Transcript HFSC - Texas A&M University

Hydraulic Fracturing
Short Course,
Texas A&M University
College Station
2005
Modeling, Monitoring, Post-Job
Evaluation, Improvements
Hydraulic Fracture
3D
Fracture
Modeling+
2
P3D and 3D Models
 FracPro (RES, Pinnacle Technologies)
 FracCADE (Dowell)
 Stimwin (Halliburton) and PredK (Stim-Lab)
 TerraFrac
 StimPlan
 MFrac
Fracture
Modeling+
3
Dimensionless Form of Nordgren
Model
w
x
2
4
0D
2
D
1
w0 D

+
t D
tD - D
D(xfD) : inverse of xfD(tD)
xD = 0
(wellbore)
w04D
i

x D
i0
Fracture
Modeling+
4
xD = xfD (tip)
dx fD
dt D
4 w03D

3 xD
w0 D  0
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
Fracture
Modeling+
5
Other Propagation Criteria
(Apparent) Fracture Toughness
Dilatancy
Statistical Fracture mechanics
Continuum Damage mechanics
Fracture
Modeling+
6
Fracture Toughness Criterion
Stress Intensity Factor KI =pnxf1/2
KIC
KI
hf
xf
(Rf)
Fracture
Modeling+
7
CDM
dD

= C n
dt
dD
  
= C

 1- D 
dt
Fracture
Modeling+
8
n 


1- D
What is the time needed for D
to start at D = 0
and grow to D = 1 ?
CDM Propagation Criterion
 x

uf =
  H,min  l + x f

 w2x=x f

Combined Kachanov parameter:
2
Cl
Fracture
Modeling+
9
2
1/ 2
f
2
Cl
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
Fracture
Modeling+
10
3D (Finite Element Modeling)
y
wellbore element
tip element
x
Fracture
Modeling+
11
Fracture Toughness Criterion
Fluid flow in 2 D
Fluid loss according to local opening time
Propagation: Jumps
Stress Intensity Factor KI > KIC ?
KIC
Fracture
Modeling+
12
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
Fracture
Modeling+
13
Leakoff calculated from fluid and layer data
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
Fracture
Modeling+
14
Fracture
Modeling+
15
Injection rate
Bottomhole pressure
Step rate test
Time
Bottomhole pressure
Step rate test
Propagation pressure
Two straight lines
Fracture
Modeling+
16
Injection rate
3 ISIP
Fall-off (minifrac)
4 Closure
5 Reopening
6 Forced closure
1
5
2
7 Pseudo steady state
8 Rebound
3
2nD injection
cycle
7
shut-in
Fracture
Modeling+
17
flow-back
Time
8
Injection rate
6
Injection rate
1st injection
cycle
Bottomhole pressure
4
Pressure fall-off analysis
(Nolte)
Ae
t D  t / te
Vte t = Vi  2Ae S p  g t D , 2Ae C L te
wte  t
Fracture
Modeling+
18
Vi

- 2S p  g t D ,  2CL te
Ae
g-function


1
g t D ,     
dtD dAD
1/ 
1/

t

A
0
A
D
D
 D
1 1 t D
dimensionless
shut-in time
area-growth
exponent

4 t D  2 1  t D  F 1 / 2, ;1   ;1  t D 
g t D ,  
1  2
Fracture
Modeling+
19
where F[a, b; c; z] is the Hypergeometric function,
available in the form of tables and computing algorithms
1

g-function
Approximation of the g-function for various exponents  (d = tD)
4
1.41495+ 79.4125d + 632.457d 2 + 1293.07d 3 + 763.19d 4 + 94.0367d 5

g  d ,   
5  1. + 54.8534d + 383.11d 2 + 540.342d 3 + 167.741d 4 + 6.49129d 5  0.0765693d 6

