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Hydraulic Fracturing
©2007
Hydraulic Fracturing For Production Enhancement
Worldwide massive application 90% of gas wells 70% of oil wells
Historically, for low-permeability reservoirs skin effect less than -6
No longer true - high perm. is common
High-Permeability Fracturing
Stimulation Skin effect from -4 to 0 or even slightly
positive
Originally an offshoot of sand production control (with skins as high as +30). Prevents fines de-consolidation
Hydraulic Fracturing Implementation
Complex operation Requires knowledge and high
competence in a number of areas of engineering and science
Large up-front investment in people, equipment and capabilities
“Massification” is crucial
Basic Principles
Injection of fracturing fluids Formation “breaks down” Fracture propagates, perpendicular
to least resistance “Proppants” are used to keep
fracture open
Principle of Least Resistance
Horizontal fracture Vertical fracture
Least Principal Stress Least Principal Stress
Production Stimulation
Long path of large permeability contrast with the reservoir is created
Flow is from the reservoir into the fracture and then along the fracture into the well
There is virtually no flow into the well from outside the fracture. If there is, the fracture should be considered as unsuccessful
A Road Analogy
Optimal Fracture Length and ConductivityLow Permeability CaseWhen there’s only one-lane roads, better buildat least one two-lane road as far as possibleDrivers will seek the better road
Assuming a fixed amount of paving material, do I build a long, two-lane road or a short multi-lane road to the wellbore, I mean, city?
Optimal Fracture Length and ConductivityHigh Permeability CaseWhen there’s already a network of two-lanes and lot of traffic,You’d better focus many lanes near the hub
Length Vs. Width
Low-permeability reservoirs require long fractures, width is secondary
High-permeability require wide fracture, length is secondary. Tip Screenout (TSO)
Length and width are interdependent through fracture conductivity.
Optimization is warranted
1-
Tip Screenout (TSO) for High-Permeability Reservoirs
Arrest of lateral growth Fracture inflation Leakoff control is another major
benefit of TSO
Vertical Fracture - Vertical Well
Bypass damage
Original skin disappears
Change streamlines
Radial flow disappears
Increased PI is the
result
p or q pJq post
Complex Fracturing
Horizontal wells Transverse vs. longitudinal
Multi-branched wells
Longitudinal Vertical Fracture - Horizontal Well
H,max
xf
H,min
H,min
Transverse Vertical Fractures - Horizontal Well
H,max
Hydraulic Fracture
H,max
D
xf
H,min
Radial converging flow in frac
Multibranch Well withFractured Vertical Branches(Horizontal "Parent" Well isDrilled above the Reservoir)
Horizontal Well with MultipleTransverse Fractures
Multibranch, Multiple-fracture Configurations for Horizontal Wells
Hydraulic Fracturing
Production or Injection Enhancement
What are we doing?
Bypass formation damage After a successful fracture any
damage skin is eliminated Radically modify flow profile into
the wellbore New pseudoskin; New
productivity index
Complementary Roles
Control of sand deconsolidation Reduce fines migration and
asphaltene production Reduce bottom water coning Improve communication between
reservoir and wellbore
Fracturing Role Expanded
Permeability Gas Oil
Low k <0.5 md k <5 md
Moderate 0.5< k <5 md 5< k <50 md
High k >5 md k >50 md
Pseudosteady State Productivity Index
pJq
pJB
khq D
2
srr
J
w
e
D
43
ln
1
Circular:
Production rate is proportional to drawdown, defined as average pressure in the reservoir minus wellbore flowing pressure
Dimensionless Productivity Index
Drawdown
Hydraulic Fracturing
Production Mechanism
Vertical Well, Fully Penetrating Vertical Fracture: Performance
wp
2xf
h2Vfp
Transient Flow Regimes Vertical Fracture - Vertical Well
Linear Fracture Flow
Bilinear Flow
Linear Formation Flow
Elliptical or Transition Flow
Pseudoradial Flow
Pseudoskin Factor, Radial Flow
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 pseudoskin factor used after the treatment
to describe the productivity for radial flow
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
Dimensionless Fracture Conductivity
Dimensionless fracture conductivity
f
ffD kx
wkC
2 xf
w
fracture conductivity
no name
Cinco-Ley and Samaniego
0
1
2
3
4
0.1 1 10 100 1000CfD
f
fD
fD
Cuu.+u.u+.+
u.u+.-.Cf
ln where005006401801
11603280651)(
32
2
use f = ln(2) for CfD > 1000
The JD of a Hydraulically Fractured Well
From Cinco-Ley and Samaniego and simple re-arrangement
fwffeD srxxr
J
/ln75.0/ln
1
fwffDff
e
D
srxCkh
Vkr
J
/lnln5.0ln5.075.0ln
1
44
33
22
11
00
44
33
22
11
00 0.1 1000
s f +
In(x
f /r w
), s
f + In
(x f
/rw)
+ 0
.5 In
(C
fD)
CfD
