Hydraulic Fracture Hydraulic Fracturing Short Course, Texas A&M University College Station 2005...
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![Page 1: Hydraulic Fracture Hydraulic Fracturing Short Course, Texas A&M University College Station 2005 Modeling, Monitoring, Post-Job Evaluation, Improvements.](https://reader038.fdocuments.in/reader038/viewer/2022110322/56649d235503460f949f93d4/html5/thumbnails/1.jpg)
Hydraulic Fracture
Hydraulic FracturingHydraulic FracturingShort Course, Short Course,
Texas A&M UniversityTexas A&M UniversityCollege StationCollege Station
20052005
Modeling, Monitoring, Post-Job Evaluation, Improvements
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FractureModeling+
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3D3D
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P3D and 3D Models
FracPro (RES, Pinnacle Technologies)
FracCADE (Dowell)
Stimwin (Halliburton) and PredK (Stim-Lab)
TerraFrac
StimPlan
MFrac
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Dimensionless Form of Nordgren Model
204
201w
x t -+
w
tD
D D D
D
D
w
x
i
iD
D
04
0
dx
dt
w
xfD
D
D
D
4
303
xD = 0 (wellbore) xD = xfD (tip)
D(xfD) : inverse of xfD(tD)
w D0 0
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Propagation Criterion of the Nordgren Model
Net pressure zero at tip
Once the fluid reaches the location, it
opens up immediately
Propagation rate is determined by “how
fast the fluid can flow
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Other Propagation Criteria
(Apparent) Fracture Toughness
Dilatancy
Statistical Fracture mechanics
Continuum Damage mechanics
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Fracture Toughness Criterion
KI
xf
hf pn
KIC
(Rf)
Stress Intensity Factor KI =pnxf1/2
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CDM
dD
dt= C n
n 1- D
dD
dt= C
1- D
What is the time needed for D to start at D = 0 and grow to D = 1 ?
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CDM Propagation Criterion
u =Cl x
l + xwf
H,
2
f
f
x=x2
f
2 1 2
min
/
Cl 2Combined Kachanov parameter:
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P3D
Pseudo 3 D Models: Extension of
Nordgren’s differential model with height
growth
Height criterion
Equilibrium height theory
or Assymptotic approach to equilibrium
Plus some “tip” effect
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3D (Finite Element Modeling)
x
ywellbore element
tip element
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Fracture Toughness Criterion
pn
KIC
Fluid flow in 2 DFluid loss according to local opening timePropagation: Jumps
Stress Intensity Factor KI > KIC ?
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Data Need for both P3D and 3D:
Layer data
Permeability, porosity, pressure
Young’s modulus, Poisson ratio, Fracture
toughness
Minimum stress
Fluid data
Proppant data
Leakoff calculated from fluid and layer data
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Design Tuning Steps
Step Rate test
Minifrac (Datafrac, Calibration Test)
Run design with obtained min (if needed)
and leakoff coefficient
Adjust pad
Adjust proppant schedule
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Step rate test
Time
Bot
tom
hole
pre
ssur
e
Inje
ctio
n ra
te
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Step rate test
Injection rate
Bot
tom
hole
pre
ssur
e
Propagation pressure
Two straight lines
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Fall-off (minifrac)
1st
inje
ctio
n cy
cle
2nD
inje
ctio
n cy
cle
flow-backshut-in
1
2
34
5
68
7
Injection rate
Time
Bot
tom
hole
pre
ssur
e
Inje
ctio
n ra
te
3 ISIP
4 Closure
5 Reopening
6 Forced closure
7 Pseudo steady state
8 Rebound
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Pressure fall-off analysis(Nolte)
eLeDpeitt tC2AtgS2AV=Ve
,
eD ttt /
eLDpi
tt tCtgSA
Vw
e2 ,2-
e
eA
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g-function
where F[a, b; c; z] is the Hypergeometric function, available in the form of tables and computing algorithms
