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7/23/2019 Tuesday 21 May 2013 - Keynote - Charles Fairhurst
1/44
Fractures and Fracturing
a presentation
by
Charles Fairhurst*
to
The International Conference for Effective and Sustainable
Hydraulic Fracturing
20-22 May 2013,
The Hilton Brisbane, Australia.
*Senior Consultant, Itasca Consulting Group, Inc. Minneapolis, USA.
Professor Emeritus, University of Minnesota. Minneapolis.
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Purposes of Hydraulic Fracturing
to enhance connectivity between existing fractures
for improved
fluid flow
conditioning
-where natural fracturing is not sufficient
(e.g. Caving of longwall goaf ;block caving in mines).
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Kirsch (1898)Circle
Inglis (1913)
Ellipse
Griffith (1921). Stress is highly concentrated at tip of
degenerate ellipse very thin crack or flaw.
Tensile Strength of Solid should be about
E/3. Actual strength is three orders lower.
Inter-atomic Force-Separation Relationship
Stress Concentrations around
holes in Isotropic Continuum
Fracture Mechanics
Linearly Elastic Fracture Mechanics (LEFM)
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Theorem of Minimum Potential Energy.
The stable equilibrium state of a system is that for whichthe potential energy
of the system is a minimum.
The equilibrium position, if equilibrium is possible,must be one in which
rupture of the solid has occurred, if the system can pass from the unbroken to
the brokencondition by a process involving acontinuous decrease of potential
energy.
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P = W +U + S +K ( + )
Changes in
P = Potential Energy of System.W = Potential Energy of Applied Forces
U = Strain Energy
S = Surface Energy
K = Kinetic Energy
F =Frictional Energy etc.
Crack accelerates, decelerates, goes
around or through grains seekingMinimum Potential Energy path.
Potential Energy Changes during
Crack Propagation throughHeterogeneous Solid under Tension Crack may stop, but rock strength may
decrease with time - and crack may extend.
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Crack Propagation from Internally Pressurized Hole in a Glass Plate
Porter and Fairhurst (1970) - after Mindlin (1939)
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Hydraulic Fracturing (1949)Unlike previous discussion, fracture extension is by fluid injection
In an impermeable medium, the viscous energy dissipation associated with driving fluid through the fracture
(Reynolds , Poiseuille laws) competes with the energy required to break the solid material.In a permeable medium, fluid leak-off further complicates the mechanics of crack propagation.
Fracturing of the rock at the crack tip is governed by LEFM i.e. the asymptotic form
w = K1s
1/2
,
w is crack aperture, and s is distance from the crack tip.
Where viscous flow dominates, the coupling between the fluid flow and solid deformation leads
to the asymptotic formw =K2s
2/3
K1, K2 are constants.
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Scaling
The discovery of scaling laws very often allows an increase,
sometimes even a drastic change, in the understanding of not only asingle phenomenon but a wide branch of science.
G.I.Barenblatt. Scaling [Cambridge Univ.Press (2003)]
Important attribute of classical analyses is that solution is given in
terms of dimensionless groups.
..
Previous analyses assumed that the medium was a
homogeneous continuum.
Will now consider rock mass.
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Rock in situ is probably the most complex material encountered in any
engineering discipline.
Pre-loaded by tectonic and gravitational loads for many millions of years,
transected with fractures and a variety of planar discontinuities, etc., the
mechanical behavior can only be determined directly in the field.
.
Mining evolved empirical rules over many, many years; well aware of
complexity
- technology going beyond limits of experience - into uncharted territory.
-direct 3D access to subsurface. (shared with Civil Engineering)
- little R&D investment in rock mechanics in past 2~ 3 decades.
Petroleum- (150 year history) - direct 1D access only; some rules ;
- intensive R&D - results proprietary.
Other subsurface engineering developments -Enhanced Geothermal,Carbon Sequestration; Drill Cuttings Injection; Tight Shales, etc.?
- Relatively little experience
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Importance of Pre-existing Fracture Networks
Enhanced Geothermal Systems - Fenton Hills, New Mexico, 1970
.idea that hydraulic pressure causes competent rock to rupture and
create a disc-shaped fracture was refuted by the seismic evidence.
Instead, it came to be understood that
hydraulic stimulation leads to the opening of existing
natural joints
that have been sealed by secondary mineralization.
Over the years additional evidence has been generated to show that the
joints oriented roughly orthogonal to the direction of the least principal
stress open first, but additional joints open as the hydraulic pressure is
increased
(Duchane and Brown GHC Bulletin Dec. 2002 p.15 GHC (Geo-Heat Center)
http://geoheat.oit.edu/7/23/2019 Tuesday 21 May 2013 - Keynote - Charles Fairhurst
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Increasingfluidpressure
Hydraulic Fracturing may be preceded by Slip on JointsIn a Permeable Jointed Rock.
