ductile failure from rock mechanical tests (Wickham, 2012).

As reviewed in Section 3, definition of brittleness is not unique due to the physical complexity of rock failure. While multiple definitions of brittleness should be permitted, a simple check of the definition is necessary to constrain the brittleness in the concept of rock failure rather than in other mechanisms. For example, most of brittleness definitions reviewed by Jin et al. shown in Table 1 are related to the rock strength and associated rock failure. As a result, these definitions of brittleness are generally acceptable. However, the definitions of brittleness by methods 19, 20, 21 and 22 in Table 1 are related to none rock strength factors such as Young's modulus and rock mineralogy, which are not acceptable as the strength is different from the stiffness even though they are both mechanical properties, while the mineralogy is a chemical property which deviates from the original definition of brittleness (i.e., a mechanical term).

4. Impact of Confinement on Brittleness and Ductility

The impact of confinement on the rock brittleness was pointed out by Holt et al. (2011) as seen in Figs. 3 and 4. Since the brittleness is strongly the function of confinement conditions, we focus on the more in-depth discussion about the relationship between brittleness and confinement.

The critical transition from brittle failure to ductile failure is an important point to be determined from the stress strain curve of the rock mechanical test. A common misconception is that this critical brittle-ductile transition point can be determined from the relationship between axial stress difference and strain by capturing the slope change of the stress-strain relation. As shown in the stress-strain curves from four triaxial tests under four different confinement pressures in Fig. 20 (Lutz et al., 2010), we cannot determine if there are any of these critical brittle-ductile transition points. At the lower confinement pressure (Pc = 1 MPa and Pc = 4 MPa), the rock failure appears to be brittle. When the confinement pressure was increased to 10 MPa, the rock failure becomes ductile. There was a slight drop of ductility when the confinement pressure was increased to 20 MPa. However, Lutz et al. (2010) presented another group of tests using the higher strength rocks (i.e., about doubled effective compressive strength compared to the previous group), as shown in Fig. 21. It can be seen that all rock failures were brittle in nature regardless of the significant changes in the confinement pressures.

ttí CL E

g 80 C

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

(Radial) Strain (Axial)

Fig. 20. Axial stress difference (axial) versus strain (axial and radial) relations from four triaxial

tests (Lutz et al., 2010).

- -1-r Effective Compressive Strength ODP1-2 (Vert), C„' = 52.28 MPa ODP1-5 (Vert), C0' = 55.43 MPa ODP1-1 (Vert), C„' = 78.85 MPa ODP1 -4 (Vert), C0'= 105.04 MPa

Pc = 20 MPa

/ 1 N^^^PC = 10 MPa /

1 Pc = 1 MPa —/ // 1 1

I / ; /

(Radial) Strain (Axial)

Fig.21. Axial stress difference versus strain relations (axial and radial) from four triaxial tests using

high strength rocks (Lutz et al., 2012).

Determining whether the material is subjected to dilation or not can only be done with the help of the relationship between axial stress difference and volumetric strain. As shown in Fig.22 (Pagoulatos, 2004), dilation did not occur until the volumetric strain passed the deflection point. The negative change of volumetric strain represents the domination of radial strain over axial strain that indicates rock dilation under compressive loading.

o.oo 0.01

Strain, (mm/mm)

Fig. 22. Axial stress difference versus various strains from one triaxial test (Pagoulatos, 2004).

The scenarios in Figs.20 and 21 indicate that the rock appears to be stiffer as the confinement pressure increases, i.e., Young's modulus increases as the confinement pressure increases. We intend to draw a similar conclusion for the brittleness even though it is not conclusive in Fig. 20 and even less certain in Fig. 21. Four stress-strain relation cases are presented in Fig. 23, while Case (A) was from rock testing (i.e., Berea sandstone) and Cases (B), (C) and (D) were from concrete testing. It is almost certain that the lower confinement pressure contribute to the more brittle material failure, and the material failure becomes more ductile as the confinement increases. It is of interest to note from Fig. 23 that material stiffness in the form of Young's modulus derived from the four groups of tests varies from case to case as: a) the stiffness varies greatly in the positive fashion, i.e., stiffness increases as confinement increases in Case (A); b) the stiffness has little change in Case (B) except for the 0.81 MPa confinement case; c) the stiffness varies in the negative manner, i.e., stiffness decreases as the confinement increases in Case (C); and d) the stiffness has no change in Case (D). The three cases for concrete testing in Fig. 23 demonstrate that the Young's modulus appears to be not related to the confinement pressures because that the material is not a real rock with the porosity being nearly zero. In contrast, the positive responses of variations in Young's modulus for the real rock [e.g., sandstone in Case (A) of Fig. 23] with respect to the increase in the confining pressures are the result of increasing rock porous space compaction under loading.