sf + In (xf /rw)
sf + In (xf /rw) + 0.5 In (CfD)
CfD, opt
1 10 100
Pseudoskin Factor for a Finite Conductivity Vertical Fracture
Penetration Ratio Proppant 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
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
JD vs CfD (moderate Nprop)
JD vs CfD (large Nprop)
Maximum Achievable PI
1.0 if
)(015.0667.01
)(089.0311.0423.0exp
6
1.0 if ln5.0990.0
1
2
2max
prop
propprop
propprop
prop
prop
propD
NNN
NN
NN
NJ
Optimal Length and Width
2Vfp = 2h wp xf
Competition 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
Tight Gas and Frac&Pack: the Extremes
Tight Gas k << 1 md (hard rock)
High permeability k >> 1 md (soft formation)
2/16.1
f
fpp hk
kVw
2/1
6.1
hk
kVx ffp
f
2/16.1
f
fpp hk
kVw
2/1
6.1
hk
kVx ffp
f
PI in Irregular ShapesPI in Irregular Shapes
Reservoir Volume now defined as
hyxV eeres
e
efDx
ef
ef
ee
ff
res
pfp y
xCI
xx
xx
hykx
whxk
kV
VkN 2
42
Proppant Number becomes,
Results for Results for NNpp <0.1 <0.1
Np=0.0001
Np=0.0003
Np=0.0006
Np=0.001
Np=0.003
Np=0.006
Np=0.01
Np=0.03
Np=0.06
Np=0.1
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.1 1 10 100 1000
CfD
JD
yyee/x/xee=0.5 =0.5
yyee
xxee
22xxff
N p J D
0.1 0.4330.0001 0.174
Np=0.0001
Np=0.0003
Np=0.0006
Np=0.001
Np=0.003
Np=0.006
Np=0.01
Np=0.03
Np=0.06
Np=0.1
0.10
0.15
0.20
0.25
0.30
0.35
0.1 1 10 100 1000
CfD
J D
N p J D
0.1 0.3360.0001 0.155
Results for Results for NNpp <0.1 <0.1
yyee/x/xee=0.25 =0.25
yyee
xxee
22xxff
Results for Results for NNpp <0.1 <0.1
0.10
0.20
0.30
0.40
0.50
0.1 1 10 100 1000
CfD
JD
ye/xe=1
ye/xe=0.5
ye/xe=0.25
ye/xe=0.2
ye/xe=0.1
Example:Example:
•NNp p =Constant = 0.03=Constant = 0.03 unadjusted
•Conclusion:Conclusion: CCfD,optfD,opt = 1.6= 1.6 maintained`
Equivalent Proppant NumberEquivalent Proppant Number
88.30A
ppe
CNN
NNpp = Proppant NumberNNpe pe = Equivalent Proppant NumberCCAA = Dietz Shape Factor
)ln(5.099.0
1max,
peD N
J
Shape FactorsShape Factors
Dietz shape factors have been used to relate the production rate with the pressure distribution within a shaped drainage volume
y e /x e C A
0.1 0.0250.2 2.36
0.25 5.380.3 90.4 16.170.5 21.840.6 25.80.7 28.360.8 29.890.9 30.661 30.88
0
5
10
15
20
25
30
35
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
ye / xe
CA
Results for Results for NNpp ≥≥0.10.1
1.0,1.0, 1.0
100
100fDp
fDeDfD,opt CN
CyC
e
eeD x
yy
25.00.1 If 52.04.5
0.251 If 6.1
1.0,
eDeD
eD
fD
yy
y
C
Where,Where,
and,and,
Results for Results for NNpp ≥≥0.1 (cont.)0.1 (cont.)
Np=0.1
Np=0.3
Np=0.6
Np=1
Np=3
Np=6
Np=10
Np=30
Np=60
Np=100
Ix=1
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
0.1 1 10 100 1000
CfD
JD
JJD,maxD,max = 1.9 at NNpp=100
yyee/x/xee=1 =1
yyee
xxee
22xxff
Results for Results for NNpp ≥≥0.1 (cont.)0.1 (cont.)
JJD,maxD,max = 5.81 at NNpp=100
yyee/x/xee=0.25 =0.25
yyee
xxee
22xxff
Np=0.1
Np=0.3Np=0.6
Np=1
Np=3
Np=6
Np=10
Np=30
Np=60
Np=100
Ix=1
0.10
1.00
10.00
0.1 1 10 100 1000CfD
JD
Results for Results for NNpp ≥≥0.1 (cont.)0.1 (cont.)
0.1
1
10
0.1 1 10 100Np
J D
,max
ye=xe
1.43ye=xe
2ye=xe
4ye=xe
5ye=xe
10ye=xe
Inverse behavior:Inverse behavior:
• JJD,maxD,max of a rectangle (ye<xe) surpasses that of a square (ye=xe) at a specific Proppant Number
•Linear behavior starts to dominate the flow regime
•Occurs at largerProppant Numbers due to the elongation of the drainage
F F -function at Opt. Values-function at Opt. Values
New function needed since past solutions are not valid after NNpp>0.1
Transition from pseudo-radial to linear
This function describes maximum dimensionless productivity index (JJD,maxD,max) as a function of optimum conductivity (CCfD,optfD,opt)
F F -function at Opt. Values (cont.)-function at Opt. Values (cont.)
1
2
3
4
5
6
0.1 1 10 100 1000 10000CfD
F
0.1 0.30.6 13 610 3060 100F,opt
FFoptopt - Line
yyee/x/xee=1 =1
yyee
xxee
22xxff
optpD FN
J
)ln(5.063.0
1max,
F F -function at Opt. Values (cont.)-function at Opt. Values (cont.)
1
2
3
4
5
6
7
8
9
0.01 0.1 1 10 100 1000 10000CfD
F
0.1 0.30.6 13 610 3060 100F,opt
yyee/x/xee=0.1 =0.1
yyee
xxee
22xxff
FFoptopt - Line
optpD FN
J
)ln(5.063.0
1max,
F F -function at Opt. Values (cont.)-function at Opt. Values (cont.)
1
2
3
4
5
6
0.1 1 10 100CfD,opt
F ,opt
xe=ye 1.43ye=xe
2ye=xe 4ye=xe5ye=xe 10ye=xe
ExampleExample
1 Fracture 4 Fractures2 Fractures
Reservoir permeability, kk = 10 md
100,000 lb of 20/40 ceramic areinjected per treatmentkkf f = 150,000 md
• Multiple fractures with same type of treatmentMultiple fractures with same type of treatment• Reservoir is split, and calculations done in one of the divisionsReservoir is split, and calculations done in one of the divisions• JJDD is then multiplied by number of fractures for cumulative value is then multiplied by number of fractures for cumulative value
Example (cont.)Example (cont.)
