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Transcript of HF short course
Fracture Design
Hydraulic FracturingHydraulic FracturingShort Course,Short Course,
Texas A&M UniversityTexas A&M UniversityCollege StationCollege Station
20052005
Fracture DesignFracture Design Fracture Dimensions Fracture Dimensions
Fracture Modeling Fracture Modeling
Peter P. ValkóPeter P. Valkó
Hydraulic FracturingHydraulic FracturingShort Course,Short Course,
Texas A&M UniversityTexas A&M UniversityCollege StationCollege Station
20052005
Fracture DesignFracture Design Fracture Dimensions Fracture Dimensions
Fracture Modeling Fracture Modeling
Peter P. ValkóPeter P. Valkó
FractureDesign
4
Well or Reservoir Stimulation?
Near wellbore region and/or bulk reservoir?
Acceleration versus increasing reserve?
Low permeability
Medium permeability
High permeability
Coupling of goals
Frac&pack
FractureDesign
5
Hydraulic Fracturing Design and Evaluation
Why do we create a propped fracture?
How do we achieve our goals?
Data gathering
Design
Execution
Evaluation
FractureDesign
6
Fractured Well Performance
Relation of morphology to performance
Streamline view
Flow regimes, Productivity Index, Pseudo-
steady state Productivity Index, skin and
equivalent wellbore radius
FractureDesign
7
Well- Fracture Orientation
MATCH
Vertical well - Vertical fracture
Horizontal well – longitudinal fracture
MISMATCH (Choke effect)
Horizontal well with a transverse vertical fracture
Vertical well intersecting a horizontal fracture
FractureDesign
8
Principle of least resistance
Horizontal fracture Vertical fracture
Least Principal Stress Least Principal Stress
FractureDesign
9
Mismatch (Choked fracture)
Typical mismatch situations:
Horizontal well with a transverse vertical
fracture
Vertical well intersecting a horizontal
fracture
FractureDesign
10
Vertical Fracture - Vertical well
Bypass damage
Original skin disappears
Change streamlines
Radial flow disappears
Wellbore radius is not a factor
any more
Increased PI can be utilized
p or q pJq post
FractureDesign
11
Longitudinal Vertical Fracture -Horizontal well
H,maxxf
H,min
H,min
Can it be done?
FractureDesign
12
Transverse Vertical Fractures - Horizontal Well
H,maxHydraulic Fracture
H,maxD
xf
H,min
Radial converging flow in frac
FractureDesign
14
Main questions
Which wellbore-fracture orientation is favorable?
Which can be done?
How large should the treatment be?
What part of the proppant will reach the pay?
Width and length (optimum dimensions)?
How can it be realized?
FractureDesign
16
Pseudo-steady state Productivity Index
pJq
pJB
khq D
2
srr
J
w
e
D
43
ln
1Circular:
Production rate is proportional to drawdown, defined as average pressure in the reservoir minus wellbore flowing pressure
Dimensionless Productivity Index
Drawdown
FractureDesign
18
Calculate the skin factor due to radial damage if
Solution of Exercise 1
w
s
s r
r
k
ks ln1
0.5 ftDamage penetration
Permeability impairment
0.328 ftWellbore radius
folds 5sk
k
ft 0.828sr
Note that any "consistent" system of units is OK.
sr
3.7]328.0
828.0ln[15 s
Exercise 1
FractureDesign
19
Assume pseudo-steady state and drainage radius re = 2980 ft in
Exercise 1. What portion of the pressure drawdown is lost in the
skin zone? What is the damage ratio? What is the flow efficiency?
Solution 2The fraction of pressure drawdown in the skin zone is given by (Since we deal only with ratios, we do not have to convert units.):
Therefore 31 % of the pressure drawdown is not utilized because of the near wellbore damage.
The damage ratio is DR = 31 %
The flow efficiency is FE = 69 %.
0.313.70.75]
0.3282980
ln[
3.7
Exercise 2
FractureDesign
20
Assume that the well of Exercise 2 has been matrix acidized and the original permeability has been restored in the skin zone. What will be the folds of increase in the Productivity Index?(What will be the folds of increase in production rate assuming the pressure drawdown is the same before and after the treatment?)