Csse A:

Rllt=it£ =t 24-C|

i 4 » u n m 11 .Lo l* Strain (%)

isrrisi■ tirainrelation* underiinwiscanilheniHisiwicktuni 2012»

o.oi Q.dj

(-[»Aainni™-ftJnri

-f 0 i 1» [J »1 H ») W JO if ^

L.ciijL![Ltliful Strain (0.00 L)

< 31 i Streu stMin rtlifionj tmdir \ aiioflMttnflaKmflBi ( L u. iw? j

i, I>im* i

-XPXI -JDtiyfl - 1KCO G ffli'ii JqdOC' jBQC 400DC ■■'■■■'!

(( i SlrL-i,> strain nclalirnih under Vnitrnsc□qfinancntj(Ansari and I.e. !9SS.i ([1 i Si re-itnin telJtioilJUJlitcr varioui«hiObhkiu?. il.it. I

Fig. 23. Four cases of stress-strain relations under various confinements.

It is understood that more brittle rock failure occurs at a lower confinement condition while more ductile failure occurs at a higher confinement condition, as demonstrated by Fig. 24 for the conceptual two-sample testing case, and by Fig. 25 for the actual six-sample testing case (You (2011).

The transition point from brittle rock failure to ductile rock failure cannot be easily captured since the transition is gradual. The case presented by Kirby (1980) using the chart between stress difference and confining pressure in Fig. 26 supports the cases in Figs. 24 and 25 that the brittle rock is under a lower confinement and the ductile rock is under a higher confinement.

Based on this concept described in Figs. 24, 25 and 26, Suppe (1985) examined rock strength in quartz rich sedimentary rocks with hydrostatic pore pressure and made assumptions that the brittle rock failure occurred in the under-deformed shallower region, while the ductile rock failure occurred in the deformed deeper formation (Fig. 27 quoted from Suppe-1985 with modification). The brittle-ductile transition point is at the intersection between bilinear lines for brittle rock strength in the under-deformed region and a nonlinear curve for ductile rock strength in the deformed region.

Tensile strength Unconffned compressive strength

Fig. 24. Example yield point is the cutoff value in the transition failure between brittle (lower confinement) and ductile (higher confinement) rock failures in the Mohr-Coulomb chart.

Ductile failure

40 M Pa

0,0 0.6 Brittle failure

a (10--)

e-ductile transition failure

Fig. 25. Lower confinement leads to more brittle failure while higher confinement leads to more ductile failure. The brittle-ductile transition is gradual (You, 2011).

2000 r

Brittle

Semi-britt!e

Ductile

Faulting

Microfracturing + Plasticity

Plasticity

' ........ I I I ii I > I I I

500 1000 1500

Confining pressure (MPa)

Fig. 26. It may be commonly known that brittle failure occurs in the low confinement condition while ductile plastic failure occurs in the high confinement condition (Kirby, 1980).

mmuimi rock ilrcntUli (MPa)

BnUle Strength

undeformed

deformed

Ductüe strength

BrittEe-d Li etile transition

Fig. 27. Brittle rock in the undeformed shallower depth versus ductile rock in the deformed deeper

depth (modified from Suppe, 1985).

5. Formation Fracability - Unrestricted Fracturing

Previous discussion indicates that rock brittleness and ductility are not related to the rock stiffness (e.g., Young's modulus) but are related to rock strength while the cutoff value between brittle and ductile range is not easy to determine due to the fact that the transition brittleness and ductility can be affected by numerous factors.

The fracability is about the quantification of ultimate rock strength, i.e., the rock failure. For hydraulic fracturing of tight reservoirs, the most important task is to determine whether the formation can be broken down under the designated pressure. In practice, the injectivity tests are usually performed to ensure the formation breakdown. The effective injectivity tests include but are not limited to diagnostic formation injection test (DFIT) and MiniFrac test (MF).