dimensionless shut-in time
area-growth exponent
D
t
A
D
DD
D dAdtAt
tgD
D
1
0
1
/1/1
1,
21
1;1;,2/1124,
1
DDDD
tFtttg
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g-function
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Pressure fall-off
,2-2-/ DeLfpfeifCw tgtCSSSAVSpp
p b m g tw N N D ,
eLeDpeitt tC2AtgS2AV=Ve
,
eD ttt /
,22- e
DeLpi
tt tgtCSA
Vw
e
wSp fnet Fracture stiffness
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Fracture Stiffness(reciprocal compliance)
Table 5.5 Proportionality constant, Sf and suggested for basic fracture geometries
PKN KGD Radial
4/5 2/3 8/9
Sf 2E
hf
'
E
xf
'
3
16
ERf
'
wSp fnet Pa/m
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Shlyapobersky assumption
No spurt-loss
,2-2- DeLfpfe
ifCw tgtCSSS
A
VSpp
Ae from intercept
g
pw
bN mN
g=0
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Nolte-Shlyapobersky
PKN KGD Radial
Leakoffcoefficient,
CL
N
e
f mEt
h
'4
N
e
f mEt
x
'2
N
e
f mEt
R
'3
8
FractureExtent CNf
if
pbh
VEx
2
2 CNf
if
pbh
VEx
3
8
3
CN
if
pb
VER
FractureWidth
eL
ff
ie
tC
hx
Vw
830.2
eL
ff
ie
tC
hx
Vw
956.2
eL
f
ie
tC
R
Vw
754.2
22
FluidEfficiency
i
ffee
V
hxw
i
ffee
V
hxw
i
fe
eV
Rw2
2
Vi: injected into one wing
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7 Calculate
(fluid efficiency)
3 Calculate Rf
(fracture extent -radius)
4 Calculate CLAPP
(apparent leakoff coeff)
5 Calculate wL
(leakoff width)
6 Calculate we
(end-of pumping width)
RE V
b pfi
N C
3
83
CR
t EmLAPP
f
eN
8
3 '
w g C tL LAPP e ( , )08
92
wV
Rwe
i
fL 2 2 /
w
w we
e L
1: g-function plot of pressure2: get parameters bN and mN
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Computer Exercise 3-1 Minifrac analysis
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Example
Permeable (leakoff) thickness, ft, 42
Plane strain modulus, E' (psi), 2.0E+6
Closure Pressure, psi, 5850
21.8 9.9 0.0 1 0
21.95 0.0 7550.62 0 0
22.15 0.0 7330.59 0 0
Time,
min
BH Injection
rate, bpm
BH Pressure,
psi
Include into inj
volume
Include into
g-func fit
0.0 9.9 0.0 1 0
1.0 9.9 0.0 1 0
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Output
Slope, psi -4417
Intercept, psi 13151
Injected volume, gallon 9044
Frac radius, ft 39.60
Average width, inch 0.4920
5
Fluid efficiency 0.1670
8
Apparent leakoff coefficient (for total area),
ft/min^0.5
0.0159
2
Leakoff coefficient in permeable layer, ft/min^0.5 0.0247
9
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From "apparent" to "real“ (radial)
64.0)arcsin()1(2
53.06.39*2
42
2
5.02
xxxr
R
hx
p
f
p
ft/min 0.024 ft/min 0.64
0.015 m/s
0.214
1085.5
ft/min 0.015 m/s1085.5
0.50.50.55
,
0.50.55,
TrueL
AppL
C
C
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Redesign
Run the design with new leakoff
coefficient
(That is why we do minifrac analysis)
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Monitoring
Calculate proppant concentration at bottom (shift)
Calculate bottomhole injection pressure, net pressure
Calculate proppant in formation, proppant in well
Later: Add and synchronize gauge
pressure
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Nolte-Smith plot
Log net pressure
Log injection time
Normal frac propagation
Tip screenout
Wellbore screenout
Unconfined
height growth
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Post-Job Logging
Tracer Log
Temperature Log
Production Log
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Radius of penetra
tion
Available Techniques for Width and Height
Measured Directly Formation Micro Scanner
Borehole Televiewer
Based on Inference Temperature Logging
Isotopes (fluid, proppant)
Seismic Methods, Noise Logging
Tiltmeter techniques
Spinner survey
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ScSb Ir
Tracerlog
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Tiltmeter Results after Economides at al. Petroleum Well Construction
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0 100 200 300 400
Fracture Half-Length (ft)
< 0.00.00.0 - 2.02.0 - 4.04.0 - 6.06.0 - 8.08.0 - 10.010.0 - 12.012.0 - 14.0> 14.0
FracCADE