Solution 3We can assume that the skin after the acidizing treatment becomes zero. Then the folds of increase is:
75.0]ln[
75.0]ln[
w
e
w
e
rr
srr
FOI
44.1
328.02980
ln75.0
7.3328.0
2980ln75.0
:Increase of Folds
The Productivity Index increase is 44 % , therefore the production increase is 44 % .
Exercise 3
FractureDesign
21
Assume that the well of Exercise 2 has been fracture treated and a negative pseudo skin factor has been created: sf = -5. What will be the folds of increase in the Productivity Index with respect to the damaged well?
6.3575.0]
328.02980
ln[
7.375.0]328.0
2980ln[
FOI
Solution 4
The ratio of Productivity Indices after and before the treatment is
The Productivity Index will increase 260 % .
Exercise 4
FractureDesign
22
Fully penetrating vertical fracture: Relating Performance to Dimensions
wp
2xf
h2Vfp
FractureDesign
23
Dimensionless fracture conductivity
Dimensionless fracture conductivity
f
ffD kx
wkC
2 xf
w
fracture conductivity
no name
FractureDesign
24
Accounting for PI: sf and f and r’w
D
fw
e
JB
kh
sr
rB
khJ
2
75.0]ln[
12
q J p
sf is a function of what?•half-length, •dimensionless fracture conductivity•wellbore radius, rw
JD is a function of what?•half-length, •dimensionless fracture conductivity•Drainage radius, re
sf is pseudo skin factor used after the treatment
to describe the productivity
FractureDesign
25
Pseudo-skin, equivalent radius, f-factor
)( fDCf
or
Prats
Cinco-Ley
w
e
r
rB
khJ
'472.0ln
2
fw
e srr
B
khJ
472.0ln
2
fx
r.Bμ
πkh
r
xs
x
r.Bμ
πkhJ
f
e
w
ff
f
e 4720ln
2
ln4720
ln
2
FractureDesign
26
Notation
rw wellbore radius, m (or ft)
r'w Prats’ equivalent wellbore radius due to fracture, m (or ft)
Cinco-Ley-Samanieggo factor, dimensionless
sf the pseudo skin factor due to fracture, dimensionless
Prats' dimensionless (equivalent) wellbore radiusf
w
x
r
w
ff r
xsf ln
But JD is the best
FractureDesign
28
Dimensionless Productivity Index, sf and f and r’w
fx
r
r
xs
xr
J
f
e
w
ff
f
e
D
472.0
ln
1
ln472.0
ln
1
fw
eD
sr
rJ
472.0ln
1
)( fDCf
w
eD
rr
J
'472.0ln
1or
Prats
Cinco-Ley
FractureDesign
29
Penetration Ratio Dimensionless Fracture ConductivityProppant Number
2 xf
ye = xe
xe
e
fx x
xI
2
f
ffD kx
wkC
fDxres
wingf,prop,f
res
wingf,prop,fprop C)(I
kV
Vk
kV
VkN 221 24
FractureDesign
30
The following models, graphs and correlations are valid for low to moderate Proppant Number, Nprop
OK, so what IS the Proppant Number?
The weighted ratio of propped fracture volume to reservoir volume. The weight is 2kf/k .
A more rigorous definition will be given later.
The following models are valid for Nprop <=0.1 ! (The
case when the boundaries do not distort the streamline structure (with respect to lower proppant numbers.)
FractureDesign
31
Prats' Dimensionless Wellbore Radius
f
w
x
r '
f
ffD kx
wkC
0.01
0.1
1.0
0.1 1.0 10 100
5.0'
f
w
x
r
fDf
w Cx
r 25.0
'
FractureDesign
32
Cinco-Ley and Samaniego graphf (CfD)= sf + ln(xf/rw)
0
1
2
3
4
0.1 1 10 100 1000
CfD
f
fD
fD
Cuu.+u.u+.+
u.u+.-.Cf
ln where005006401801
11603280651)(
32
2
use f = ln(2) for CfD > 1000
FractureDesign
33
Infinite or finite conductivity fracture
Note that after CfD > 100 (or 30), nothing happens
with f.
Infinite conductivity fracture.
Definition: finite conductivity fracture is a not infinite
conductivity fracture (CfD < 100 or 30)
(Other concept: uniform flux fracture, we will learn
later.)