Hubbert and Willis (1957) defined the breakdown pressure as:

Pb = 3sh-s-Pp + s (15)

where ah is the minimum horizontal stress, aH is the maximum horizontal stress, Pp is the reservoir pore pressure, and at is the rock tensile strength. Eq. (15) applies to the wellbore conditions in which the borehole wall is intact and impermeable, and the borehole wall effective tensile stress is less than the rock tensile strength.

From the MiniFrac tests, Raaen and Brudy (2001) recognized that higher injection pressure is required to breakdown the brittle formation than to breakdown the ductile formation (Fig. 28).

Breakdown

Breakdown

Time [mirtj

(a) BHP in brittle formation

40. 42 5 45 47.5 50. 52.5 55 Time [min|

(b) BHP in ductile formation

Fig. 28. Breakdown of brittle formation (a) and ductile formation (b) by injection (Raaen and

Brudy, 2001).

In the ductile breakdown of Fig. 28(b), the slope change of the bottom hole pressure (BHP) has been mostly interpreted as the indication of fracture initiation. Bai (2011) considered it either as an indication of fracture initiation (i.e., LOP) or as the indication of ductile behavior of rock failure

(i.e., in the period of brittle-ductile transition). Bai (2011) compared the pressure responses in the MiniFrac tests between the brittle formation and ductile formation as shown in Fig. 29 and provided the detailed calculation of various pressures under either brittle or ductile conditions .

Subscript: /p \p 1 - brittle rock ' lopv^bi^ 2-ductile rock • □ '*•. Pp- pore pressure Pb - breakdown pressure Pc - closure pressure Pba - bleed off pressure P,slp - instantaneous shut-in

;/\ PLOP2 / S.^'SIPI pressure PL0P - eakoff pressure

/ P V ......Pd

Pc2 " -—; p ; F bo2

/ Stiffness of rock mass Flow in rock mass

Fig. 29. Different pressure responses in the MiniFrac tests from the rocks with different properties

(Bai, 2011).

In summary, fracability defines the degree of easiness to which a formation can be fractured. Generally speaking, fracability is related to the rock strength but can be associated with many other factors besides the rock strength. The following items can be considered as some key factors to identify the preferred perforation spots with high fracability:

Small confinement Dominant elastic deformation Thermally enhanced (heating) Large permeability and porosity High density of natural fractures or micro fractures Not cemented No super seals Open fractures In tensile stress zone

Like brittleness, it is difficult to define the fracability by a single equation due to the influences of multiple factors. Based on the discussion in this paper especially aspired by the scenario illustrated in Fig. 24, the following simplified criteria are proposed to define the fracability for all practical purposes:

• No fracability: Fb = 0 where the breakdown pressure cannot be achieved during DFIT or MiniFrac tests.

• Maximum fracability: Fb = 1 where the breakdown pressure can be achieved and fracture extension has been verified during DFIT or MiniFrac tests.

• Variable fracability: 0 < Fb < 1 according to the degree of easiness of obtaining the breakdown pressure. In particular:

o Low fracability: 0 < Fb < 0.5 where breakdown is ensured in the ductile formation but the fracture geometry is limited.

o Average fracability: Fb = 0.5 where breakdown pressure is achieved.

o High fracability: 0 .5 < Fb < 1 where breakdown pressure and fracture extension are achieved and the fracture geometry is sufficient.

Based on the discussion of this paper, the better fracability should be near the formation of lower confinement, and lower UCS. Fig. 30 shows the decreased fracability is related to the larger UCS and increased effective normal stress. Conversely, increased fracability is associated with the smaller UCS and decreased effective normal stress.

Employing the concept described in Fig. 30, the detailed UCS measured in the laminated shale/sand section can be used for identifying the effective injection intervals, as shown in Fig. 31 where the selected perforation locations are formation intervals with lower UCS and more fracable rocks. It should be emphasized that fracability is a dimensionless term which is a relative term with respect to the ease of fracturing.

The most fracable intervals are usually the weak spots which could be prone to excessive sand production. For shale gas reservoirs, this is usually not an issue. As a result, the preferred perforation intervals are those relatively weak spots, as shown in Fig. 32.

