Module C: Hydraulic Fracture
Behavior: Assumptions and Reality
LACPEC – 2007
Short Course on Petroleum Rock Mechanics
Maurice B. Dusseault
University of Waterloo
Hydraulic Fracturing Uses

To enhance well productivity (drainage area)
 Propped
fractures in reservoirs, geothermal well
fracs, access to naturally fractured zones ....

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Introduce thermal energy (steam fractures)
Stress measurements (step-rate tests,
Minifrac™, LOT, XLOT)
For massive solid oilfield waste (NOW)
injection (SFI)
Drill cuttings annular reinjection
Acidizing, for “choking” rates, other uses
Deep biosolids injection (Los Angeles – 2008)
E.g.: Choking Production
Propped fracture chokes off the
high-k zone, allowing a larger
production proportion from lower
zones, increasing recovery ratios
Poor recovery
from lower
sand bodies
high k sand body
medium k sand
medium k sand
shales
medium k sand
Used in the North Sea by Statoil to choke production
from the higher k upper layers to get higher overall RF
Hydraulic fracturing produces
more oil, but not all are happy
HF
Operations design
Depths, properties,
initial stresses, etc…
growth
Courtesy Natchiq Corp
In situ stresses
Pressures vs time
HF involves lithostratigraphic model, HF model, operations
design and execution, monitoring and post-analysis
Conventional Assumptions





Fractures propagate as a planar surface
through a solid, linear elastic material
The material is assumed to have an
intrinsic resistance to fracture (eg: KIC)
The far-field stresses stay constant, and
the material properties as well
Fractures are approximately symmetric
Other similar assumptions are common, and
these assumptions are used in developing
models that are used in analysis
E.g.: Fractures are Symmetric
sulphur
Fractures reflect the local stress field,
and tend to elongate asymmetrically
salt
saltdome
dome
fracture
gas
oil
Section A-A′
A
A´
Close
wells
salt
More distant wells
Clearly, not all fractures are symmetric or in the same
orientation! Local stress fields are important!
Typical Model Attributes

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Rock behaves as a Linear-Elastic material
Fracture orientation remains constant
Constant fracture tip toughness (KIC)
controls propagation
Mode I (opening mode) fracture only, no
shear of rock occurs
Bleed-off using a 1-D flow model = ƒ(1/t)
Fluid buoyancy effects often ignored
Constant permeability assumed
Simplifications are necessary for modeling,
but they must be robust!
e.g. Rock Stiffness is Constant
Stiffness - E
E = Stiffness (Young’s Modulus or Bulk Modulus)
assumption
Sandstones are granular media…
These materials display E = ƒ(σ′)
High φ sandstones are strongly non-linear
This affects predictions, behavior
Effective stress - σ′
Be aware of assumptions; make sure they are reasonable
Impact of Modeling Assumptions

In soft, weak sandstones, the various
assumptions made in fracture modeling lead
to a number of problems
 Length
in SWR* is greatly over-predicted
 Aperture predictions are invalid
 Predicted injection pressures rise with time
 Fracture orientation is constant
 Fractures are truly horizontal
 There is no associated formation shearing
 Non-linear bleed-off ignored (L, Dt)

And so on…
*Soft, Weak Rock
Be aware of assumptions; make sure they are reasonable
So What Do We Do??

We behave as responsible engineers:
 Recognize
that models are simplifications
 Learn more about stresses, geomechanics
 Calibrate models in real field cases
 Understand that production changes stresses
 Take measurements when it is feasible

Design on “expected” behavior, but…
 Expect
the unexpected
 Learn from the data for your cases, and,
 Understand the physics behind fracturing

This is what engineering is all about
Be aware of assumptions; make sure they are reasonable
Behavior of Hydraulically
Induced Fractures
Fracture Growth is Complex!
Poor fluid
diversion
Horizontal
fractures
?
?
Upward
fracture
growth
Out-ofzone
growth
?
?
?
Twisting
fractures
Pay
Pay
?
“Perfect”
fracture
Multiple fractures
dipping from vertical
?
T-shaped
fractures
Pinnacle Tech. Ltd.
Fracture models cannot predict highly complex behavior
Controls on Fracture Direction
In situ stresses are the major control!!!
 Fractures propagate normal to s3
 Local fracture propagation direction may be
affected by joints, fractures, bedding, but
for short distances only
 Stresses may also be changed by production
and injection processes!