Volume
(ft 3 )Number of fractures
x e (ft) y e (ft) y e /x e N p
1.74E+08 1 1,867 1,867 1 0.0898.71E+07 2 1,867 933 0.5 0.1784.36E+07 4 1,867 467 0.25 0.356
Number of fractures
y e /x e C fD,opt I x x f (ft) w (in)
1 1 1.60 0.236 220.1 0.2822 0.5 1.64 0.233 217.6 0.2854 0.25 1.44 0.249 232.4 0.267
Fracture Dimensions Fracture Dimensions
Drainage area and Proppant NumberDrainage area and Proppant Number
Example (cont.)Example (cont.)
Number of fractures
y e /x e F opt
1 1 1.6422 0.5 1.7864 0.25 2.377
optpD FN
J
)ln(5.063.0
1max,
Number of fractures
y e /x ePer-Well
J D,max
Cumm. J D,max
1 1 0.46 0.462 0.5 0.50 0.994 0.25 0.44 1.77
Hydraulic Fracturing
Stress and Stress Distribution
Stresses In Formations
v
H
g dz 0
v v p
h v p p
1
abs
eff
abs
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
-3000
-2500
-2000
-1500
-1000
-500
0
-2500
-2000
-1500
-1000
-500
0
Cur
rent
Dep
th ,
m
Ground Surface
Influence of Lithology on In-Situ Stress Distribution
Data from hydraulic fracturing
Stress Representation
zz
zy
z
y
x
yy
xx
zx
xz
yz
xy
yx
(b)
zz
z
rz
zr
rr
r
z
z
r
r
Fracture Initiation Pressure
For perfectly vertical well
pbd = 3H,min- H,max + To - p
Hydraulic Fracturing
Rock and Fracture Mechanics
Linear Elasticity And Rock Mechanics,
Stress and Strain Concept Linear Elasticity Material Properties,
Interrelation Uniaxial Compression Test
Plane Stress - Plane strain PKN-KGD-Radial
E =Fl
A l
D lv = - l D
D/2
D
A
F
l
l
Uniaxial Loading Test to Obtain Linear Elastic Parameters
Interrelations Of Various Elastic Constants Of An Isotropic Material
Ideal Crack Shapes
Pressurized Line Crack Plane strain Net Pressure - Superposition How to apply?
Width equations More complex models
Pressurized Line Crack
x
y
c
u(x)
p(x)
x
Tip
r
Line Crack
220'
4)( xcp
Exw n
For constant pressure inside the frac the solution is:
c
x
y
E' is the plane strain modulus (almost same as Young's)E' = E/(1-v2)
Plane Strain
x
y
All strains remain on this plane
Notions of Plane Strain
Stress and resulting strain remain on a plane which can be repeated infinite times
Vertical and horizontal plane options Vertical plane strain is for fractures
whose length is considerably larger than the height
Horizontal plane strain, repeated many times, is for fractures whose height is much larger than their length
Plane strain viewsVertical PlaneStrain Condition
Horizontal PlaneStrain Condition
w0(x=0)
Application: Basic 2D Models
0,wPKN ww
wKGDww
wellbore tip
hf
PKN
KGDhf
ww,0
ww
xf
qi
qi
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 dxxc
xcxp
cK )(
2
1
xc
KI : proportionality const
xc
1
Fracture toughness, Fracture toughness, KIC
Tip Propagation Pressure
fIctip x
Kp48
xc
Fracture toughness, Fracture toughness, KIC
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)
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:
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
Rheology, Fluid Flow in Fractures, Proppant Transport
Stress - Shear Rate Material Properties Flow Geometries Foam
Plastic
Pseudoplastic
Newtonian
Dilatant
Sh
ear
Str
ess,
Shear Rate, .
Yield Pseudoplastic
Idealized Rheological Behavior of Fluids
Rheological Constitutive Equations
Apparent Viscosity
Sh
ear
stre
ss,
Shear rate,
a
.
