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Qingfeng Tan
Two Dimensional Hydraulic Fracture Simulations Using FRANC2D
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Vapor extraction well intersecting horizontal hydraulic fracture, from Bradner (2002)
kfrx/ k10 100 1000 10000
1
10
Flow Index
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Importance of 2-D
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Objective
Develop and apply a model for predicting the forms of curving hydraulic fractures in two dimensions
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Overview• Previous work
– Vertical and horizontal fracture– Analytical models
• Theoretical Analysis– Coupling mechanical and fluid flow analysis
• Code Development– Automatic propagation (EXC_AUTO_DRIVER_FLOW)– Fracture form calculation routines– Fluid flow simulation routines
• Application– Shallow soil model– Effects of layering and lateral residual compression
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Hydraulic Fracture DesignVertical Fractures
a
Qh
X
Y
Z Horizontal Fractures
(a)
(d)(c)
(b)
a
Qd
Z
r
Q
a
d
Z
r
Y
Z
Q
h
X
a
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Previous ModelsPressure
Length
Aperture
time
time
time
1
1
CtfP
2
2
Ctfa
3
3
Ctf
)],,,([ 3,2,1 QKEff
)2.05.0( 1 C
)44.025.0( 2 C
)5.011.0( 3 C
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Simulate Hydraulic Fracture
• Fracture aperture—analyze as elastic displacements due to fluid pressure
• Fluid pressure—analyze as flow in deforming fracture
• Propagation—require stress intensity to equal critical value
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Problem with Analysis in 2-D
• Fracture curves-- numerical methods for stress analysis required
• Fracture propagation-- analyze as a series of quasi static models. Requires many analyses to be conducted.
Need FEM method with automatic regridding around fracture
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FRANC2D• 2-D stress and displacement• Developed for structural
fracture mechanics applications
• Auto regrid around fracture• Fluid flow within
fracture not included
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Fracture with Fluid Flow-Coupled Approach
• Modify FRANC2D to perform mechanical analysis, then calculate geometry of fracture, caused by fluid pressure, and other loadings
• Fluid flow analysis adjust fluid pressure due to the shape changes of fracture, coupled with mechanical analysis
• Propagation criterion: is decided by fracture geometry and fluid pressure
ICI KK IK
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Flow and Deformation CouplingP
ress
ure
Ape
rtur
e
From 1-D implicit solution; flow bc at well, head bc at tip
From FEM elasticity solutionx
x
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Propagation
• KI =Stress intensity factor
• KI=KIc for propagation
• KIC is material property, called fracture toughness.
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How to ensure KI=KIc?P
ress
ure
Ptip
KI
Ptip
KIc
x
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Code Development• Fracture propagation control routine
-EXC_AUTO_DRIVER_FLOW
• Fracture geometry calculation routines-EXC_LENGTH_FLOW-EXC_APER_FLOW-EXC_VOLU_FLOW
• Fluid flow simulation routines-FLUID_FLOW_INIT
-FLUID_FLOW_CALC
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Automatic Propagation Subroutine
ICI KK
• Fluid flow and mechanical analysis coupling to decide pressure and geometry
•Propagation criterion: KI=KIC
•Auto-remesh around fracture tip
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Fracture Form Calculation• Length – EXC_LENGTH_FLOW• Aperture – EXC_APER_FLOW• Volume – EXC_VOLU_FLOW• Obtain Crack node info• Calculation in each segment, then integral
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Fluid Flow and Aperture Subroutine
• Calculate new heads using initial aperture• Calculate aperture using new head• Calculate heads using new aperture• Repeat and compare heads and apertures between
successive iterations• Converge when change is less than tolerance,
usually less than 7 iterations
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Propagation Subroutine•Calculate KI for pressure at tip
•Adjust pressure at tip slightly, redo fluid pressure calculations, and calculate new KI
•Use two values of KI and pressure tip to interpolate new value of pressure tip that should give KI=KIc
•Check KI and revise pressure tip as needed until KI is within tolerance of KIc
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VerificationUniform Pressure: Model Setting
P•Infinite elastic media
•Uniform pressure
•Radial symmetric
a
z
r
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Verification-Driving Pressure
5
10
0 5 10 15Time(min)
Pre
ss
ure
(KP
a)
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Verification (II): Fracture Length
1
3
5
0 5 10 15Time(min)
Le
ng
th(m
)
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Verification (III): Fracture Aperture
0.5
1.0
1.5
0 5 10 15Time(min)
Ap
ert
ure
(mm
)
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Error Analysis
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
1 2 3 4 5
Length (m)
Re
lati
ve
Err
or
Error PError aError d
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Applications
• Hydraulic fracture in shallow soil:- Gravity
- Fluid injection
• Soil with under-lying softer material
• Soil with high lateral residual stress
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Forms of Hydraulic Fractures in the Field
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Field Data Adoption
• Four cross-section selection
• Each cross-section starts from center of fracture to the edge of it, perpendicular with each other
• Fracture path, uplift, and sand extent data are adopted
0 5 10 15 feet
0.1
0.3
0.5
0.7
N
0.9
Cross 1
Cross 4Cross 3
Cross 2
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General case-Model Setting
Depth
0 m
-2 m
12 m
-5 m
Distance from well0 m
frx-1.6 m
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Vertical Stress During Propagation
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Pressure Log
0
10
20
30
40
50
60
0 2 4 6 8
Time (minutes)
Pre
ss
ure
(p
si)
Measured
Simulated
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Fracture Form
-1.8
-1.5
-1.2
-0.9
0 1 2
Distance from center of fracture (m)
De
pth
be
low
gro
un
d s
urf
ac
e (
m)
simulatedWell H Cross-s 1Well H Cross-s 2Well H Cross-s 3Well H Cross-s 4
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Aperture and Uplift
0.00
0.02
0 1 2 3 4
distance from center (m)
Up
lift
fro
m f
ield
, or
sim
ula
ted
ap
ertu
re
simulated
Well H cross 1
Well H cross 2
Well H cross 3
Well H cross 4
Average radial extent of sand
(m)
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Effects of Layeringob
serv
ed
-2
-1.5
-1
-0.5
0
0 1 2 3 4 5
E2=2000psi, E1 = 5000psi
E1=E2=5000psi
E2=3000psi, E1=5000psi
E2=4000psi, E1=5000psi
Sim
ulat
ed
Richardson
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Effects of Lateral compression
-1.8
-1.2
-0.6
0
0 1 2 3 4 5 6 7
Distance from Wellbore (m)
Dep
th (
m)
Fracture Path from lowresidual area
Fracture path from highresidual compressionregion
v
hv
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Conclusions
•FRANC2D has been modified to simulate hydro-mechanical coupling conditions during hydraulic fracturing.
•A new simulation tool, HFRANC2D?, is available
• The model has been verified using analytical solutions, error within a few percent
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Conclusions, applications
• Gentle bowl-like forms of hydraulic fractures in shallow soils can be predicted.
• Effects of state of stress and material properties can be predicted and results resemble field observations.