6. Formation Fracability - Restricted Fracturing

The formation breakdown scenario shown in Fig. 29 generally represents the formation fracturing under unconfined conditions. The examples of such conditions are: a) the hydraulic fracture grows out of payzone as a result of low stress contrast between the payzone and the bounding layers; and b) the fracturing occurs in the homogeneous formation where no permeability contrast between the perforated intervals and adjacent intervals can be identified.

Shear stress

A: Möhr circle for small UCS (more fractable) 6: Möhr circle for medium UCS (less fractable) C: Möhr circle for large UCS (least fractable)

Decreased fracability Increased fracability

Effective normal stress

Fig. 30. Smaller UCS corresponds to larger fracability while greater UCS is related to decreased

fracability.

5000 lOOOO 15000 20000

UCS (psi)

Fig. 31. Preferred perforation areas can be determined from the smaller UCS intervals, which is

more fracable.

Fig. 32. Selecting desired perforation intervals from the weak spots.

In reality, unrestricted fracturing cases are rare since the free fracture extension can be frequently hindered as a result of: a) contained fracture growth within the payzone due to stress, modulus, or permeability contrasts between the payzone and the bounding formations; b) localized screen out that restricts the free fracture propagation; c) formation heterogeneities that form the discreted compartments of flow domains; and d) insufficient net pressure to extend the hydraulic fracture in the growing mode, etc.

Using the different signatures of bottom hole pressure responses during the injection (i.e., increasing pressure without obvious breakdown for contained fracturing and declining pressure with clear picture of formation breakdown for uncontained fracturing) , Bai et al. (2005) showed the geometric contrasts between the contained fracture growths within the payzone and uncontained penny shape fracture growths (Fig. 33).

For the restricted fracturing, the formation toughness plays a big role to reduce the fracture growth. Bai (2011) provided a detailed relationship between breakdown pressure and fracture toughness. In fracture mechanics, the mode 1 fracture toughness KIC represents the inherent ability of a material

(e.g., a rock) to withstand a given stress field intensity at the tip of a fracture and to resist progressive tensile fracture extension.

Pressures showthe fractures are difficult to grow because of containments

300 1000 12D0 ütjäcleü Volume {bb(

Fig. 33. Comparison between contained fracturing and uncontained fracturing with respect to fracture geometry and injection pressure (Bai et al., 2005).

For the hydraulic fracturing without using proppant, the fracture can be created only when the net pressure is sufficient to overcome the formation toughness. The net pressure is equal to the difference between the injection pressure and the closure stress. Papanastasiou (2002) depicted the fracture propagation as a result of significant net pressure which exceeded the fracture toughness KIC. As shown schematically in Fig. 34, the fracture grows when the fluid pressure exceeds the closure stress which creates positive net pressure and overcomes the fracture toughness Ki(+). In contrast, the fracture shrinks when the fluid lag occurs in the fracture tip area which creates negative net pressure and fracture toughness Ki(-). The mode 1 fracture toughness KIC is the summation of Ki(+) and Ki(-). Therefore, the fracture toughness is the critical rock strength value. If the positive net pressure exceeds this critical toughness value, the fracture will grow. Once the fracture grows bigger, the net pressure may consequently drop. As a result, the fracture will stop growing until the net pressure being increased to the level that again exceeds the fracture toughness. The dynamic process continues as long as the net pressure is continuously built up.

Injection well pressure P

i— d

(Negative toughness)

Distance

Fluid lag

Fracturing fluid

Fig. 34. The hydraulic fracture grows when the net pressure (i.e. Pn = Pw - Pc) is positive. The fracture shrinks in the region where the net pressure is negative. The resistance for the fracture growth is the fracture toughness (Papanastasiou, 2002).

In Table 1, Jin et al. (2014) defined the brittleness from the weight percentage of brittle silicate minerals (e.g., quartz, feldspar, and mica, or QFM) and brittle carbonate minerals (e.g., calcite and dolomite) while excluding the ductile clay minerals.

The fracability index from Jin et al. (2014) is an arithmetic average of brittleness shown in Table 1 and fracture toughness, as indicated as follows:

BQC + KIC

where KIC is the mode 1 fracture toughness (i.e., tensile fracture).

Considering the rock with greater fracture toughness as one of the primary fracture barriers where the formation is less fracable, Jin et al. (2014) provided fracability index chart from the cross plot between the fracture toughness and the normalized brittleness index, as shown in Fig. 35.