FractureDesign
34
reservoir
proppedwingfprop
e
proppedwingf
e
ff
fDxprop
kV
VkN
hkx
Vk
kx
wxk
CIN
,2
2
,1
2
2
2
4
4
Proppant Number - Various ways to look at itVarious ways to look at it
Nprop= const means
fixed proppant volume
FractureDesign
38
Optimal length and width
2Vfp = 2h wp xf
Struggle for propped volume: w and xf
fpfp xhwV
f
pffD kx
wkC
2/1
hkC
kVx
fD
ffpf
2/1
f
fpfDp hk
kVCw
2Vfp = 2h wp xf
FractureDesign
39
The Key Parameter is the Proppant Number
0.5
0.4
0.3
0.2
Dim
en
sio
nle
ss P
rod
uc
tivit
y I
nd
ex
, J
D
10-4
10-3
10-2
10-1
100
101
102
Dimensionless Frac ture Conduc tivity, C fD
0.001
0.003
0.006
N prop=0.0001
0.01
0.03
0.06
0.0003
0.0006
I x=1
Xe
2X f
Y e
X e=Y e
0.1
High permFrac&Pack
Medium perm
FractureDesign
40
2.0
1.5
1.0
0.5Dim
en
sio
nle
ss P
rod
uc
tivit
y I
nd
ex
, J
D
0.1 1 10 100 1000
Dimensionless Frac ture Conduc tivity, C fD
N prop=0.1
0.3
0.6
1
3
6
10
30
60
100
Xe
2X f
Y e
X e=Y e
I x=1
The Key Parameter is the Proppant Number
Low permMassive HF
Medium perm
FractureDesign
41
Let us read the optimum from the JD
Figures!
dimensionless fracture conductivity
(for smaller Nprop)
penetration ratio
(for larger Nprop)
FractureDesign
42
0.5
0.4
0.3
0.2
Dim
en
sio
nle
ss P
rod
uc
tivi
ty I
nd
ex
, JD
10-4
10-3
10-2
10-1
100
101
102
Dimensionless Frac ture Conduc tivity, C fD
0.001
0.003
0.006
N prop=0.0001
0.01
0.03
0.06
0.0003
0.0006
I x=1
Xe
2X f
Y e
X e=Y e
0.1
CfDopt=1.6
Optimum for low and moderate Proppant Number
FractureDesign
43
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
Dim
en
sio
nle
ss P
rod
uc
tivi
ty I
nd
ex
, JD
0.01 0.1 1
Penetration Rate, IX
N prop=0.1
0.3
0.6
1
3
6
10
30
100
Xe
2X f
Y e
X e=Y e
Optimum for large Proppant Number
FractureDesign
44
Tight Gas and Frac&Pack: the extremes
Tight gas k << 1 md (hard rock)
High permeability k >> 1 md (soft formation)
2/1
f
fpfDoptp hk
kVCw
2/1
hkC
kVx
fDopt
ffpf
2/16.1
f
fpp hk
kVw
2/1
6.1
hk
kVx ffp
f
FractureDesign
46
Exercise No 1
Determine the "folds of increase" if 40,000 lbm proppant
(pack porosity 0.35, specific gravity 2.6, permeability
60,000 md) is to be placed into a 65 ft thick formation of
0.5 md permeability. Assume all proppant goes to pay.
The drainage radius is re = 2100 ft, the well radius is rw = 0.328 ft, the skin factor before fracturing is spre = 5.
Determine the optimal fracture length and propped
width.
FractureDesign
47
575.0]328.0
2100ln[
1
)(,
propoptD
pre
post NJ
J
J
Folds of Increase
40,000 lbm proppant, specific gravity 2.6, pack porosity 0.35packed volume is 40,000/62.4/2.6/(1-0.35) = 380 ft3
1: Proppant Number 2: Max Folds of Increase
FracPi0.467
1.0
6521005.0
3801060222
33
ftftmd
ftmdN prop
0.0768
FOI: 6.8 with respect to skin 5FOI: 3.8 with respect to skin=0
467.01.0ln5.099.0
1
FractureDesign
48
The volume of two propped wing is 2V1wp = 380 ft3
If the proppant number is not too large: the optimal fracture
half-length is
The propped width is
Optimum frac dimensions
mm) (1.8 in. 0.075h x
Vw
f
1wpp
ft 468 md) ft)(0.5 (651.6
md) (60,000 2
ft 380
x
1/23
f
1wpV
FractureDesign
49
Computer Exercise: High Perm
Determine the optimal fracture length and propped width
if 40,000 lbm proppant (pack porosity 0.35, specific
gravity 2.6, permeability 60,000 md) is to be placed into
a 65 ft thick formation of 50 md permeability.