By massive injection processes (+Dp)
By thermal effects (DT)
By production (depletion) effects (-Dp)
By solid waste injection (DV)
Local Fabric and Fracturing
Locally, fracture
follows fabric;
globally, fractures
follow stress fields
s3
s3
Local stress field around
the borehole (10 D max)
Joint system in the rock
In strong, jointed rock (carbonates), HF locally follows the
joints, but at a large scale, the regional stresses dominate…
Goals and Reality
Or
1200 ft
Or
500 ft
450 ft
Pay
zone
What we want
What we get
Design → Implement → Monitor → Analyze → Learn
Multiple Zone Stimulation
Pay zone
Pay zone
Pay zone
What we want
What we get
Understanding HF will help us design stimulations
Why Vertical Fractures Rise
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Fracture fluid gradient is almost always
less than the s3 gradient = excess Dp is
generated at the top of the fracture
Rise rate can be affected by fluid density
Rise rate can be affected by leak-off
rates (more leak-off = less rise)
Rise rate can be affected by in situ
stresses and stiffness of overlying strata
Rock strength is largely irrelevant in
stopping large vertical fractures rising!!
Why Fractures Rise
Fracture fluid has a
density of < ~1.2
 The gradient of lateral
stress (dsh/dz) is
much more than this
value
 Thus, there is an extra
driving pressure at top
 Deficiency in driving
pressure at bottom
 Fracture tends to rise

pressure
(stress)
lateral
stress
vertical
fracture
injection
point
positive
driving
force
fluid pressure
stress gradient
is typically
17-23 kPa/m
fracture fluid
gradient is
10-13 kPa/m
s3
injection
point
pressure and stress
are about the same
at the injection point
pressure
deficiency
E.g.: 30 m high, Δp = (21 – 11) x 30 m = 300 kPa!
Fractures Rise Out of Zone
injection
wellbore
E2
shale
overburden
t4
t3
reservoir
t2
E1
t1
perforations
If there is no difference in Δσ3, fractures tend to rise
“Horizontal” Fractures
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These tend to occur at shallow depth, in
heated or large DV cases, in high tectonic
stress cases (s3 = sv, thrust regime)
Tend to climb away from injection point
Tend to be highly asymmetric in shape
Propagation of a shear band well in advance
of the parting fracture plane is common
Shallow rising fractures tend to “pan-out”
under stiff, competent strata (eg:
cemented zones, shale interface)
Almost impossible to numerically model in a
physically rigorous manner
“Horizontal” Fractures in SWR*

Horizontal fractures do not grow  s3
pinj > sv
injection
least principal stress = sv
s3
fractures tend to rise
gently in this case
borehole
fracture
pans-out
under shale
asymmetric
geometry
*SWR = Soft, weak rock such as unconsolidated sandstones
“Horizontal” fracture behavior remains poorly understood
Different Stresses in Strata
Often, fractures do not rise out of the zone,
they stay in the zone and propagate laterally.
Why?
 This usually means that σ3 (= σhmin) in the
upper zone is larger than in the lower zone
 This forms a barrier to upward propagation

 The

larger the contrast, the better the barrier
Under this condition, it is easier to grow
laterally than to grow upward, because of the
stress barrier at the top of the zone
Blunting Upward Growth
stress
shmin
sv
This is the “ideal”
fracture, only attained
when higher stresses
in the overburden
blunts fracture rise
High lateral stress
“blunts” vertical growth
Key!!
Fracture grows
in the zone of
lower shmin
depth
Is this common? Yes – relaxed basins, offshore, …
Natural shmin (PF) Variations
Absolute stress values
Stress gradient plot
stress
hydrostatic
po
shmin
sv
shmin
z
sv
z
shale
sandstone
shale
salt
(po is undefined
in salt beds)
limestone
shale
depth
Pore pressure distribution
depth
Frac gradient, PF, is fracture pressure/depth = shmin/z
GoM Case

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In the GoM, it is typical that the shales
have higher lateral stresses than the sands
In other words, PF (shales) > PF (sands)
This provides a “stress barrier” to upward
propagation of hydraulic fractures
It is the common case in all gravitational
basins, also common in normal fault basins
However, this may not apply at great depth
 Shales
have undergone diagenesis, σ changes…
 Lateral stresses in shales now lower than sands

Also, not in tectonic basins, near salt…
Lower Overburden s3 Case
stress
shmin
Normal
s case
depth
sv
Fracture
retreat
Preferential
propagation in the
zone of lower shmin
Initial
fracture
growth
phase
Case of Low Overburden PF

In this case, for tectonic reasons or
diagenetic alterations:
 The
overlying cap rocks (shales or siltstones)
have a lower PF than the reservoir rocks
It doesn’t matter if the overlying rocks are
impermeable (shale), strong (limestone) or
of low porosity (anhydrite):
 Fractures will tend to rise through them,
rather than propagate laterally
 In some parts of the world, deep gas
fractures can rise 4000 m to the sea floor!

