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8/11/2019 7 Papanastasiou P Hydraulic Fracturing
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Hydraulic Fracturing:Basic Concepts and Numerical Modelling
Panos Papanastasiou
Department of Civil and Environmental Engineering University of
Cyprus
1991-2002 in Schlumberger Cambridge Research
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Hydraulic fracturing
Petroleum engineering
stimulate oil and gas reservoirs,
cuttings re-injection
Environmental engineering
waste disposal in shallow formations,
cleaning up contaminated sites
Geotechnical engineering
injection of grout, dam construction
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Outline
Basic fracturing theory: controlling parameters fracture opening, propagation, modes, initiation, closure
Perforating for fracturing
Fracture geometry
deviated and horizontal wellbores
tortuosityand multiple fractures
Hydraulic fracturing modeling
physical processes, geometrical models, height growth, net-pressure
Fracturing weak formations
elastoplastic modeling, experiments on soft rocks (DelFrac)
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Why hydraulic fracturing in Petroleum engineering?
Bypass near-wellbore formation
damage
drilling induced, fines invasion-migration,
chemical incompatibility
Extend a conductive path deep into
the formation
increase area exposure to flow
Reservoir management tool
change flow, fewer wells, wellplacement, IVF, frac&pack, screen-less
completion
h
packer
packer
hydraulicfracture
water
gas
Oil
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Fracture Openingmin
pf w
2L x
y
min
yy
Fracture opens if the net pressure
pnet=pf - min >0
Fracture opening
w(x)=4 pnet (L2-x2)1/2/E
E=E/(1-2) is the plane strain modulus
maximum width for x=0
for constant height: W=4 pnet L/E
for radial fracture: W=8 pnet R/ ( E)
singular stress at the crack tip, for x=L
yy=pnet [x/(x2-L2)1/2-1]
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Fracture Propagation The stresses ahead of the crack tip are singular
characterized by the stress intensity factor KI
ij= [KI / (2 r )1/2] f() + ...
example: an elliptical crack, KI = pnet L 1/2
A crack will propagate if
KI = KIC
KIC is a material parameter called fracture toughness.
Typical values for rocks are 0.1 - 2 MPa m1/2
ij
r
pnet
L
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Fracture Modes
p p
p
p p p
I. opening mode II. sliding mode III. tearing mode
tensile fractureshydraulic fractures
drilling induced
faultsshear fractures andturning of fracturesnear wellbore
splitting of thecrack front,multiple fractures
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Fracture Initiation in Open Holes
Fracture initiation at lower pressures
large contrast between insitu stresses
high pore pressure, e.g. eject at low rates prior pressurization
preexisting flaws and natural fractures
h
H
breakout
Pb = 3h
-H
-p+T
p is the formation pressureT is the tensile strength
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Breakdown pressure
Pb = 3h-H-p+T
p is the formation pressure
T is the tensile strength
no fluid penetration, upper bound
Closure stress
ISIP in low permeability formations
2ndcycle
time
BHP breakdown pressure
ISIP
closure stress
Pore pressure
tensile strength
flow rate
open
valves
Pressure vs Time Analysis
Fracture Initiation and Closure
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Perforated Cased Holes
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weak rocks
1. reduce multiples2. risk of sanding
h
H preferentialdirection
1. low breakdown pressures
h
Hpreferentialdirection
strong rocks
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Near Wellbore Fracture Geometry
h
H preferential direction
High flow rates and viscosityresults in high breakdownand smooth fracture paths
Low flow rates and bad cementbond results in breakdownpressures:multiple fractures and tortuosity
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Experiments in Delft Fracturing Consortium (1997)
Deviated and Horizontal Wells
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Fracture Tortuosity
Gradual or sharp fracture re-orientation to the preferred plane resultsin width restriction near the well
Tortuosityoccurs
in high differential stress fields
in deviated wells
in long perforated intervals and in phased perforations
in reservoirs with natural fractures
Problems near-wellbore friction resulting in pressure drop
premature screen-out due to proppant bridging
H
h
Multiple Fractures
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Propagation of multiple fractures away from the wellbore area
Multiples occur
in multiple or long perforated intervals with phased perforations
in deviated wells where the separation between fractures is large compared to the
fracture height
in reservoirs with natural fractures
Problems
increase treating net-pressure
reduced fracture widths: increase screenout potential
increased leakoff: lower efficiency
Reduced fracture length
Multiple Fractures
h
L
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surface
reservoir
v
axial fracturestransverse fractures
wellbore drilled // tomaximum horizontal stress
wellbore drilled // tominimum horizontal stress
overburden
h
Horizontal Wellbores
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Modelling Hydraulic Fracture Propagation
Optimize the treatment (pumping schedule, proppant stages)
increase well production
reduce cost
Control where the fracture is growing
avoid fracturing near layers with different content: oil, gas, water
create long fractures in some layers
Predict the response during treatment
Post-evaluation of the treatment
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Physical Processes in Hydraulic Fracturing
Viscous fluid flow in the fracture
Fluid leakoff in the formation
Rock deformation
Fracture propagation
Proppant transport
pw
vl
wp
net
v vpf
KI=KIC
vs
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Pressure Loading on Fracture Surfaces
Pressure drop: dp/dx=12 q/w3
Net pressure pnet=pf - hgives KI(+)>0
Closure stress over fluid-lag gives KI
(-)