The drainage radius is re = 2100 ft, the well radius is rw = 0.328 ft, the skin factor before fracturing is spre = 5.
(Assume all proppant goes to pay.)
FractureDesign
50
Computer Exercise: Tight gas
Determine the optimal fracture length and propped width
if 40,000 lbm proppant (pack porosity 0.35, specific
gravity 2.6, permeability 60,000 md) is to be placed into
a 65 ft thick formation of 0.01 md permeability.
The drainage radius is re = 2100 ft, the well radius is rw = 0.328 ft, the skin factor before fracturing is spre = 5.
(Assume all proppant goes to pay.)
FractureDesign
51
Economic optimization
Production forecast
Transient regime
Stabilized
Economics: Converting additional production into value
Time value of money
Discounted revenue
NPV
FractureDesign
52
Costs and Benefits
The more proppant (larger proppant
number) the higher Productivity Index, if
the given proppant volume is placed
according to the optimal dimensionless
fracture conductivity
The more proppant, the larger costs
How large should be the treatment?
NPV optimization
FractureDesign
55
Design Input Data
Petroleum Engineering DataHydrocarbon in Place, Drainage area, Thickness,
Permeability
Rock PropertiesYoung’s modulus, Poisson ratio,
Fracture toughness, poroelastic const
Stress State
Leakoff
Proppant and Other Fluid properties
Operational constraints
FractureDesign
57
Young's modulus and Poisson ratioUniaxial test
xxFA
xxl
l
yyD
D
D
D/2
l
l
F
A E xxxx
xxyy
Linear stress-strain relations
FractureDesign
59
Formation Classification
Two types Consolidated and tight E = 106 + psi Unconsolidated and soft E = 105 - psi
FractureDesign
60
Poroelasticity and Biot’s constant
αpσ σ Total Stress = Effective Stress + [Pore Pressure]
FractureDesign
61
Who Carries the Load?
Force Pore FluidGrains
Biot’s constant
Total Stress = Effective Stress + [Pore Pressure]
FractureDesign
62
Stress State in Formations Far Field and Induced Stresses, Fracture Initiation and Orientation
Stress versus Depth
Minimum Horizontal Stress
Magnitude and Direction
FractureDesign
63
Total (absolute) horizontal stress
D
v dzg0
pvv
pvh
1
'
ppvh
1
The simplest model:
1) Poisson ratio changes from layer to layer2) Pore pressure changes in time
FractureDesign
64
Crossover of Minimum Stress
80x1060 20x106 40x106 60x106
Stress, Pa
Dep
th f
rom
orig
inal
gro
und
surf
ace,
m
Original Vertical Stress
True Vertical Stress
Minim
um H
orizontal Stress
Critical Depth 977 m
-3000
-2500
-2000
-1500
-1000
-500
0
-2500
-2000
-1500
-1000
-500
0
Cur
rent
Dep
th ,
m
Ground Surface
FractureDesign
65
Frac gradient
Basically the slope of the minimum
horizontal stress line 0.4 - 0.9 psi/ft
Extreme value: 1.1 psi/ft or more
Overburden gradient gradient
Slope of the Vertical Stress line 1.1 psi/ft
Stress Gradients
FractureDesign
67
Linear Elasticity + Fractures
The force opening the fracture comes from net pressure
Net pressure = fluid pressure - minimum principal stress pn = p - min
The net pressure distribution determines the width profile
Plane strain modulus and characteristic half length
FractureDesign
68
Ideal Crack Shapes (Plane strain)
Half length c
pn(x)
Deformation (distribution)net pressure (distribution)
21
EEPlane - strain modulus:
w
Plane strain: Infinite repetition of the same picture (2D)
FractureDesign
69
Shape of a pressurized crack, pn=cons
pn : net pressure
c : half length
“characteristic dimension”
22
'
4)( xc
E
pxw n
npE
cw
'
40
Width
Max Width
linearity preserved
w
c
FractureDesign
70
Height and Width in Layered Formation
Pinch point
Contained?Breakthrough?Run-away?Up or Down?Width?Hydrostatic pressure?Height control?What can be measured?