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Brittleness

Fig. 35. Formation fracability chart from the relationship between fracture toughness and formation

brittleness (Jin et al., 2014).

It is seen from Fig. 35 that smaller fracability is associated with greater fracture toughness while the relationship between the toughness and the brittleness is nonlinear due to the additional influence of mineralogy on fracability shown in Eq. (16).

7. Verification of Fracability

Rock fracability is related not only to the formation mechanical properties but also to the in-situ stress conditions of stimulated reservoir rocks. In the sedimentary rocks such as the laminated sandstone - shale sequences, shale is often subjected to the higher lateral stress than that of sandstone due to greater lateral rock strength. As described in Fig.36, the stimulated wider fracture widths in sandstone layers and narrower fracture widths in shale layers are the result of the stress contrasts where the wider width corresponds to the lower stress and vice versa. In the hydraulic fracturing design for a vertical well, the fracture width is along the direction of minimum horizontal stress while the fracture length is parallel to the direction of maximum horizontal stress. Similarly to the case of fracture width, greater stimulated fracture length can be achieved when the hydraulic fracture is subjected to the smaller lateral stress and vice versa, as depicted in Fig. 37.

The stress value also has an impact on the depth of perforation penetration. Based on the laboratory testing of various rocks, the reversed relationship between the applied stress and the rock perforation penetration depth was reported by Halleck et al. (1988), as shown in Fig. 38.

V ? V > v\ ¥■ ■■' V > S3i ': ■ 3ft '

Overburden (contact)

OJ c o

M . >■

Medium stress

Low stress

Higher stress Lower stress

High stress

Medium width

(vertical

w,f,'V Large width

profile °

Smaller width Larger width No width

________StrEss profile __

Underneath Layer (contact)/

Fig. 36. Schematics showing smaller fracture width due to higher in-situ stress in shale layers and greater fracture width due to lower in-situ stress in sandstone layers from a hydraulic fracturing

stimulation.

K't ■ Vi . K'f • V. • K't • V;

Medium stress i Low stress | Higher stress i

Overburden

Medium length ^ ^ Large length

Smaller length

Underneath Layer

_. _2_- . ______J

Fig. 37. Schematics showing smaller fracture length due to higher in-situ and greater fracture length due to lower in-situ stress from a hydraulic fracturing stimulation.

v a. ja;

A Limestone f Sandstone

Applied Stress (MPa)

Fig. 38. Reversed relationship between rock penetration and applied stress (Halleck et al., 1988).

Based on the analysis of stress impact on the stimulated fracture geometry, it appears that most fracable formation intervals are those subjected to the lowest stress. Naturally, the stress is not the only factor that dictates the fracture geometry. Other mechanical contrasts such as formation Young's modulus and rock compressive strength also have significant impact on the stimulated fracture geometry. The fracture height containment can frequently be achieved if the mechanical contrasts (e.g., Young's modulus and rock compressive strength) are sufficiently large, as illustrated in Fig. 39.

Among other factors, the impact of rock compressive strength on reservoir stimulation has been recognized in the past. King (2009) reported the perforation tests on various types of rocks that had different compressive strengths, as shown in Fig. 40 where the largest perforation length (or depth, 16") had been achieved on the Austin Chalk that had the lowest compressive strength (i.e., 2200 psi), which was in contrast to the smallest perforation length (7") on the Carthage Dolomite that had the highest compressive strength (i.e., 13000 psi).

Weeks (1974) provided the reverse relationship between the penetration depth and rock compressive strength (i.e., greater penetration depth related to smaller compressive strength) based on the core testing in the normalized graph shown in Fig. 41.

As the rock strength can be defined from the subjected effective stress (i.e., difference between stress and pore pressure), Grove et al. (2009) presented the reversed relationship between the perforation penetration depth and the in-situ effective loading stress, as shown in Fig. 42.

Upper Contact Laver

Larger value

Bottom Contact Layer

Fig. 39. Schematics showing the required sufficient contrasts to contain fracture height between layers (A) and (B) with respect to: a) stress, b) Young's modulus, and c) rock strength.

Fig. 40. Greater perforation penetration can be obtained in the rock with smaller compressive

strength (King, 2009).

jC u c

a 0) a

Q_ d; a

aj c <u

4 6 8 10 12 16 IB

Rock Compressive Strength (1000 psi)

Fig. 41. Penetration depth is inversely related to rock compressive strength (Weeks, 1974).