2
1.47835 + 81.9445 d + 635.354 d 2 + 1251.53 d 3 + 717.71 d 4 + 86.843 d 5

g d ,    

3  1. + 54.2865 d + 372.4 d 2 + 512.374 d 3 + 156.031 d 4 + 5.95955 d5 - 0.0696905 d 6
8
1.37689 + 77.8604 d + 630.24 d 2 + 1317.36 d 3 + 790.7 d 4 + 98.4497 d 5

g d ,    

9  1. + 55.1925 d + 389.537 d 2 + 557.22 d 3 + 174.89 d 4 + 6.8188 d 5 - 0.0808317 d 6
Fracture
Modeling+
20
Pressure fall-off
t D  t / te
Vte t = Vi  2Ae S p  g t D , 2Ae C L te
wte  t
Vi

- 2S p  2CL te g t D , 
Ae
Fracture stiffness
pnet  S f w


pw   pC  S f Vi / Ae - 2S f S p  - 2S f CL te  g t D , 
Fracture
Modeling+
21
pw  bN  mN  gt D ,  
Fracture Stiffness
(reciprocal compliance)
pnet  S f w
Pa/m
Table 5.5 Proportionality constant, Sf and suggested  for basic fracture geometries
Fracture
Modeling+
22
PKN
KGD
Radial

4/5
2/3
8/9
Sf
2E '
h f
E'
x f
3E '
16 R f
Shlyapobersky assumption
No spurt-loss




Vi
pw   pC  S f
- 2S f S p  - 2S f CL te  g t D , 
Ae


bN
Ae from intercept
mN
pw
g
g=0
Fracture
Modeling+
23
Nolte-Shlyapobersky
Leakoff
coefficient,
PKN 4/5
KGD 2/3
h f
x f
4 te E '
 mN 
2 te E '
 mN 
Radial 8/9
8R f
3 t e E '
 m N 
CL
Fracture
Extent
Fracture
Width
xf 
2 E Vi
h 2f bN  pC 
we 
Vi

x f hf
 2.830C L t e
Fluid
Efficiency
Fracture
Modeling+
24
he 
we x f h f
Vi
xf 
E Vi
h f bN  pC 
we 
Vi

x f hf
 2.956C L t e
he 
Rf  3
we 
Vi: injected into one wing
Vi
2 
Rf

2
 2.754C L t e
we x f h f
Vi
3E Vi
8bN  pC 
he 
we R 2f
Vi

2
1: g-function plot of pressure
2: get parameters bN and mN
3
Calculate Rf
(fracture extent -radius)
8bN  pC 
m 

t E'
8R f
4
Calculate CLAPP
(apparent leakoff coeff)
CLAPP 
5
Calculate wL
(leakoff width)
8
wL  g (0, )2CLAPP te
9
6
Calculate we
(end-of pumping width)
Fracture
Modeling+
25
Rf  3
3E Vi
7
Calculate h
(fluid efficiency)
we 
3
Vi
N
e
R  /2
2
f
 wL
we
h
we  wL
Computer Exercise 3-1 Minifrac
analysis
Fracture
Modeling+
26
Example
Permeable (leakoff) thickness, ft, 42
Plane strain modulus, E' (psi), 2.0E+6
Closure Pressure, psi, 5850
Fracture
Modeling+
27
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
21.8
9.9
0.0
1
0
21.95
0.0
7550.62
0
0
22.15
0.0
7330.59
0
0
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), 0.0159
ft/min^0.5
2
Fracture
Modeling+
28
Leakoff coefficient in permeable layer, ft/min^0.5
0.0247
9
From "apparent" to "real“ (radial)
hp
42
x

 0.53
2 R f 2 * 39.6
rp 

x (1  x )

2
2 0.5

 arcsin(x )  0.64
CL, App  5.85 105 m/s0.5  0.015ft/min0.5
CL,True
Fracture
Modeling+
29
5.85 105
0.015