Upper tip Far-field Stress
Lower tip
Questions:
FractureDesign
72
Stress Intensity Factor
weighted pressure at tip
Pa · m1/2
psi - in.1/2
Weighting function: the nearer to tip, the more important the pressure value
stress distributionat tip
c
c
nI dx
xc
xpcK
22
)(2
xc
KI : proportionality const
xc
1
FractureDesign
73
Stability of Crack, Propagation
Critical value of stress intensity factor:
Fracture Toughness KIC
Propagation: when stress intensity factor
is larger than fracture toughness
FractureDesign
74
Application: Fracture Height Prediction
Height containment: why is it critical?
Fracturing to water or gas
Wasting proppant and fluid
Can it be controlled?
Passive: safety limit on injection pressure
Active: proppant (light and heavy)
FractureDesign
75
Calculation Based on Equilibrium Fracture Height Theory
fluid pressure
far field stress
profile
FractureDesign
76
Stress Intensity Factor at the Tips (calc) = Fracture Toughness of the Layer (given)
Kh
y yp y
y
ydy
p
u dnI,top
-1
1
=
1
1
Kh
y yp y
y
ydy
p
u dnI,bottom
-1
1
=
1
1
Two equations, two unknowns
FractureDesign
78
yh
h h huu
p u d
12
yh
h h hdd
p u d
12
k p gh h
cpd u
00 2
k gh
y yp
u d1
2
ykkyp 100)(
Notation
)()()( yypypn
FractureDesign
79
Input to a Height Map Calculation
hp 50 ft 15.24 m
1 3000 psi 20.68 MPa
2 3500 psi 24.13 MPa
3 4000 psi 27.58 MPaKIC,2 1000 psiin.1/2 1.01 MPam1/2
KIC,3 1000 psiin.1/2 1.01 MPam1/2
62.4 lbm/ft3 1000 kg/m3
FractureDesign
80
Calculated Height Map
-1200
-1000
-800
-600
-400
-200
0
200
400
600
800
1000
3000 3100 3200 3300 3400 3500 3600 3700 3800
300
-300
0
21 26
psi
MPa
200
100
-100
-200
Tip Location
[m]
Tip Location
[ft]
Treating Pressure
(after HFM)
FractureDesign
81
How to Use a Height Map?
1 Off-line:
Assume a height, make a 2D design,
Calculate net pressure (averaged in time)
Read-off a better estimate of height
2 In-line:
P3D design (3D),
Calculate net pressure at a location
Adjust height to equilibrium
FractureDesign
83
Fluid Loss in Lab
t
Cu L
L
tC2S=A
VLp
L
Lost
mmm : units
AL
m :unit Ssm
mor
s
m :unit C
p
2
3
L
y = 0.0024 + 0.000069x
0 10 20 30 40 50 60Square root time, t1/2 (s1/2)
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
Lost
vol
ume
per
unit
surf
ace,
m
2CLSp
FractureDesign
84
Fluid Loss in the Formation: Ct
Flow through filtercake covered wallfiltercake build-up and filtercake integrity
Flow through polymer invaded zone“viscosity” of polymer in formation
Flow in bulk of formationcompressibility, permeability, viscosity of
original reservoir fluid
cvWt CCCC
1111
FractureDesign
85
Description of leakoff through flow in porous media and/or filtercake build-up
Concept of leakoff coefficient
Integrated leakoff volume:
Leakoff Width
t
Cu L
L
tACV LL 2
tCA
Vw L
L
LL 2
2/1
2/1/
s
sm
s
m
mmm
Where are those “twos” coming from?
What is the physical meaning?
FractureDesign
87
Step rate test
Injection rate
Bot
tom
hole
pre
ssur
e
Propagation pressure
Two straight lines
FractureDesign
88
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
FractureDesign
89
Pressure fall-off analysis(Nolte)
eLeDpeitt tC2AtgS2AV=Ve
,
eD ttt /
eLDpi
tt tCtgSA
Vw
e2 ,2-
e
FractureDesign
90
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
FractureDesign
92
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
FractureDesign
93
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
FractureDesign
94
Shlyapobersky assumption
No spurt-loss
,2-2- DeLfpfe
ifCw tgtCSSS
A
VSpp
Ae from intercept
g
pw
bN mN
FractureDesign
95
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