Hydro-Shearing
Hydraulic
Fracturing
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Fracture
representation
3D Discrete
Fracture Network
(DFN)
Intact rock
representation
(including brittlefracture)
Synthetic Rock Mass (SRM)
Bondedparticle
assemblyintersected
withfractures(SRM)
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13
The consequence is that each element appears to bephysically isolatedfrom its neighbors during one time step;
Thus
Explicit Finite Difference Method - The Calculation Cycle.(Results of each cycle can be superimposed to form a movie of evolution of deformation)
Forces are fixed
duringthis
calculation
Strain rates are
fixed duringthis
calculation
(forallmass-points)
(forallelements)
All Itasca codes use an explicitsolution method that marches on in time
(even for static problems). Cundall, 1970.
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Observed Path of Hydraulic Fracture as revealed by Mine-Back
Courtesy Jeffrey et al; CSIRO
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Response to Complexity and Lack of Understanding in Engineering.
1. Develop empirical rules based on experience.
2. Develop theory to refine and improve practice.
Industrial Revolution later development of Continuum Mechanics.Rock Mechanics in Mining and Civil Engineering. (3D access to rock mass)
Petroleum - 1D access (borehole) greater research emphasis (proprietary)
Limits to Empiricism
requires practical experience;
applicable only within bounds of available experience.
Proposed applications of Hydraulic Fracturing to situations where
Little prior experience.
No time to develop empirical rules.
Enhanced Numerical Modeling and Observational Tools are Available.
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Numerical Experiments.
Rock mechanics models fall into the class of data-limited problems;
one seldom knows enough about a rock mass to model it unambigously.
The purpose of modelling data-limited problems is to gain understanding
and to explore potential trade offs and alternatives, rather than to make
absolute predictions
A model is an aid to thought, rather than a substitute for thinking.
plan the modelling exercise in the same way as you would plan a laboratoryexperiment.
(Starfield and Cundall, 1988)
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Major Challenge
is to define
realistic
Discrete Fracture Networks (DFNs)
especially for borehole access situations.
Progress!
Do DFN characteristics depend significantly on rock
formations e.g. crystalline; sedimentary?
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Fracture Imaging
Schlumberger
P
P
P
P P
S
S
P
Imaging of reflected waves (PtPand StS) when the tool is above or
below the fracture.
Imaging with mode conversions(PtS and StP) when the fracture is
between the transmitter and
receiver.
Waves return to the tool based on
the geometry of the event relative
to the tool:
Up-dip reflector imaged when the
tool is above the fracture
Down-dip reflector imaged when
the tool is below the fracture
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Horizontal well with open fractures away from the wellbore
Schlumberger
24
00
-20
20
-40
F
eet
X000 X100 X200 X300 X400 X500
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Summary #
Reflections from monopole receivers have been
used to successfully image structure and fractures
Depth of investigation can vary greatly, but can
beas much as 140 ft on each side of theborehole.
Bridges the resolution gap between wireline and
seismic data.
Complementary data from Stoneley mobility,
Anisotropy, Rock properties and potentially
Radial Profiling can be acquired in the same
pass.
0.1 1.0 10 100
0.1
1.0
10
100
Range [m]
Resolution[m]
ultra-
sonic
sonic
2D seismic
3D seismicVSP
(3D)Deep
Acoustic
Imaging
The Acoustic Gap
0.1 1.0 10 100 1000
100
10
1
0.1
10
D.Grael et al*; Borehole Acoustic Reflection Survey (BARS) from Modern, Dipole Acoustic Logs for High-Resolution
Seismic-Based Fracture Illumination and Imaging SPWLA (Soc. Petrophysicists and Well Logging Analysts),
53rd
Annual Logging Symposium, June 16-20, 2012 Cartagena , Columbia .
*D. Grae, G. A. Ugueto C., J. A. Roberts, H. Yamamoto, T. Oliver and G. Martine
7/23/2019 Tuesday 21 May 2013 - Keynote - Charles Fairhurst
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(a)Micro
Seismic
Indication
of
Upward
Migration
of
Fluidalong Fault during HydraulicFracturing
(b)NumericalExplanationof
UpwardMigration.
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In Situ Stress and Critically Stressed Sub-Surface
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In-Situ Stress State
1. Magnitude and Orientation affected by undetected fractures/faults
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Observed variability of normal stress across a thrust fault at the URL, Pinawa,Canada.
Local In situ Stresses Affected by Local Variations on Faults
How do In situ Stresses Change with Rock Type;
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Limestone
H > V> h
Argillite(indurated clay)
H = V = h
Limestone
V > H > h
In
Situ
Stresses
Change
with
Rock
Type
(Underground
Research
Laboratory,
Bure.
France)
How do In situ Stresses Change with Rock Type;
Relevance to Tight Gas Shales ?