*Mark of Schlumberger
EOJ Fracture Profile and Proppant Concentration
Texaco E&POCS-G 10752 #D-12Actual05-23-1997
-0.45 -0.30 -0.15 0 0.15 0.30 0.45
Wellbore Hydraulic Width(in)
5600 6400 7200
Stress(psi)
7300
7350
7400
7450
7500
Pressure Match with 3D Simulation
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3D Simulation
0 50 100 150 200 250
Fracture Half-Length - ft
0
0.05
0.10
0.15
0.20
0.25P
rop
pe
d W
idth
- in
0
1000
2000
3000
4000
5000
Co
nd
uctivity (K
fw) - m
d.ftPropped Width (ACL)
Conductivity - Kfw
FracCADE
*Mark of Schlumberger
Flow Capacity Profiles
Texaco E&POCS-G 10752 #D-12
Actual05-23-1997
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Well Testing: The quest for flow regimes
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Design Improvement in a Field Program
Sizing
Pad volume for “generic” design
More aggressive or defensive proppant schedule
Proppant change (resin coated, high strength etc.)
Fluid system modification (crosslinked, foam) Proppant carrying capacity
Leakoff
Perforation strategy changes
Forced closure, Resin coating, Fiber reinforcement, Deformable particle
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Example: Tortuous Flow Path
Analysis of the injection rate dependent
element of the treating pressure
Does proppant slug help?
Does limited entry help?
Does oriented perforation help?
Extreme: reconsidering well orientation:
e.g. S shaped
![Page 42: Hydraulic Fracture Hydraulic Fracturing Short Course, Texas A&M University College Station 2005 Modeling, Monitoring, Post-Job Evaluation, Improvements.](https://reader038.fdocuments.in/reader038/viewer/2022110322/56649d235503460f949f93d4/html5/thumbnails/42.jpg)
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Misalignment
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Fracture Orientation: Perforation Strategy after Dees J M, SPE 30342
max max
From overbalanced perforation
From underbalanced perforation
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High Viscosity slugs
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Proppant Slugs
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Forcheimer Equation
Cornell & Katz
Case Study: Effect of Non-Darcy Flow
2vk
v
L
p
2avk
v
L
p
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Non-Darcy Flow
Dimensionless Proppant Number is the most
important parameter in UFD
res
propfprop V
V
k
kN
2
Effective ProppantPack Permeability
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Non-Darcy Flow
Effective Permeability
Reynolds Number
Re1 N
kk nom
eff
vk
N nomRe
keff is determined through an iterative processDrawdown is needed to calculate velocity
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Non-Darcy Flow Coefficient
Several equations have been developed mostly from lab measurements (empirical equations)
General form of equation
where is 1/m and k is md
cbfk
ax
8101
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SPE 90195
Optimum FractureTreatment Design Minimizes the Impact of Non-Darcy Flow Effects
Henry D. Lopez-Hernandez, SPE, Texas A&M University, Peter. P. Valko, SPE, Texas A&M University, Thai T. Pham, SPE, El Paso Production
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Case Study: Reynolds number
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Case Study: Proppant number
Comparison for 20/40 Norton Proppants
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Pro
ppan
t N
umbe
r
Naplite® Interprop® Sintered Bauxite
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Case Study: Max possible JD
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Case Study: Optimum frac length
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Case Study: Optimum frac width
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Summary
Increasing role of evaluation
Integration of reservoir engineering, production engineering and treatment information
Cost matters
Expensive 3D model does not substitute thinking
Still what we want to do is increasing JD