0 80 -

Q> Û c O

QJ 060

"8 0.40-

0.00 + 0

♦ <7 '

-----------

♦ ♦

♦ 0 (Ambient pore pressure}

aeff- effective stress ot- total stress pp-pore pressure a (Biot coefficient)

Effective Stress (kpsi)

Fig. 42. Reversed relationship between penetration depth and effective loading stress (Grove et al.

2009).

Generally speaking, the interval with higher rock strength is the barrier and the opposite is true (i.e., the interval with lower strength is the recommended perforation interval.). Fig. 43 shows an example of identifying barriers and fracable intervals in the shale reservoir. The carbonate interval (GR in Track 2) is identified as the barrier that should be avoided which has the higher strength (UCS in Track 4), greater density (RHOB in Track 5), and lower porosity (NPHI in Track 6). In contrast, the upper shale section is identified as the recommended fracable interval which has the lower strength (UCS in Track 4), smaller density (RHOB in Track 5), and greater porosity (NPHI in Track 6).

Fig. 43. Recommended perforation interval with lower rock strength and avoided perforation interval with higher rock strength in shale reservoir.

8. Conclusions

In the present study of stimulating unconventional shale gas reservoirs, the brittleness index profile along the reservoir payzone to identify the most desirable perforated intervals has become a common practice and has been considered as an indispensable geomechanics component in the approaches by the petro-physical domain. However, this paper challenges the validity of the brittleness index profiling method. The following conclusions are drawn as the result of the presented study:

• Formation brittleness and ductility are not related to the formation mechanical properties such as Young's modulus and Poisson's ratio as commonly used in the brittleness index

profiling. Instead, formation brittleness and ductility are related to the rock strength such as unconfined compressive strength (UCS) or fracture toughness.

• It is ambiguous to relate the formation brittleness to the formation fracability as brittle formation may have a greater rock strength under higher confinement that is more difficult to fracture, and vice versa.

• The formation fracability is about the ultimate rock failure defined by the formation breakdown pressure. The breakdown pressure can be identified in the unrestricted fracturing. Unconfined compressive strength (UCS) is a good benchmark for the correlated breakdown pressure. However, it is difficult or sometime impossible to identify the breakdown pressure in the restricted fracturing since the fracturing is limited in size and is often localized while the extended free fracture propagation is not seen from the bottom hole pressure response. Under this condition, the formation fracability may be determined from the fracture toughness based dynamic fracturing process.

• Disassociating formation brittleness from formation fracability allows us to correctly determine the most fracable formation intervals to perforate.

• This paper proposes an effective approach to select the desirable stimulating intervals, i.e., select the weak spots determined from the formation UCS profile to establish the perforated intervals. The proposed method is supported by many early experimental studies.

References

Alassi, H.T., Holt, R., Nes, O-M, and Pradhan, S., 2011. Realistic geomechanical modeling of hydraulic fracturing in fractured reservoir rock, CSUG/SPE 149375, Canadian Unconventional Conf., Alberta, CA, Nov. 15~17.

Altindag, R., 2003. Correlation of specific energy with rock brittleness concepts on rock cuttings, The Journal of the South African Institute of Mining and Metallurgy, 103(3), 163-172.

Andreev, G.E., 1995. Brittle failure of rock materials: test results and constitutive models, Taylor & Francis.

Ansari, F., and Li, Q., 1998. High strength concrete subjected to uniaxial compression, ACID Materials Journal.

Bai, M., 2011. Risk and uncertainties in determining fracture gradient and closure pressure, 45th US Rock Mechanics/Geomechanics Symposium, San Francisco, CA, June 26-29, 11-132.

Bai, M., Green, S., and Suarez-Rivera, R., 2005. Effect of leakoff variation on fracturing efficiency for tight shale gas reservoirs, Proc. 40th U.S. Rock Mechanics Symposium, Anchorage, Alaska, USA.

Baron, L. Loguntsov, B., and Pozin, E., 1962. Determination of the Properties of Rocks, Gosgortekhizdat, Moscow.

Bishop, A.W., 1967. Progressive failure with special reference to the mechanism causing it, Proc. Geotech. Conf., Oslo, 142-150.