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Aseismic slip induced by forced fluid flow as detected by P-wave tomogrqphy
(Soultz-sous-Frets, France) Cornet et al; 2012
(a) The injection program (black curve is flow rate; blue curve is well-head pressure; horizontal axis is time in
days;
(b) 3D view of the seismic cloud with respect to the GPK2 borehole. Vertical axis is depth and horizontal axes
are distances respectively toward the north and toward the east; and
(c) Horizontal projections corresponding to the yellow horizontal plane. The vertical green plane is shown as
line AB in the plots of part c. P-wave velocity tomography for sets 2,3 and 4 are indicated respectively by
orange, yellow and green colors in the injection program. The vertical axis corresponds to North.
20%Drop
in
Vp.
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Vp 6.4km/s=1.00
Vp 5.1km/s=0.80
Aseismic Deformation
20%dropinPwavevelocityinregion
~500moutsideseismiccloud.
2.0E+07
d
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0
5
10
15
20
25
0 2 4 6 8 10
BoreholePressure(MPa)
Total
Time
(days)
0.0E+00
2.0E+06
4.0E+06
6.0E+06
8.0E+06
1.0E+07
1.2E+07
1.4E+07
1.6E+07
1.8E+07
0 250 500 750
Pressure(Pa)
Distance(m)
2days
6days
7days
8days
9days
10days
0.0E+00
2.0E+06
4.0E+06
6.0E+06
8.0E+06
1.0E+07
1.2E+07
1.4E+07
1.6E+07
1.8E+07
2.0E+07
0 250 500 750
Pressure(Pa)
Distance(m)
2days
6days
7days
8days
9days
10days
=104 mD
Fluid Flow into Far -Field
continues
after Borehole Depressurization.
=250mD
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9
Why Doesnt Microseismicity Correlate
With Production?
The Total Rock Volume
Affected by
Microseismicity
Accounts for Less
Than 1% of Gas
Production in First 6
Months
IngrainInc
Micro-permeabe gas shales.
Courtesy Prof.A.Nur
Stones
have
begun
to
speak,
because
an
ear
is
there
to
hear
them.
..
7/23/2019 Tuesday 21 May 2013 - Keynote - Charles Fairhurst
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g p ,Cloos,ConversationswiththeEarth(1954),4
Fracture
Network
Engineering.
Synthetic
Rock
Mass
and
Synthetic
Seismicity
Modelsarecomparedwithobservedmicroseismic signalsforrealtime controlof
fracturenetworkdevelopment. (EnhancedGeothermalSystems.)
Microseismicity predicted
and
observed.
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Rock Conditioning
In situ Rock Weakening /Size Reduction
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Pre-Splitting (Atlas Copco)
Plexiglas after Detonation of Explosive in Hole
(Persson et al; (1970) ISRM Congress, Betgrade (1970)
Rock Conditioning - Hydraulic (Gas) Fracturing
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C l i
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Conclusions.Hydraulic Fracturing applications increasingly important for extraction of resources and
injection /disposal of waste products.
Pre-existing fracture systems have dominant effect on hydra-frac development and related
stimulation procedures.
Rock Fracture Mechanics is potentially as broad as classical Fracture Mechanics.
Rock mass embraces wide variety of constitutive behaviors; rock is not critically
stressed everywhere in crust; concept can be very misleading.
Micro-seismic detection systems are essential but do not identify full response of system to
stimulation additional geophysical tools needed.
Datalimited nature of Earth Resource Engineering problems gives added importance
to analysis and modeling.
Numerical experiments (scalable) can be major aid to practical advance but will require
planning/co-ordination to allow sound Mechanics-Informed practical decisions.
Fracture Network Engineering is sound goal, but requires considerable additional
development.
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Thank you
- to the organizers of Hydraulic Fracturing 2013
for the invitation to participate in the Conference
and to present this Lecture;
- to the audience for your attention.
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Back - up Slides
D/R = 0.1 D/R = 0.2Potential for core damage during
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0
0
0.2
2 4
0.4
0.6
D/R = 1D/R = 2
t
t
tt
t
o
o
oo
o
/
/
/ /
/0.00
0.50
0.25
t o/
0.00
0.50
0.25
t o/
0.0
1.0
0.5
t o/
0.0
1.0
0.5
Maximum
Maximum Maximum
Maximum
= 0.05
= 0.5 = 1.0
= 0.1
Core Depth / Core Radius, D/R
t
o
/
Max.tensilestressincore
Far-fieldstress
,
D
R
g gcoring operation
Numericalresults
Best fit curve
Let
Let
n
m
=
=
=
=
t
ti
c
c
c
o
o
o
tensile strength
induced tension in core
compressive strength
in-situ horizontal stress
[n ~ 0.1]
[m ~ 0.5]
Then core damage occurs if
>
>
n/m
0.2i.e.,
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