m/s0.5 
ft/min0.5  0.024ft/min0.5
0.214
0.64
Redesign
Run the design with new leakoff
coefficient
(That is why we do minifrac analysis)
Fracture
Modeling+
30
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
Fracture
Modeling+
31
Nolte-Smith plot
Log net
pressure
Tip
screenout
Wellbore
screenout
Normal frac
propagation
Unconfined
height growth
Log injection
time
Fracture
Modeling+
32
Post-Job Logging
Tracer Log
Temperature Log
Production Log
Fracture
Modeling+
33
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
Fracture
Modeling+
34
Sc
Sb
Ir
Trace
r
log
Fracture
Modeling+
35
Tiltmeter Results
Fracture
Modeling+
36
after Economides at al. Petroleum Well Construction
Pressure Match with 3D Simulation
FracCADE
EOJ Fracture Profile and Proppant Concentration
T exaco E&P
OCS-G 10752 #D-12
Actual
05-23-1997
7300
< 0.0
0.0
0.0 - 2.0
2.0 - 4.0
4.0 - 6.0
6.0 - 8.0
8.0 - 10.0
10.0 - 12.0
12.0 - 14.0
> 14.0
7350
7400
7450
7500
5600
6400
7200
-0.45
-0.30
-0.15 0 0.150.300.450
Stress(psi)
Fracture
Modeling+
37
*Mark of Schlumberger
Wellbore Hydraulic Width(in)
100
200
300
Fracture Half-Length (ft)
400
3D Simulation
Texaco E&P
OCS-G 10752 #D-12
Actual
05-23-1997
FracCADE
5000
0.20
4000
0.15
3000
0.10
2000
Propped Width (ACL)
0.05
0
0
Conductivity - Kfw
50
1000
100
150
Fracture Half-Length - ft
Fracture
Modeling+
38
*Mark of Schlumberger
200
0
250
Conductivity (Kfw) - md.ft
Propped Width - in
Flow Capacity Profiles
0.25
Well Testing: The quest for flow regimes
Fracture
Modeling+
39
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
Fracture
Modeling+
40
 Forced closure, Resin coating, Fiber
reinforcement, Deformable particle
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
Fracture
Modeling+
41
Misalignment
Fracture
Modeling+
42
Fracture Orientation: Perforation
Strategy
after Dees J M, SPE 30342
max
From
overbalanced perforation
Fracture
Modeling+
43
max
From
underbalanced perforation
High Viscosity slugs
Fracture
Modeling+
44
Proppant Slugs
Fracture
Modeling+
45
Case Study: Effect of Non-Darcy Flow
Forcheimer Equation
p v
2

 av
L
k
Cornell & Katz
p v
2

 v
L
k
Fracture
Modeling+
46
Non-Darcy Flow
 Dimensionless Proppant Number is the most
important parameter in UFD
Effective Proppant
Pack Permeability
N prop 
Fracture
Modeling+
47
2k f V prop
k
Vres
Non-Darcy Flow
 Effective Permeability
keff
knom

1  N Re
 Reynolds Number
knom v
N Re 

Fracture
Modeling+
48
keff is determined through an
iterative process
Drawdown is needed to
calculate velocity
Non-Darcy Flow Coefficient 
Several equations have been developed
mostly from lab measurements (empirical
equations)
General form of  equation

8
1x10 a
kf 
b
c
where  is 1/m and k is md
Fracture
Modeling+
49
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
Fracture
Modeling+
50
Case Study: Reynolds number
Fracture
Modeling+
51
Fracture
Modeling+
52
Ka
tz
Th
au
v in
ta
l
low
M
oh
an
ty
Da
rc
yF
an
d
Te
ke
M
ar
Pe
ti n
nn
se
ya
ta
nd
l*
Ji n
-B
au
x it
e*
et
al
*
et
al
Interprop®
M
al
on
ey
Do
na
l
Ku
ta
so
v*
Jo
ne
s
an
d
Naplite®
M
ac
Ja
nic
e
et
al
ee
rts
m
a
Fr
ed
er
ick
G
Li
Er
gu
n
Da
nc
un
Co
ok
e*
Be
lh
aj
et
Co
al
le
an
d
Ha
rtm
an
Proppant Number
Case Study: Proppant number
Comparison for 20/40 Norton Proppants
Sintered Bauxite
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
Case Study: Max possible JD
Fracture
Modeling+
53
Case Study: Optimum frac length
Fracture
Modeling+
54
Case Study: Optimum frac width
Fracture
Modeling+
55
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
Fracture
Modeling+
56