Can Fractures Drop?
stress
shmin
sv
Fracture grows
in the zone of
lower shmin
depth
Only limited downward growth
potential exists in real cases
Dropping Fractures
May occur in zones of stress reversion (see
sections on Stresses in the Earth)
 May occur in massively depleted zones
 May occur if the fracture fluid is
extremely dense (e.g. a borate brine
workover fluid)

 Because

the p gradient > σhmin gradient
Only in these cases can one expect that
fractures will have a significant downward
component
Induced Changes in Stress Fields

Near-field stresses are altered by fracture
a pressure increase
causes the stresses
to increase as well
primary
fracture
Dp
secondary fracture
s3 +Ds3
dilated zone
fracture tip
high pressure zone
p > s3 (original)
View from above of vertical fracturing
Fracture Direction Changes
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
A fracture pushes the rock apart, so the
fracture pressures are higher than s3
As the fracture L grows, the fracture
aperture also grows; this increases the
stress normal to the fracture
Near the well, it now becomes easiest to
propagate in a different direction
This is done deliberately in Frac & Pack
Also, the injection plane may flip back and
forth between the two directions
This has been measured in real frac jobs…
Lessons from Nature…
Dikes, ring dikes, sills, etc., are all hydraulic fractures
Orientation Changes in Nature
s3
minor arctuate
ring-dike swarms
original minimum
principal stress
s3
major ring-dike
en-echelon
older dikes
Stress changes take
place during vulcanism
minimum stress
direction becomes
radial after shrinkage
stock
pre-ring-dike
radial dykes
Dikes propagate  to the σ3 direction
First event – radial dikes and stock, then cooling, shrinkage
Second injection event: ring dikes, because σ3 now radial
Rick Dike Complex, Scotland
Spanish Peaks, Colorado
σ3
σ3
Curvilinear dike means a curvilinear σ3 stress field
existed at the time of injection
Sequence of Events…





Initially, stock is emplaced with radial
dikes (hydraulic fractures) generated
because of reduced sq, high sr
Vulcanism stops, rock cooks, country rock
is altered (porosity decreases), shrinkage,
etc. leads to lowered sr
The new generation of dikes propagate
normal to s3, which is now radial (sr)
Thus, the arctuate ring dikes cut across
the older radial dikes!
Proof of stress changes in nature
Spanish Peaks – Dike Pattern
Spanish Peaks – Stress Modeling
Fracture Orientation Changes
Fracture geometry after
first 2/3 of main treatment
Probable fracture geometry
at end of pumping
Creation of new
vertical frac  to
original vertical frac
Wellbore
Limited further growth
of N80°E fracture
vertical frac
horizontal frac
Courtesy Pinnacle Technologies
Tiltmeter data during fracturing confirms multiple
orientations and flipping of growth plane
Depletion and Fractures
The well-known depletion effect changes the
total stresses in the well influence region
 Not all wells are depleted evenly
 There are other effects associated with:

 Proximity
of no-flow boundaries
 Lithological differences (stratification)
 Reservoir heterogeneity, plus Df, Dk with Dp
 Compaction and stress redistribution

Combined, these give an “uncertainty” as to
fracture direction after the depletion of a
field
Depletion Effect Heterogeneity
Original fracture orientation,
virgin reservoir conditions
Fracture orientation in a mature field
with infill wells, altered p, refracs…
source: SPE 29625
by Wright et al.
initial
production
shmin
injection
Local effects have
overridden initial
stress orientations
sh 

1 
sv +
1  2
sp +X
1 
s p  pp
(X is a “fudge” factor)
Depletion is never uniform; it alters the local stress fields,
in this case, the orientation looks close to random!
Depletion and Pressurization
Suppose in situ stresses are similar (±5-8%)
 If fractures originally horizontal, s3 = sv

 Depletion
can reduce shmin to below sv
 This means refracs will be vertical!

If fractures originally vertical, shmin = s3
 Pressurization
can increase sh to above sv
 This means fracs may become “horizontal”
during an injection process! (Especially heating)
Be careful, Dp can change frac orientations!
 Re-determine your fracture directions in
wells if this is critical to the process

Increase in s3  DOrientation
pBD, breakdown pressure
Bottom Hole Pressure
Sudden propagation
Large-scale stress change
with continued injection
s3
s3
Increase in σ3
Time (or V if constant injection rate used)
Pressure-induced volume change + aperture effects
change stresses in the region around the fracture plane.
Fractures and Stresses
Different stresses (shmin) and entry port distributions change fracture disposition
low
closure
stress
high
closure
stress
Point
source
Unrestricted entry
Distributed
limited entry
Multiple points,
limited entry
Courtesy Pinnacle Technologies
Multiple Zone Fracturing
Frac fluids will tend to only enter upper
zone where the lateral stresses are lowest
 A point-source fracture may grow up, not
down, making things worse…
 To achieve a more uniform distribution:

 Measure
stresses to get an idea of contrasts
 Use perforation strategy (size and spacing) to
give more entry capacity in lower zones
 The upper zone is “choked back”
 Design must be based on rate and viscosity
calculations to achieve best results
Can We Fracture Loose Sand?