Parallel Plates (Slot Flow)
w
L
h
Flow
Limiting Elliptic Cross Section
Flow
L
w0
h
Application: Pressure drop in the fracture
Material Balance
Leakoff Delineation
Geometry Evolution (History)
During Pumping
During Shut-in
Bulk Fluid Loss, Detailed Leakoff, Material Balance
Material Balance Leakoff as Material
Property Formal Material
Balance Power-Law
Assumption
Filtercake, Invaded Zone, Reservoir And Pressures For Fluid Leak-Off
Invaded Zone
Filtercake
p
pi
pface
pres
Open Fracture
Invaded zone
Filtercake
UninvadedReservoir
pfpf
pi
Open Fracture
Carter Leakoff Model (Bulk Fluid Loss Concept)
y = 0.0024 + 0.000069x
0 10 20 30 40 50 60
Square 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,
VL/A
L (
m)
m/sin velocity""
t
Cv L
L
S+t2C=A
VpL
L
Lost
mmm
AL
s
mCL in
2CLSp
i
2i
A
Material balance variables
Formal Material Balance for One Wing
V = 2A C t + A SL L L L pCarter I Equation in lab:
Opening-Time Distribution Factor
V =V 2A C t A Si L e p 2
peL St2Cw
w
2
2A=AL :here
A
Less than 2
eitq
peLi St2Cw=
A
V2
is about 1.5
Nolte’s Power Law Assumption
/1D
DD
A
tA
A A AD e / t t tD e /
2/30
g
dAdt-t
C=Ve eA t
LLoffe 0
12
eLe
Loffe
tCA
V
2
peL St2Cgw
w
2)(0
Max 2
g0 Function
0.0
0.5
1.0
1.5
2.0
0 0.5 1 1.5
g0
4/3
/2
Nolte range
Apparent and "True" Leakoff: rp
qi
qL/2
2qi
Rf
hp
qL/2
rp Factor for Radial Fracture
xh
Rp
f
2
h p
R f
21arcsin2
xxxr p
F o r c i r c u l a r
f
pp h
hr :rrectangulaFor
Coupling Of Elasticity, Flow And Material Balance
Width PK KGD No-Leakoff
Derivation of the Original Perkins-Kern Width Equation
Assumptions Height is constant Elasticity: Vertical plane strain (but decoupled) Flow in limiting ellipsoid cross section Newtonian fluid Net pressure is zero at tip No leakoff
Perkins-Kern Width Equation
Elasticity: Rheology: '
20 E
phxw nf
fhw
q
L
p3
0
64
34
3'8
nf
n
ph
iE
dx
dp
4
344
,
'320
f
fwn h
ixEp
41
41
41
0, '57.3
'
512
E
ix
E
ixw ff
w
41
0,0 xxwxw fw 628.055
4
4
PKN Constant Injection - No Leakoff
41
4541
4541
3
'24.2
'625
512
E
hix
E
hixhxwit ffff
ff
54
51
4
351
3
'
512
625t
h
Eix
ff
5
15
125
1
20, '
2560t
hE
iw
fw
51
51
6
2441
2,
'80t
h
iEp
fwn
KGD
'
4
E
pxw nf
w fhw
q
L
p3
12
41
241
241
'22.3
'
336
f
f
f
fw hE
ix
hE
ixw
www 785.04
For 2xf<hf the horizontal plane strain assumption (KGD) is more appropriate
For 2xf>hf the vertical plane strain assumption (PK) is physically more acceptable
Comparison Of Width Equations
w
w
x
h
x
hGK
PK
f
f
f
f
21 625
32 512
20 95
21 4 1 4 1 4/ / /
.
Hydraulic Fracturing
Design Procedure
Pumping Time, Fluid Volume, Proppant Schedule: Design of Frac Treatments
Pumping time and fluid volume: Injected = contained in frac + lostlength reached, width created
Proppant schedule: End-of-pumping concentration is uniform, mass is the required
Given: Mass of proppant, target length, frac height, inj rate, rheology, elasticity modulus, leakoff coeff, max-possible-proppant-added-conc
1 Calculate the wellbore width at the end of pumping from the PKN (Power Law version)
2 Convert max wellbore width into average width
3 Assume a = 1. 5 and solve the material balance for injection time, (selecting sqrt time as the new unknown)
4 Calculate injected volume
5 Calculate fluid efficiency
22
11
22
122
2222
1
0, '
14.2198.315.9
n
fn
fn
inn
n
n
n
nw E
xhqK
n
n=w
0,628.0 we ww
022
)Sw(tκ C t
xh
qpeL
ff
i
eii tqV
i
eff
i
fee V
wxh
V
V=
Pumping Time, Fluid Volume
Adjustment for
Several ways…see page 111 in UFD One way, according to Nolte
= 1.33e + 1.57 (1 - e )
Nolte’s Power Law Proppant Schedule:
fpad1 V/Vi0
C/C e
1
slurry
y =
0 1
1
1ie VcM
1
11
0
dxx
1
1)1( padfArea
1
1Area
Nolte's proposition:select fpad=
ie VcM
1
1
1 Calculate the Nolte exponent of the proppant concentration curve
2 Calculate the pad volume and the time needed to
pump it
3 The required max proppant concentration, ce
should be (mass/slurry-volume)
4 The required proppant concentration
(mass/slurry-volume) curve
5 Convert it to “added proppant mass to volume of
clean fluid” (mass/clean-fluid-volume)
e
e
1
1
ipad VV
epad tt
pade
pade tt
ttcc
iee V
Mc
propp
added cc
c
1
Proppant schedule
Design Logic Specify available proppant, volume and kf
Know your k and h
Assume frac height and fraction of proppant reaching the pay layer
Determine proppant number
Determine optimum CfD
Determine optimum length and propped width
Given the target length, find pumping time and slurry efficiency
Create proppant schedule providing uniform distribution of proppant in the fracture at the moment of shut-in
If necessary, iterate on frac height
Introducing…
HF2DPKNHF2DPKN
Input Parameters Proppant mass for (two wings), lbm
This is the single most important decision variable of the design procedure
Sp gravity of proppant material (from 2.6 to 3.5) Porosity of proppant pack (e.g. 0.35) Proppant pack permeability, md
One of the most important design parameters. Retained permeability including fluid residue and closure stress effects, might be reduced by a factor as large as 10 in case of non-Darcy flow in the frac Realistic proppant pack permeability would be in the range from 10,000 to 100,000 md for in-situ flow conditions. Values provided by manufacturers such, as 500,000 md for a “high strength” proppant should be considered with caution.
Max prop diameter, Dpmax, inch From mesh size, for 20/40 mesh sand it is 0.035 in.
Input Parameters (cont.) Formation permeability, md Permeable (leakoff) thickness, ft Wellbore Radius, ft Well drainage radius, ft
Needed for optimum design. (Do not underestimate the importance of this parameter!)
Pre-treatment skin factor Can be set zero, it does not influence the design. It affects
only the "folds of increase" in productivity, because it is used as basis.
Fracture height, ft Usually greater than the permeable height. One of the
most critical design parameters. Might come from lithology information, or can be adjusted iteratively related to the frac length.
Plane strain modulus, E' (psi) Hard rock: about 106 psi, soft rock 105 psi or less.
Input Parameters (cont.)