Buller, D., Hughes, S., Market, J., Petre, E., Spain, D., and Odumosu, T., 2010. Petrophysical evaluation for enhancing hydraulic stimulation in horizontal shale gas wells, SPE 132990, SPE Annual Technical Conference and Exhibition held in Florence, Italy, 19-22 September.

Chiu, H.K., and Johnston, L.W., 1983. The uniaxial properties of Melbourne mudstone, Proc. 5th Congr. ISRM, V.1, Melbourne, A209-A214.

Copur, H., Bilgin, N., Tuncdemir, H., and Balci, C., 2003. A set of indices based on indentation tests for assessment of rock cutting performance and rock properties, J. of South African Inst. of Min. and Metallurgy, 103(9), 589-599.

Grove, B., Heiland, J., Walton, I., and Atwood, D., 2009. SPE J. Drilling and Completion, 678-685.

Hajiabdolmajid, V., and Kaiser, P., 2003. Brittleness of rock and stability assessment in hard rock tunneling, Tunneling and Underground Space Technology, 18(1), 35-48.

Halleck, P.M., Saucier, R.J., Behrmann, L.A., and Ahrens, T., 1988. Reduction of jet perforator penetration in rock under stress, SPE 63th ATCE, SPE 18245, Houston, TX, USA.

Holditch, S.A., 2006. Tight gas sands, JPT 58(6): 86-93, SPE 103356.

Holt, R.M., Fj^r, E., Nes, O.M. and Alassi, H.T., 2011. A shaly look at brittleness, 45th US Rock Mechanics / Geomechanics Symposium, ARMA 11-366, San Francisco, CA, USA, June 26-29.

Honda, H., and Sanada, Y., 1956. Hardness of coal, Fuel, 35, 45-461.

Hudson, J.A. and Harrison, J.P., 1997. Engineering Rock Mechanics - An Introduction to the Principles, Pergamon, Elsevier Science, Amsterdam, Netherland.

Hubbert, M.K., and Willis, D.G., 1957. Mechanics of hydraulic fracturing, Trans. SPE-AIME. 210, 153-168.

Hucka, V., and Das, B., 1974. Brittleness determination of rocks by different methods, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 11(10), 389-392.

Ingram, G.M., and Urai, J.L., 1999. Top-seal leakage through faults and fractures, the role of mudrock properties, Geological Society, London, v.158, 125-135.

Inyang, H.I., 1991. Development of a preliminary rock mass classification scheme for near surface excavation, Int. J. Surface Min. and Reclamation, 5, 65-74.

Jarvie, D.M., Hill, R.J., Ruble, T.E., and Pollastro, R.M., 2007. Unconventional shale-gas systems: the Mississippian barnett shale of north-central Texas as one model for thermogenic shale-gas assessment. AAPG Bulletin 91 (4), 475-499.

Jin, X., Shah, S.N., Rogiers, J.C., and Zhang, Bo, 2014. Fracability evaluation in shale reservoirs -an integrated petrophysics and geomechanics approach, SPE 168589, SPE Hydraulic Fracturing Technology Conference, Woodlands, TX, USA.

Kahraman, S., 2002.Correlation of TBM and drilling machine performances with rock brittleness, Eng. Geol. 65, 269-283.

Kirby, S.H., 1980. Tectonic stresses in the lithosphere: constrains provided by the experimental deformation of rocks, J. Geophys. Res., 85, 6353-6363.

King, G.E., 2009. Perforation basics - how the perforating processes work, George E. King Engineering.

Lawn, B., and Marshall, D., 1979. Hardness, toughness, and brittleness: an indentation analysis, J. of American Ceramic Soc., 62(7-8), 347-350.

Lu, X., 2005. Uniaxial and triaxial behavior of high strength concrete with and without steel fibers, Ph.D. Dissertation, New Jersey Institute of Technololgy, USA.

Lutz, S.J., Hickman, S., Davatzes, N, Zemach, E., Drakos, P., and Tait, A.R., 2010. Rock mechanical testing and petrologic analysis in support of well stimulation activities at the desert peak geothermal field, Nevada, Proc. 35th Workshop on Geothermal Reservoir Engineering, Stanford Univ., CA, USA.

Miskimins, J.L., 2012. The impact of mechanical stratigraphy on hydraulic fracture growth and design consideration for horizontal wells, Search and Discovery Article #41102, Tulsa Geological Society Lunch Meeting, Nov. 27.