Some suppose that this is not possible
because the sand will just collapse
Actually, you can do this easily in the lab
The walls stay perfectly intact because of
the seepage force
This arises from Δp/Δl (Same process as
mud support forces in borehole stability.)
It acts outward (in the direction of the
pressure gradient) and supports the
fracture walls as long as there is flow
Fracture in a Sand
This is a fracture
created by injecting a
viscous plaster
 To create a fracture in
sand, inj. rate > leak-off
rate
 This “forces” a fracture
to open to accommodate
the fluid
 However, is it a shear
process before a tensile
parting process?

t
t
s’
s’
Origin of the Seepage Force
F = sADp
F = force
s = shape factor
gradient direction
A = grain area
Dp = drop in p
F
p
f
pf - Dp
A
flow direction
This is a model of one grain of sand
Seepage Force in Fracturing







Pressure drop creates a force on each
grain in the fracture wall
Force is proportional to the product of
gradient, cross-section, and grain width
It is a genuine body-force, like gravity, and
acts outward from the fracture face
Force acts in the direction of gradient
This is why a fracture in an unconsolidated
sand can be generated without a KIC
An important factor in soft, weak rocks
Shearing processes must be taking place!
Hydrodynamic Forces

The hydrodynamic force on grains
p
p-Dp
F
Seepage force
= F = Awp/l
fracture
flow
p
p-Dp
porous flow
The pressure gradient
leads to an outward
seepage force which
keeps grains in place,
permitting creation of
a fracture in a sand
Low-Angle Shearing
**high shear
stress zone
low-k shale stratum
high-k
reservoir
high p
area,
sH > sv
sH > sv
sv
sH
low-k shale stratum
**slip can occur in front of a fracture parting plane
Low-angle shearing happens in many thermal projects
Fracturing and Shear

Fracture injection (thermal or nonthermal) can lead to shearing
 Pore
pressures are > σ3, so there is no effective
stress; hence frictional strength = very low
This is most serious in the case of
“horizontal” fractures (sv = s3)
 Shearing is in the form of a low-angle
thrust fault mechanism
 Shear planes concentrate along the bottom
of strong, stiff beds (cemented streaks)
 Many examples in Alberta (CSS steam inj.)

Fractures and Casing Shear
lean oil
sands
fracture
plane
A
B
C
silty bed
oil
sands
s1
s3
A: early shear, occurring at the base of a shale bed
B: later shear, at the top of the formation
C: well showing some distortion, not failed yet
Vertical exaggeration = x2 to x3
injection
well
Do Fractures Initiate Suddenly?






In intact rock, yes, because the value of sq
is the highest at the borehole wall
However, in many cases, sq can be reduced
in a zone near the well
In this case, the fracture initiates well
before breakthrough
It grows slowly and gives a non-linear
response
When it passes the peak sq, it then
“shoots” out suddenly
The p-t response is quite non-linear
Non-Linear Response
bottomhole pressure
propagation
breakthrough
stable fracture propagation
fracture initiation occurs very early
virgin reservoir pore pressure
po
non-linear response
time (constant pumping rate)
Fracture is initiated and grows well before it breaks through and extends
This is usually the case in weak rocks like tar sands…
Rock Stiffness Effects
Rock stiffness (E) affects aperture: high E,
low aperture; low E, large aperture
 Aperture affects hydraulic pressure
distribution in the fracture (low aperture =
higher losses)
 Therefore, high E impedes propagation in that
stratum, low E enhances propagation
 Some rocks can deform plastically (UCS,
chalk, coal, high f dirty sands ...)

Effects of Stiffness (E)
A'
Section A-A'
softer stratum
stiffer stratum
A
s3
Stiffness controls fracture aperture: wider in lower E rocks
Formation Stiffness Effects
If stresses are not a factor, fractures will tend
to be blunted in stiffer strata, propagating
laterally more easily than vertically
High “E”
Low “E”
stress
Stiff overburden
shmin
Soft reservoir
depth
A stiff caprock can blunt upward growth
Rock Stiffness Effects
Softer overburden
Stiff reservoir rock
Low “E”
High “E”
Fractures that propagate into a less stiff
rock will tend to extend preferentially in
that material, other things being equal.
Conversely, propagation into soft strata is easier…
Permeability Effects





High k stratum generates massive blunting
Propagation potential reduced if a new
high-k stratum encountered (loss of
hydraulic E)
In extremely low-k strata (shales), no
bleed-off, distant propagation, high p
generated
Bleed-off changes with time as the
pressure gradients change with inflow
Fluid-loss control agents can be used wisely
Blunting in a High-k Zone
A
Section A-A
Low k
stratum
“Blunting” through
high k zone effect
High k
stratum
Low k
stratum
Fracture retreats after
high k zone intersected
A
Fracture before
intersection
Higher k, higher leak-off, more blunting…
Rock Strength Effects





Rocks are jointed, fissures, bedded, flawed
Fracture will “find” these flaws immediately
Resistance of such materials to propagation
is minimal with a a large fracture length
If strength is correlated to another
property (k, E, s3), it may “appear” to be
important
In general, strength (fracture toughness) is
largely irrelevant for large fracs
Local Fabric and Fracture
Locally, fracture
follows fabric;
globally, fractures
follow stress
s3
s3
The strength of the intact rock
is not relevant in this case
Joint system in the rock
Monitoring Fractures