Slurry injection rate (two wings, liq+ prop), bpm Rheology, K' (lbf - secn'/ft2) Rheology, n' Leakoff coefficient in permeable layer, ft/min0.5
The leakoff coefficient outside the permeable layer is considered zero. If the frac height to permeable layer ratio is high, the apparent leakoff coefficient calculated from this input will be much lower than the input for this parameter. If the leakoff is significant outside the net pay, you may want to adjust this parameter when you adjust fracture height.
Spurt loss coefficient, Sp, gal/ft2
The spurt loss in the permeable layer. Outside the permeable layer the spurt loss is considered zero. See the remark above.
Input Parameters (cont.)
Max possible added proppant concentration, lbm/gallon fluid (ppga) The most important equipment constraint. Some current mixers
can provide more than 15 lbm/gal neat fluid. Often it is not necessary to go up to the maximum technically possible concentration.
Multiply optimum length by factor This design parameter can be used for sub-optimal design. Play!
Multiply pad by factor Play (if necessary)!
(More input for TSO, Continuum Damage Mechanics)
Computer Exercise: Medium Perm Design Example
Computer Exercise: Tight Gas Design Example
Computer Exercise: High- Perm (Frac&Pack) Example
3D (Finite Element Modeling)
x
ywellbore element
tip element
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
The Value of Information The available data are never enough
(“data hunger”) Input accuracy is always in question The models may behave “strange” Sensitivity the value of
information What is the uncertainty? How much difference does it make at the
bottomline? (“We do not do fracs for Poisson ratio”)
What is the cost to improve accuracy of the data?
Hydraulic Fracturing
High-Permeability Fracturing
Early “frac packs” viewed primarily as an extension to gravel packing Sand exclusion Sand deconsolidation control
HPF has replaced gravel packs in many petroleum producing areas New PI (bpd/psi) allocated to larger rate or lower
drawdown, or any combination
Transition towards hydraulic fracturing 40/60 gravel --> 20/40 or larger proppant HEC fluid --> Crosslinked fracturing fluids
Advent Of High Permeability Fracturing (HPF)
HPF In View Of Gravel Packing
Progressive deterioration of gravel-pack permeability (increased skin)
Leads to decline in well production Counteracting decline with increased
pressure drawdown Results in accelerated pore-level
deconsolidation and additional sand production
The Gravel Pack Scenario
Assume k=50 md, h=100 ft, B=1.1, =0.75 cp and ln re /rw=8.5
Calculate PI and q for 1000 psi drawdown Ideal (undamaged) 5 bpd/psi or 5,000 bpd Some damage (s=10) 2.3 bpd/psi or 2,300 bpd Gravel pack (s=30) 1.1 bpd/psi or 1,100 bpd
s
rr
B
kh
pp
qJ
w
ewfe 472.0ln2.141
From CfD vs. sf graph, sf = -3 Fracture conductivity, CfD = 1 Fracture length, xf = 50 ft
Calculate PI and q for 1000 psi drawdown Ideal (undamaged) 5 bpd/psi or 5,000 bpd Some damage (s=10) 2.3 bpd/psi or 2,300 bpd Gravel pack (s=30) 1.1 bpd/psi or 1,100
bpd HPF (s=-3) 7.7 bpd/psi or 7,000 bpd HPF (s=-1) 5.6 bpd/psi or 5,600 bpd
vs. The HPF Scenario
HPF In View Of Competing Technologies
Production from high-rate water packs reported to deteriorate with time.
Production may progressively improve during the first several months following a HPF job.
Skin Values Reported by Tiner et al. (1996)
Gravel Pack High-Rate Water Pack HPF
+5 to +10 excellent +2 to +5 reported 0 to +2 normally
+40 and higher reported 0 to -3 in some reports
Key Issues In HPF
Tip screenout concept Net pressure and fluid leakoff
Soft formations, low elastic modulus values Fluid volumes relatively small, potential for
high leakoff rates
Fundamentals of leakoff in HPF Carter leakoff (modified) Mayerhofer (filtercake based) Fan and Economides (series resistance)
Tip-Screenout
Fracture Inflation
Packed Fracture
Width Inflation With the Tip-Screenout Technique
Comparison of Conventional and HPF Design Concepts
- End of Job for Conventional Design -
BHP
Tip-Screenout
Injection Rate
Time
Injected SlurryConcentration
Fracture Creation(Conventional)
TSO
Fracture Inflationand Packing
Fracturing Fluid and Proppant Concentrations in Fracture:
Pad Injection
Slurry Injection
At TSO
After FIP
CÑ + FRACTURA
B-5
-X.5
2
Fracturing a High-Permeability Well in Venezuela
Fracturing Pressure Record and Match
GEOMETRIA DE LA FRACTURA REALIZADA
Hydraulic Fracturing
Fracturing Fluids and Proppants
Fracturing Fluids
Oil-basedWater-based Mixtures of oil and water called emulsions Water-based containing nitrogen and/or carbon dioxide gasOil-based containing nitrogen and/or carbon dioxide gas