MPE (Modern Plastics Encyclopedia), 1996. The McGraw-Hill Companies.

Niwa, Y., and Kobasayashi, S.H., 1974. Effect of couple-stresses distribution in specimens of laboratory tests, Proc. 3rd Congr. ISRM, V. 2, Denver, USA, 197-201.

Pagoulatos, A., 2004. Evaluation of multistage triaxial testing on Barea sandstone, M.S. Thesis, Univ. of Oklahoma, Norman, USA.

Papanastasiou, P., 2002. Hydraulic fracturing: basic concepts and numerical modeling, Dept. of Civil and Environmental Eng., Univ. of Cyprus, Cyprus.

Quinn, J.B., and Quinn, G.D., 1997. Indentation brittleness of ceramics: a fresh approach, J. of Materials Sci., 32(16), 4331-4346.

Raaen, A.M., and Brudy, M., 2001. Pump in/flowback tests reduce the estimate of horizontal in-situ stress significantly, SPE 71367, SPE Annual Technical Conference and Exhibition, New Orleans, USA, 30 September-3 October.

Rickman, R., Mullen, M., Petre, E., Grieser, B., and Kundert, D., 2008. A practical use of shale petrophysics for stimulation design optimization: all shale plays are not clones of the Barnett shale, SPE 115258, SPE ATCE, Denver, CO, USA, Sept. 21-24.

Romanson, R., Pongratz, R., East, L., and Stanojcic, M., 2011. Novel, multistage stimulation processes can help achieve and control branch fracturing and increase stimulated reservoir volume for unconventional reservoirs, SPE 142959, SPE / Europec / SPE ATCE, Vienna, Austria, May 23~26.

Sehgal, J., Nakao, Y., Takahashi, H., and Ito, S., 1995. Brittleness of glasses by indentation, J. of Materials of Sci. Letters, 14(3), 167-169.

Sone, H., and Zoback, M., 2013. Mechanical properties of shale gas reservoir rocks - part 1: static and dynamic elastic properties and anisotropy: Geophysics, V.78, #5, 381-392.

Sone, H., and Zoback, M., 2013. Mechanical properties of shale gas reservoir rocks - part 2: ductile creep, brittle strength, and their relation to the elastic modulus: Geophysics, V.78, #5, 393-402.

Suppe, J., 1985. Principles of Structural Geology, Prentice-Hall, Eaglewood Cliffs, New Jersey, USA.

Ticona, 2000. Designing with Plastic, The Fundamentals, Ticona, Prod. Info. Services, Florence, KY, USA.

Van Dam, D.B., Papanastasiou, P., and de Pater, C.J., 2002. Impact of rock plasticity on hydraulic fracture propagation and closure, SPE 63172, SPER ATCE, Dallas, TX, USA, Oct. 1~4.

Walsh, J.B., and Brace, F.A., 1964. A fracture criterion for brittle anisotropic rock, J. Geophys. Res., V.69, 3449-3456.

Wang, F.P., and Gale, J.F., 2009. Screening criteria for shale-gas system, Gulf Coast Asso. of Geological Soc. Transactions, 59, 779-793.

Weeks, S.G., 1974. Formation damage or limited perforation penetration? Test well shooting may give a clue, Journal of Petroleum Technology, 979-984.

Wickham, 2012. Structural Geology, Chapter 5, Rheology, Univ. of Texas at Arlington, USA, GEOL 3443 course book.

Yang, Y., Sone, H., S., Hows, A., and Zoback, M.D., 2013. Comparison of brittleness indices in organic-rich shale formations, 47th US Rock Mech. Symposium, San Francisco, USA, June 23~26.

Yagiz, S., 2009. Assessment of brittleness using rock strength and density with punch penetration test, Tunnelling and Underground Space Tech., 24(1), 66-74.

You, M., 2011. Strength and damage of marble in ductile failure, J. Rock and Geotech. Eng., 3(2), 161-166.

Zehnder, A.T., 2012. Fracture Mechanics, Springer Sci. & Business Media, Lecture Notes in Applied and Computational Mechanics, V.62.

Zhang, J.J. and Bentley, L R., 2005. Factors determining Poisson's ratio. CREWES Research Report, Vol. 17.