Precision real-time tilt monitoring (<3000m)
Microseismic monitoring using geophones at
depth relatively near the fracture site
Pressure-time response in the injection well
Impedance tests in a propped fracture
Borehole geophysical logging (T, tracers)
Other methods are problematic at best
 Implies a “poorer” method of monitoring
Hydraulic Fracture Mapping

Characteristic
deformation pattern
makes it easy to
distinguish fracture
dip, horizontal and
vertical fractures
Gradual “bulging” of
earth’s surface for
horizontal fractures
 Trough along
fracture azimuth for
vertical fractures
 Dipping fracture
yields very
asymmetrical bulges

Dip = 0°
Maximum Displacement:
0.0020 inches
Dip =90°
Maximum Displacement:
0.00026 inches
Dip = 80°
Maximum Displacement:
0.00045 inches
Tiltmeter Fracture Mapping
Tilts measured
 Mathematical sol’n
 If depth > 3 km, tilt
measurements are
quite difficult
 One solution is use
of borehole
tiltmeters
 Mapping has
recently been
achieved at > 3km

Surface tiltmeters
Depth
Downhole
tiltmeters in
offset well
Fracture
Courtesy Pinnacle Technologies
Fracture and Tilt Vectors
Courtesy Pinnacle Technologies
Vertical
Azimuth
Horizontal
1000 feet
North
Measured Tilt -- 250 nanoradians
Tiltmeter Site
Theoretical Tilt -- 250 nanoradians
Frac: Vertical Azimuth: N39°E Dip: 87° W Depth: 2300 ft
1000 feet
North
Measured Tilt -- 500 nanoradians
Tiltmeter Site
Theoretical Tilt -- 500 nanoradians
Wellhead
Frac: Horizontal Azimuth: N/A Dip: 6° N
Depth: 2900 ft
Reality and Tilt Modeling
Inversion of tilt data is
based on relatively
simple and symmetric
source functions.
It is nevertheless quite
powerful in giving
orientation and size of
fractures.
Actual fracture
dimensions
Estimated fracture
dimensions
Lessons Learned







HF behavior is complex, but understandable
Stress fields dominate fracture propagation
behavior, strength is almost irrelevant
Almost all fractures rise, except when there
is a stress barrier
Permeability, stiffness, etc. are important
second-order effects
Fractures change directions over time!
Monitoring fracture behavior is feasible
Geomechanics concepts are essential for HF
Additional Materials on Hydraulic
Fracture Behavior
Volume Change Effects
+DV has an effect similar to +DT
 +DV can occur through fluid injection and
through injection of a slurry
 -DV occurs during depletion, or during
solids production (Cold Heavy Oil
Production with Sand for example)
 Stress changes large enough to change the
fracture orientations happen regularly with
injection or production volume changes

p Gradients
High pressure liquid injection
A
d
low k
A
very slow flow
shale
rapid flow
high k
Dp
B
p
sandstone
shale
p
B
Dp
d
High gradients across the fracture wall support the sand
Pressure Gradients





In a fracture, assume that p ~ constant
At the advancing fracture tip, we always
have very high local pressure gradients
On the flanks, near the injection point, p
gradients become flatter with time
+Dp (p increase) involves s, hence +DV,
therefore the total stresses should
increase
Thus, facture gradients will increase with
continued injection if there are no
additional effects (e.g. thermal effects…)
Poroelastic Effect

+p causes +s3, leads to higher inj. pressure
Δp
s3 +Ds3
pressured region
fracture
Some Thermal Aspects of
Hydraulic Fracturing
Thermal Effects





The large-scale vertical stress is governed
by the force of gravity and the free
surface
-DT decreases sh = vertical fracs with time
+DT increases sh = horizontal fracs
All thermal processes, in the absence of
other effects, eventually lead to the
generation of “horizontal” fracturing
CO2 fracs lead to easier and fatter fracs
because of the thermal cooling
T Gradients
Hot fluid injection
A
d
low k
A
shale
conductive heat flow
convective heat flow
high k
DT
B
T
sandstone
shale
T
B
DT
steep T
gradients
d
Temperature Gradients






In permeable rocks and high injection
rates, heat transfer is convective
(advective)
Steep t-gradients are maintained for long t
In adjacent low-k rocks, it is conductive
Gradients flatten out toward steady state
DV differences lead to regions where s3 >
p, others where s3 < p (frac condition)
Thus, fracture gradients and orientations
evolve with thermal processes
Heat and Stress Fields

Near-field stresses are altered by fracture
Temperature increase
primary fracture
causes stresses to
increase near fracture
DT
s3 +Ds3
high pressure zone
p > s3 (original)
secondary fracture
heated zone
fracture tip
Thermal Fracturing
Clearly, large DT alters stress fields
 Heating leads to horizontal fracs (sv  s3)
 Cooling leads to vertical fracs (shmin  s3)
 We can do some interesting things:

 Multiple
+DT fracs in horizontal wells
 Multiple –DT fracs in geothermal wells
 Zonal control using cooling fracs
 Heating to restrict fracture (increase pfrac)
 Cooling encourages borehole wall fracs
 Other processes as well
Hot Fluids DOrientation
pBD, breakdown pressure
Bottom Hole Pressure
Sudden propagation
sv
Large-scale stress change
with continued heating
s3]initial
Time (or V if constant injection rate used)
s3]farfield
CSS - First Cycle Responses
pressure
A
B
C
D
original sv (= g·z)
initial shmin (= s3)
“thief” zone
A: pBD, usually > sv
B: p falls off
C: p rises with DV
D: fluid losses?
shmin = s3
time
Fracture orientation changes with rapid steam injection into
low permeability tar sands, leading to “horizontal” fracs
Pressure Rise in CSS

Initially, virgin s3 controls pP, but:
from the volumes injected, and
 DV from expansion (DT in rock  DV  +Ds),
 DV





Leads to increase in the local stresses (sh )
Locally, sh becomes > sv (now = s3)
Fractures become horizontally dominated
Now, overburden + p losses govern pP
Generally, pinj  1.15 - 1.25 sv
Heat Losses - CSS 1st Cycle

If shmin << sv, vertical fractures
 These
fractures rise substantially (gf << s3)
 Break-through to overlying high-k zones common
 Irrecoverable heat loss (fractures close when p <s3)

If shmin > sv, “horizontal” fractures
 May
exist as the natural state in shallow reservoirs
 May be induced by injection and DT effects

Nevertheless, these will rise to top of zone
 Uneven
heating, loss of some of the lower resource
 With time, downward propagation occurs (slowly)
Horizontal Well DT Effects
+DT
The first vertical steam fracture increases s3, leading to
initiation of a second fracture, likely farther down the
casing. s3 in region 2 goes up, a third fracture starts…
Eventually, shmin is no longer s3;
then fractures change orientation
+s3
s3
sv
1
+s3
2
3
Stable Thermal Fracturing








Horizontal well ║ to s3 , fractures vertical
Thermal fracturing  +DV  +Ds3 (local)
Thus, in first fracture, pfrac as s3 (locally)
After some t, easier to fracture elsewhere
Frac #1 is near heel, others step toward toe
The process continues until s║ to well is no
longer s3, then frac orientations will change
New orientations are related to [s]initial
Fractures are stable until [s] is altered
Cooling-Induced Fractures
To
To
Water
displacement
front
DT
DT
front
DT
sHMAX
shmin
DT
Cooling shrinks the rock, stresses drop, PF drops…
Geothermal Fracturing
Hot fluids out
Cross-section
Cold water in
Large propped fracture
Massive cooling by conduction
“Daughter” fractures
propagate at 90° to the
mother fracture, heat
exchange becomes better.
ΔT as great as 300ºC lead to large stress changes, in this
case, leading to initiation and propagation of new fractures
Massive Water Re-injection
Water may be injected hot or after cooling
 DT between target stratum and H2O leads
to thermoelastic stress changes
 Beneficial or detrimental, depending on
various factors (e.g. IOR or disposal?)
 A subtle interplay exists:

 Conductive
versus convective heat transfer
 Permeability of strata involved is important
 In situ stresses in all strata are important
Benefits of Water Re-Injection
Cold water injection is common
 Thermoelastic shrinkage develops (DTDV)
 Stresses near the injector are reduced:

 Fracture
aperture increases, keff goes up
 Intact rock k remains about the same
 s3 drops, and pinj may become > s3
Lower pinj needed to achieve Qinj
 Less pump power needed to achieve Qinj
 Injection wells perform better!

Cooling-Induced Shearing
adjacent wells
region of high shear
overburden
warm
reservoir
sHMAX < sv
-DT
t
+ve
-DT
T in the reservoir
t
-ve
max shear
Cooling can also lead to casing shear (shear fracture)
Water Re-Injection Problems
Mainly during water-flooding (IOR)
 Thermoelastic shrinkage develops (DT=DV)
 Stresses in the flooded zone drop

 Fracture
aperture increases, keff goes up
 Bounding rocks may reach pinj > s3
 Loss of seal, excessive channeling
Conformance is impaired, efficiency lost
 Effect may be greatly delayed in time
 Effects are largely irreversible

Thermal Cooling Effect on SRT*
*Step-Rate Test
pressure
before injection
pfrac
after injection
pfrac
lowered
pfrac near wellbore
higher pfrac far from wellbore
rate
Thermal Stress Alteration







Stresses are coupled to ΔT through ΔV
calculations (thermal volume change…)
 is the coefficient of thermal expansion
ΔV =  ΔT, is calculated for each unit volume
ΔV is then put into the s & Δp model
Flow problem is solved (both advection and
conduction) to get {ΔT}
Conductive heat flow included, if important
Now, the thermal-geomechanical model will
give stresses (from both Δp and ΔT)!
Parameters for DT Analysis