Exclusively oil-based in the 1950’sMore than 90% water-based in the 1990’s
Nitrogen and carbon dioxide systems in water-based fluids are used in about 50% of treatments
CMHPG Guar HPG
40 #/Mgal Hydration Curves - Recent Samples
0
5
10
15
20
25
30
35
40
45
0.1 1 10 100 1000 10000
Time, t (min)
Vis
cosi
ty a
t 51
1 1/
sec,
(cP
)
Guar- New
CMHPG
Guar - Old
HPG
Crosslinked Fracturing Fluids
Crosslinker Gelling Agent pH range ApplicationTemp. Deg. F
B, non-delayed guar, HPG 8-12 70-300B, delayed guar, HPG 8-12 70-300Zr, delayed guar 7-10 150-300Zr, delayed guar 5-8 70-250Zr, delayed CMHPG, HPG 9-11 200-400Zr-a, delayed CMHPG 3-6 70-275Ti, non-delayed guar, HPG,
CMHPG7-9 100-325
Ti, delayed G, HPG, CMHPG 7-9 100-325
LIQUID DELAYED BORATE
LIQUID FAST BORATE
SOLID FAST BORATE
40# gel not crosslinkedWith 4#per gal sand
40# crosslinked gelWith 4#per gal sand
KEROSENE DIESEL BLACK OIL
Phosphate Ester
Phosphonate Ester
Phosphinic Acid
Iron Activator
Aluminum activator
Additives
Breakers Causas de daño:
Flido, overdisplac., start pdn
Time
Viscosity
Minimum Proppant Transport Threshold Total Pump
Time
Proppant Transport Drives Breaker Packages and Schedules
Added Breakers and Imperfect Delay
Mechanisms Necessitate Extra Fluid Viscosity
Fluid Testing
Compatibility RheologyFluid LossProppant carrying capacityResidue in the proppant packFilter-cake residueBreaking
Plot Viscos vs T
Proppant Selection
Strength Size Sphericity Quality
Brady 12/20
Ottawa 20/40
Oglebay 30/50
Ceramic 3 20/40
Ceramic 2 20/40
Ceramic 1 20/40
16/20
20/40
Resin –Coated Proppants
16/20
Types of Proppant
d
Stress on Proppant and Fatigue
Hydraulic Fracturing
Injection Test Interpretation
Step rate test
Time
Bot
tom
hole
pre
ssur
e
Inje
ctio
n ra
te
Step rate test
Injection rate
Bot
tom
hole
pre
ssur
e
Propagation pressure
Two straight lines
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
Pressure Fall-off Analysis (Nolte)
eLeDpeitt tC2AtgS2AV=Ve
,
eD ttt /
eLDpi
tt tCtgSA
Vw
e2 ,2-
e
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
g-function
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
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
Shlyapobersky Assumption
No spurt-loss ,2-2- DeLfpf
e
ifCw tgtCSSS
A
VSpp
Ae from intercept
g
pw
bN mN
Nolte-Shlyapobersky
PKN KGD Radial
Leakoffcoefficient,
CL
Ne
f mEt
h '4
Ne
f mEt
x '2
Ne
f mEt
R '3
8
FractureExtent CNf
if
pbhVE
x
2
2 CNf
if
pbhVE
x
38
3
CN
if pb
VER
FractureWidth
eL
ff
ie
tC
hxV
w
830.2
eL
ff
ie
tC
hxV
w
956.2
eL
f
ie
tC
R
Vw
754.22
2
FluidEfficiency
i
ffee V
hxwi
ffee V
hxw
i
fe
e V
Rw2
2
Vi: injected into one wing
Example
In a minifrac test 39.75 m3 (10,500 gal) fluid was injected
into one fracture wing during 20 minutes. Estimate the
leakoff coefficient, if E’ = 16.9 GPa, the closure pressure
is pC = 22.1 MPa (3200 psi), the permeable height is
9.75 m (32 ft)
Use the Radial model for analysis.
1 – plot 2 – get slope and intercept
,8/9ΔtgMPa 1.4 -MPa 32.54p D
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
Analysis of Injection Test Example
Created Fracture Radius,Apparent Leakoff Coefficient
ft 94.7m 28.91021.210254.38
75.391069.13
8
'33
77
10
3
CN
if pb
VER
ft/min 0.0015 m/s1085.5
1069.112003
)104.1(8.288)(
'3
8
0.50.55
10
6
,
N
e
fAPPL m
Et
RC
Since only hp = 9.75 m is permeable ,
the ratio of permeable to total surface
rp is less than 1
From “Apparent" to “Real"
214.0)arcsin()1(2
1687.02
5.02
xxxr
R
hx
p
f
p
ft/min 0.0070 m/s 107.2
ft/min 0.214
0.0015 m/s
0.214
1085.5
0.50.54
0.50.55
L
L
C
C
Computer Exercise Minifrac Analysis
Redesign
Run the design with new leakoff
coefficient
(That is why we do minifrac analysis)
Treatment Execution
Pump schedule Proppant schedule Treatment flowback and forced
closure
Hydraulic Fracturing
Fracture Propagation
Fracture Propagation
Elasticity
Friction
Material balance
Propagation criterion
Elementary Material Balance
Ac(x)
w(x)
h(x)
x+x
x
q(x)
q(x+ x)
w0
A w hc f4 0
Differential Models: Nordgren
E w
x
h C
t -+ h
w
tf L
f
'
128
8204
20
+Wellbore Boundary +Tip Boundary
q = -w h
64
p
xf n
03
Pressure Loss in Limiting Ellipsoid Flow
p
x
E
h
w
xn
f
'
20
Linear Elasticityvertical plane strain
q
x+
2h C
t - x+
h w
t= 0
f L f
0
4
Material Balance
Dimensionless Variables Of The Nordgren Model
x c x
t c t
w c w
p c w
D
D
D
n D
1
2
0 3 0
4 0
ci
C E hc
i
C h E
ci
C E hc
E i
C h
1/ 3
L f4
2/ 3
L5
f
1/ 3
L2
f
1/ 3
L2
f4
1
5
8 22
2
3
2
4
2 2
128 16
32 4
' '
'
'
Other Propagation Criteria
Fracture toughness
Dilatancy
Statistical fracture mechanics
Continuum damage mechanics
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 ?