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HF Geometrical Models
h
L
flow
PKN
L
h
o
w
KGD
Planar 3D
flow
Radial
R
flow
Fully 3D
D MODELS
Fracture Profiles in Layered Formations
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Fracture Profiles in Layered Formations
shale 1
shale 2
shale 3
sandstone1
sandstone 2
pay zone
stress profile
verticalwidthprofile
T-shape fracture
Fracture may not penetrate deep to
the optimum length
Fracture may connect several pay
zones separated by shale layers
Fracture may grow in non-productive
layers
Problems with proppant placement
Indirect Vertical Fracturing (IVF) forsand control
F t ti
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Fracture tip
High net-pressures (pnet=pfrac-min)
high apparent fracture toughness: due to scale effect, confining
pressure, heterogeneities and plasticity
flow behaviour near the tip: fluid-lag, rock dilation
underestimation of the closure stress (min
)
3,max
1,min
pfrac
high shear stress:
plastic zonefluid lag
cohesive zone
Elasto plastic HFmodel
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Elasto-plastic HF model
Fluid-flow in the fracture
Newtonian viscous fluid, lubrication theory:
dp/dx=12 q/w3
Rock deformation Mohr-Coulomb flow theory of plasticity
Fracture propagation
Cohesive model
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0 2 4 6 8
fracture length (m)
fracturehalf
-width(m)
Finite element analysis
fully coupled solution, special
continuation algorithm
meshing/remeshing
Fl id fl
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Fluid-flow
Boundary conditions
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Rock deformation
Propagation criterion
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Propagation criterion
I iti l l ti
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Initial solution
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Numerical Implementation
Finite Element Discretization
8 node element 6 node interface elements
Finite Differences for Fluid Flow
Coupling of fluid-flow with rock-deformation
Arc-length algorithm based on volume control
Meshing/ remeshing
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Fracture propagation
-3.7
-2.7-1.7
-0.7
0.3
1.3
2.3
3.3
4.3
0 0.5 1 1.5 2
fracture length (m)
n
et-pressure(MP
a)
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0 0.5 1 1.5 2
fracture length (m)
fra
cturehalf-width
(m)
plasticity
plasticity
elasticity
elasticity
tiptip
Plastic fractures are wider and shorterthan the elastic fractures
Fluid-lag is smaller in the plasticfracture
Apparent fracture toughness
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Apparent fracture toughness
0
1
2
3
4
5
6
7
0.5 1 1.5 2 2.5
fracture length (m)
n
et-pressure(MP
a)
0
1
2
3
4
5
6
7
8
9
10
0 0.05 0.1 0.15 0.2
fractu re extension (m)
apparen
ttoughness(MP
am^0.5
)
elasticity
plasticity plasticity
elasticity
Apparent fracture toughness ishigher for the plastic fracture
Fracture closure
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Fracture closure
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0 2 4 6 8
fracture length (m)
fracturehalf-width(m)
-2
-1
0
1
2
3
4
5
6
7
0 2 4 6 8
fracture length (m)
net-pressu
re(MPa)
plasticity propagation
closure
Plastic fracture closes first nearthe tip Fracture is open at zero net-pressureand closes at negative values
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0
2
4
6
8
10
12
14
0 5 10 15
distance from the wellbore (m)
princ
ipalstresses(M
Pa)
0
0.1
0.2
0.3
0.4
0.5
0.6
0 5 10 15
distance from fracture face (m)
yieldfactorf failure line
S_z
S_h
S_H
Stresses after fracturing
The rock formation is more stable afterfracturing
The closure stress on proppant is lowernear the wellbore
Dislocation model
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Dislocation model
Position and strength of super-
dislocations
zero stress intensity factor at the crack
tip
stresses satisfy Mohr-Coulomb yieldcriterion at dislocations
total crack-opening-displacement is
maximized
Papanastasiou and Atkinson (2000)
Fracturing WeakRocks
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Fracturing Weak Rocks
Rock dilation: narrower fracture near the tip is a wronghypothesis
Plastic yielding: plays a shielding mechanism increasing
the effective fracture toughness
contrast of insitu stresses
effective Youngs modulus, rock strength pumping parameters: flow rate x viscosity
Fractures are wider and shorter, compared with the elastic
model
B k i l i d li d t fl t t f t
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Break in slope in pressure decline does not reflect true fracture
closure, for soft rocks. Closure stress might be underestimated
Use apparent toughness and unloading modulus in the HF
simulators.
Closure stress on proppant
higher near the tip and lower near the wellbore
more uniformly distributed with increasing fracture length
Formation Stability
decrease of stresses after fracturing
reduced risk of formation failure
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Experimental Set-up (DelFrac)
pump
h
pressure
transducer
fracture
c
clamps lvdt
Acoustictransducer
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Rough fracture surface with dry tip
fluid front
fracture tip
Pressure andwidth in plaster experiments
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Pressure and width in plaster experiments
ch , ch ,
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Closure in plaster
confining stress
confining stress
Strong Plaster: Weak Plaster
Delft Fracturing Consortium Results
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Optimum completion configuration
Perforations with 0/180 gave best link-up, but perforation spacing must be very
small for link-up
Fractures at unfavourable perfs propagated only at low stress contrast;
optimum phasing different for high/low stress contrast
Perforation orientation has little impact
Multiple fractures may be induced even for good perforation link-up
Fracture pressure has a strong positive influence on fracture
geometry
Fracturing in the annulus is important in practice. It has a large
impact on pressure and geometry.