Specific heat of minerals, cm (convection)
Bulk specific heat of rock, cb (conduction)
Thermal conductivity, ij (conduction)
Hydraulic conductivity, kij (convection)
Thermal expansion coefficient (ij)
Rates of injection, Qinj
In situ stresses, sij, for all involved strata
Stratigraphy, porosity, etc. ...
DT by Convection or Conduction?
Tinj
Tinj
shale
k~0
sandy shale
low k
sandstone
high k
shale
k~0
radius
pure conduction
mixed conduction-convection
pure convection
pure conduction
depth
90% Tinj
Fracture Where sv = s3
p
solids injection
pinj
pinj~1.1-1.3sv
pisip = sv
reservoir pressure
4-16 hours continuous injection
time
This is a case of massive solids re-injection
Injection Rate Effects






p in the fracture = , s, , V/t, ...)
To create a short, fat fracture, use high rates
and a viscous fluid (trade-offs are vital)
To create a short, thin fracture, use a lowviscosity fluid and low rates
Extremely high rates can locally change
stresses, generating locally orientated “arms”
FracPack is a good example of rate effects
We deliberately use high rates, high viscosity,
and heavy proppant load to get better effects
bottomhole pressure
High Proppant Concentration
Treatment
pressures
σv - vertical stress
σhmin - least principal stress
po - virgin reservoir pore pressure
Proppant
concentration
time (constant pumping rate)
Frac-&-Pack is widely used to create short thick fractures
High Rate Fractures
s3
fat fractures,
close to hole
sq increases!
cement
casing
extra
wings
!
sr increases!
proppant forced between casing
and rock, sometimes called the
“halo effect”, verified in 1999
Frac & pack, high rate
fracs, high  fracs
Increase in Confining Stress
Y
Shear
stress
Shear strength
of the rock
Frac & Pack increases the confining stress,
making the sand stronger and Improving arching
Normal stress
Restressing the disturbed sand also strengthens it
Is Lab Testing Valuable?
There have been many large rock fracture
cells built, even huge sand boxes of many
cubic metres
 Results from these have been of little
practical value in general (although the
owners of these would argue vociferously)
 The complex reality in situ for fracturing
is difficult to replicate in any lab
 Given history to date, we must conclude
that modeling and measurements are best,
lab simulation is not of great use

Vertical Fracture Plane in
a Sandbox, U. of Waterloo
Horizontal Fracture in a
Sandbox, U. of Waterloo
New Completion Approaches?

Why fracture soft, weak rocks?
 To
increase flow to wells
 To mitigate sand production tendencies
 To introduce heat, fluids, etc.
 To change stress state (stress rotation)

New completions approaches with a period
of solids production followed by a highrate sand-propped fracture are quite
promising
New Completion Approaches
First, produce some sand
Then, re-stress with Frac-and-Pack
sq
sq
Completion in Weak Sands

Produce 10-100 m3 of sand deliberately
 Dilation
occurs, k goes up
 Pore throats are larger, less fines plugging
 Well becomes a better actor

Then, use a high sand content fracture
 Re-stresses
the sand near the well (stronger)
 Large proppant gives –ve skin on the well
 Large-diameter well effect (high k)
 Use resin-coated proppant to eliminate sanding

Will give a better well, fewer workovers
Summary of Fracturing in Soft
Weak Rocks (Unconsolidated
Sandstones)
Leak-Off Behavior





Assumption: Permeability is constant
Fact: Permeability alterations are large
Dilation of UCSS through shear dilation
Opening of joints and fissures from Ds
effects
Fissure dilation from pressure effects
Thus, leak-off predictions contentious
Solution: Incorporate changes in leak-off
behavior as a function of Dk
This turns out to be very challenging
Dilatancy and Ds

Shearing dominates in SWR and UCSS
shear leads
to dilation
Dilation causes DV
and attendant stress
changes
σ3 +Δσ3
Dilation is a consequence of
shearing from high pressure
and differential stresses
dilating region,
high permeability
fracture
Shear dilation is not accounted for in fracture models
Fracture Tip Processes
Assumption: KIC governs propagation
 Fact: tip resistance is essentially zero in:




Poorly consolidated rocks (no tensile strength)
Highly fractured cases (little tensile strength)
Large hydraulic fractures (scale effect on To)
Thus, KIC = 0, and predictions are in error
 Solution: Develop models where KIC is not used
explicitly. (static equilibrium?)
 This is being attempted now by some research
groups, but it is challenging…

Tip Stresses in HF
Net driving pressure pnet = pfrac - σhmin
vertical
borehole
s
3
fracture
stress
excess (driving) pressure
fracture tip
pf must be higher than least
principal stress for fracturing
to occur
high tensile stresses
at the fracture tip
fracture
strength
distance
Mode I Dominates DE
Assumption: Mode I dominates ΔEnergy
 Fact: MS monitoring shows shear
dominates

 In
all SWR, flanks exhibit MS Mode II activity
 Dilation implies shearing, so does compaction
 SWR have extremely low KIC
Thus, shear processes are first-order
 Solution: Incorporate Mode II (bedding
slip, shear dilation, ...) into FEM models
 Until shear energy dissipation is included,
history matching will remain contentious