CDM Propagation Criterion
u =Cl x
l + xwf
H,
2
f
f
x=x2
f
2 1 2
min
/
Cl 2Combined Kachanov parameter:
CDM
xfD
10-4
10-3
10-2
10-1
100
101
102
103
10-3 10-1 101 103 105 107
tD
C lD D
2
0.01
1
0.1
0.001
0.0001
Fracture Propagation With CDM
10-1
100
101
102
10-3 10-1 101 103 105 107
tD
wD
, p D
0.0001
0.001
0.1
1
C lD D
2
0.01
C lD D
2
Fracture Propagation With CDM
10-3 10-1 101 103 105 107
10-2
10-1
100
10-2
tD
C lD D
2
0.0001
0.001
0.010.1
1
Fracture Propagation With CDM
Real-Time 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
Nolte-Smith Plot
Log net pressure
Log injection time
Normal frac propagation
Tip screenout
Wellbore screenout
Unconfined
height growth
Evaluating the effectiveness of the treatment
Estimating the subsequent production behavior of the well, and
Checking the accuracy of fracture design and fracture height models used to predict fracture geometry
Fracture Height Measurements
Radius of penetra
tion
Available Techniques
Measured Directly Formation Micro Scanner
Borehole Televiewer
Based on Inference Temperature Logging
Isotopes (fluid, proppant)
Seismic Methods, Noise Logging
Tiltmeter techniques
Spinner survey
ScSb Ir
Tracerlog
Tiltmeter Resultsafter Economides at al. “Petroleum Well Construction”
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 P3D Simulation
P3D Simulation
0 50 100 150 200 250
Fracture Half-Length - ft
0
0.05
0.10
0.15
0.20
0.25
Pro
pp
ed
Wid
th -
in
0
1000
2000
3000
4000
5000
Co
nd
uctivity (K
fw) - m
d.ft
Propped Width (ACL)
Conductivity - Kfw
FracCADE
*Mark of Schlumberger
Flow Capacity Profiles
Texaco E&POCS-G 10752 #D-12Actual05-23-1997
3D (Finite Element)
x
ywellbore element
tip element
Hydraulic Fracturing
Execution of High-Permeability Fractures
Generalized Job Sequence For HPF
Perforate Run the gravel-pack screen assembly Spot/soak acid to clean up perforations Perform and interpret pre-treatment
diagnostic tests Design TSO pumping schedule based
on design variables from diagnostic tests(cont.)
Perforations For HPF
12 shots per foot with “big hole” charges Limited number of 0o or 180o phased
perforations in heart of pay interval Clean formation breakdown Near-well tortuosity Prevent unpacked perforations
Arguments for and against overbalanced and underbalanced perforating
Screenless And Rigless HPF Completions
Reduces $$ and simplifies treatments Paves the way for multiple-zone HPF
completions and thru-tubing recompletions Resin-coated tails to control proppant
flowback; success reported (Kirby et al., 1996)
Rigless coiled tubing completions
Treatment Flowback and “Forced Closure”
Flow fracture fluids back out of well immediately after end of pumping at 10 gpm to 2-3 bpm (requires flowback manifold)
Think of as “reverse gravel packing” rather than causing rapid fracture closure
Supercharged fluids assist fracture/well cleanup
Reduces proppant settling Reduces proppant flowback, a
counter-intuitive result
Hydraulic Fracturing
Fracturing Equipment andField Practices
Fracturing Equipment
Hydration unit Blender Chemical additives system Proppant transport Frac pumps Hi/Lo Pressure manifold Monitoring and control van QA/QC van
Hydration Unit
Blender
100 bpm-35,000 lbpm sand2 dry/3 liquid chemical feeders
Chemical Additives System
Proppant Transport
Frac Pump
2400 bhp frac pump
Hi/LO Pressure Manifold
Monitoring And Control Van
Batch Mixed
control vanQA/QCvanproppant
transports
frac
pum
ps
frac
tank
s
wellbl
ende
r
treating line
pop-off valve
valve
pressure relief line
plug valve
check valve
pressure transducers
conveyor belt
Real Time Mixing With Pit Suction Manifold
control van
frac
pum
ps
well
treating line
pop-off valve
valve
pressure relief line
plug valve
check valve
pressure transducers
proppanttransports
pit s
ucti
onm
anif
old bl
ende
r
conveyor belt
QA/QCvan
hydr
atio
n un
it
Real Time Mixing
proppanttransports
frac
tank
s
blen
der
conveyor belt
control van
frac
pum
ps
well
trea
ting
line pop-off valve
valve
pressure relief line
plug valvescheck valve
pressure transducers
QA/QCvan
hydr
atio
n un
it
HI/LO pressuremanifold
Quality Control Philosophy
Start of quality control (QC) was motivated 20 years ago by poor service quality
Producing companies began to exercise various forms of “quality control”
Today QA/QC represents a broad swath of self-policing quality control schemes Checklist, filled out in the field Incentive-ized marketing strategy Latest avante garde business psychology
Quality Control
Fracture treatment should, and can, be carried out as it was designed Pre-treatment planning Well maintained and functioning equipment Trained, conscientious and well-informed
personnel Intense tracking of each fracturing material
and critical treatment parameters Post-treatment evaluation
Quality Control For HPF
Many early treatments failed because of equipment problems and lack of QC on fluids and proppants
Adoption of intense quality control measures common to MHF was slow for HPF
Slowed introduction of HPF Now common for producing company to
supply consultant or in-house specialist to oversee quality control
Standard Fracturing QA Procedures
Pre-job Testing Prior to pumping, each frac tank is strapped and
tested for specific gravity, pH and temperature. A sample is taken from each tank and tested with gelling agent for viscosity and crosslink time. A composite fluid sample is tested with chemicals from location.
Proppant Validation Proppant sieve analysis is provided on location. If
proppant does not meet acceptable standards, each compartment is tested individually.
Standard Fracturing QA Procedures
Pre-job Inventory Prior to the start of the job, the Stimulation
Treatment Check List is filled out with beginning volumes of all chemicals and frac fluid on location. Proppant storage is visually inspected and compared to weight tickets.