Shearing Near a Fracture

Shear energy dominates over Mode I
σ3 = σhmin
σHMAX
Shearing on fracture flanks during
HF of SWR has been detected
microseismically in the field.
Shearing occurs
on the flanks of
the fracture.
At the tip, parting occurs, little ΔEnergy
Mode II Shear and Dp
σ1 = σv
σ3 = σhmin
MS emissions will cluster around the incipient faulting
relative fault motion
drop in lateral stress
through production
b. Reactivation of thrust faulting
a: Reactivation of normal faulting
σ1 = σHMAX
σ3 = σv
increase in σHMAX and
p through injection
Real Fracture Issues






Rock stiffness is non-linear: E = ƒ(s
Poroelastic effects lead to +DV and -DV
Many unconsolidated sandstones are
actually cohesionless; is KIC = 0?
Strength is a function of scale KIC = ƒ(L/Lo
Rock shear on flanks is a dominant source of
energy expenditure (+ shear dilation)
Cohesion loss occurs during shearing,
dilation and straining in general (weakening)
E.g.: Sands are Non-Linear
Young’s
modulus
(stiffness)
Linear behavior: low f, few fractures
Mildly non-linear: intermediate f,
naturally fractured strata, etc.
Highly non-linear: high f unconsolidated
sandstones, highly fractured reservoirs
Effective confining stress - s3
Reality in Soft, Weak Rocks








Dilation or contraction accompanies shear
Cohesion loss during shear is irreversible
Fracture opening can alter local stress
fields
Fractures can change their orientation
Large permeability changes can occur
Fracture toughness is essentially zero
DT and Dp can change fracture behavior
Other factors as well…
Low-Angle Shearing
**high shear
stress zone
low-k shale stratum
high-k
reservoir
high p
area,
sH > sv
sH > sv
sv
sH
low-k shale stratum
**slip can occur in front of a fracture parting plane
Low-angle shearing happens in many thermal projects
Fracturing and Shear

Fracture injection (thermal or nonthermal) can lead to shearing
 Pore
pressures are > σ3, so there is no effective
stress; hence frictional strength = very low
This is most serious in the case of
“horizontal” fractures (sv = s3)
 Shearing is in the form of a low-angle
thrust fault mechanism
 Shear planes concentrate along the bottom
of strong, stiff beds (cemented streaks)
 Many examples in Alberta (CSS steam inj.)

Fractures and Casing Shear
lean oil
sands
fracture
plane
A
B
C
silty bed
oil
sands
s1
s3
A: early shear, occurring at the base of a shale bed
B: later shear, at the top of the formation
C: well showing some distortion, not failed yet
Vertical exaggeration = x2 to x3
injection
well
Soft Weak Rock Fracturing I
HF models work OK in stiff “elastic” rocks
 They fail in the following cases:

 When
the “limits” are pushed (V, p, T...)
 In near-isotropic stress fields
 In cases of excessive or non-linear bleed-off
 In soft, weak rocks (coal, PCS, Chalk...)

Most “interesting” fracture jobs are now
taking place in PCS, gas sands...
Soft Weak Rock Fracturing II

Plasticity effects include the following:
 Fabric
collapse and contraction
 Massive yielding and shear dilation
 Blocky material slip (with fissures)

These processes change properties:
 Stiffness
changes with dilation, cohesion loss
 Permeability alterations are massive
 Other effects are important
Soft Weak Rock Fracturing III

Conventional simulators have problems:
 Elastic
response often violated (Frac-and-Pack)
 Bleed-off assumptions often wrong
 In a “no-cohesion” material, no fracture resistance
actually exists at the propagating fracture tip
 Rotation of stresses around fracture is ignored
 Thermal advection alters stresses massively

An opinion exists in the industry that these
are fatal for PCS, coal, thermal fracture
modeling. For these materials, we need more
physically correct models
Soft Weak Rock Fracturing IV





Are simple, better solutions available?
Is good field data available? (probably yes)
Is it necessary to go to a full FEM
approach; are analytical approximations
possible?
When are “fudges” acceptable for
empirical design, using existing simulators?
Can we improve our understanding of the
physics involved in HF in weak materials?
Behavior of Soft, Weak Rocks

Mechanical properties

Deformation response
 Compressive and tensile
strength
 Dilation-contraction
 Thermal expansion
Permeability vs s, 
 Thermal conductivity
 Acoustic properties:
impedance, attenuation
 Effect of damage


Compression and
extension triaxial
tests, plus a thermal
cell
Transport properties


These properties can be
assessed with existing
laboratory facilities
Fracture in Soft, Weak Rocks:
Assumptions vs Reality

Current attributes
linear poroelastic
 fracture tip toughness
 constant orientation
 constant permeability
 isotropic properties
 no shear dilation
 other simplifications


Actual behavior, SWR
non-linear s behavior
 zero tip toughness (?)
 orientation changes
 flow properties altered
 anisotropy is common
 shearing dominates DE
 other realities