Job Testing and Recording Fluids and chemicals are physically strapped every
5,000 gallons or as often as possible. Samples of the pad and 2-3 slurry stages are taken along with corresponding proppant samples.
Standard Fracturing QA Procedures
Real-Time QA In addition to normal treatment displays of rate,
pressure, net pressure and sand concentration, the following parameters will be displayed and recorded: pH, fluid temperature, viscosity and all additive rates.
Post-job Reports In addition to the standard treatment outputs, the
treatment report includes the following: Proppant Sieve Analysis and QC Form, Water Quality Control Form, Frac Fluid Blending and QC Form, and Stimulation Real Time Report.
Hydraulic Fracturing
Evaluation Techniques
Fracture Treatment Evaluation
Real-time analysis Fracture height and orientation Well testing Evaluation of HPF treatments--
a unified approach Production results Evaluation of real-time HPF treatment data Post-treatment PTA in HPF
Decision-Making On Site
Big 3 fracturing variables: ct, po, h Prepare crossplots before going to field:
Read Vs directly; %Pad = (1-F.E.) / (1+F.E.) Sensitivity runs on q, E, fluid properties
Vs
po or CDM
F.E.
po or CDM
c t
c t
Start Job Prepad Pad Flush1 2 3 4Sand-laden 20/40
Lo
g
p
Type IV
Type III
Type II
Type I
Log t
Real time pressure response types, indicating increasing risk of screenout
(Nolte-Smith Plot)
Fracture Geometry and Height Growth
A
H,min
1
2 3 4H,max
v
Shale
Shale
0.90.80.70.60.50.40.30.20.1
pnet /
hf /h
C
31 2
hhf
B
Pn
et
Fracture Height And Fracture Orientation
Temperature log R/A tracer survey Seismic imaging, active and passive Tiltmeter arrays, surface and downhole Borehole elongation caliper Oriented core (anelastic strain
relaxation) Empirical observations
Well Testing
Pre-fracture well tests are not possible in low permeability formations
Post-fracture well test intended to obtain permeability and fracture extent, simultaneously
Different combinations of the unknown parameters can give a good fit
In HPF, the permeability is usually known and the primary goal is to evaluate the created fracture
Know What The Analysis Plot Should Look Like
fracture linear bilinear
pseudo-radial
boundary dominated
formation linear
DimensionlessFracture Conductivity CfD
kt
ctxf
2khTsc [m(p)]
qTpsc
2khp
qBµ
Region of Bilinear Flow
Region of Linear Flow
Dimensionless Time, tDxf
Dim
ensi
on
less
Pre
ssu
re,
pD
10-2
10-1
1
10
10-5 10-4 10-3 10-2 10-1 1
0.1
0.5
1
510
50100500
pD = Oil
pD = Gas
tDxf =CfD =kfw
kxf2
Dimensionless Pressure and Pressure Log-Derivative for a Fractured Vertical Well
Well Testing: The Quest for Flow Regimes
Bilinear Flow Analysis Equations
5.0211.44
kcmh
Bqwk
tBf
000708.0
ppqB
khs if
wff ppqB
khs 0
00708.0
Buildup
Drawdown
m=63.8 psi/hr1/4
2600
2650
2700
2750
2800
0 0.5 1 1.5 2
teqB1/4, hrs1/4
pw
s, p
si
Bilinear Flow Analysis
Limitations of Bilinear Flow Analysis
Applicable only to finite-conductivity fractures Bilinear flow may be hidden by wellbore
storage Requires independent estimate of k To estimate xf there is a need for pseudoradial
flow regime
Linear Flow Analysis Equations
000708.0
ppqB
khs if
wff ppqB
khs 0
00708.0
Buildup
Drawdown
21064.4
tLf ckhm
Bqx
0
1000
2000
3000
4000
5000
6000
0 2 4 6 8 10 12 14 16 18
taLeq1/2, hrs1/2
pa
ws,
psi
Linear Flow Analysis
Limitations of Linear Flow Analysis
Applicable only to wells with high-conductivity fractures
Wellbore storage may hide linear flow period Long transition period between end of linear flow
(tLfD < 0.016) and beginning of pseudoradial flow (tLfD > 3)
Requires independent estimate of k To estimate wkf there is need for pseudoradial flow
regime
Evaluation Of HPF Treatments--A Unified Approach
Evaluation of real-time HPF treatment data Step-wise approach for evaluation of bottomhole
treating pressures outlined by Valkó et al. (1996): Leakoff coefficient from minifrac using minimum assumptions
(e.g. radial geometry and Nolte-Shlyapobersky method) Almost automatic procedure to estimate created fracture
dimensions (“slopes analysis”) Convert results to equivalent fracture extent and conductivity Conduct for large number of treatments from various
operators to build data bank
Slopes Analysis
HPF treatments often exhibit numerous increasing pressure intervals which are interrupted by anomalous pressure decreases
Slopes analysis provides a simple tool for examining such behavior
Design parameters Minimum user input beyond real treatment data Relatively independent of fracture propagation model Not be a history matching procedure Screening tool based on well-defined (reconstructible)
algorithm
R
2i
qL /2qL /2
qL /2
qL /2
i
iA = (/2)R2
HPF Radial Fracture Geometry
Slopes Analysis Assumptions
Created fracture is vertical with a radial geometry
Fluid leakoff can be described by the Carter leakoff model plus Nolte power-law type area growth
Fracture packing radius may vary with time, being allowed to increase or decrease
Hydraulic fracture radius (which defines leakoff area) cannot decrease, and is the maximum of the packing radius that has occurred up to a given time
(cont.)
Slopes Analysis Assumptions (cont.)
During regular width-inflation periods, the pressure slope is defined by linear elastic rock behavior and fluid material balance with friction effects being negligible
Injected proppant is distributed evenly along the actual packing area during each incremental period of arrested extension/width growth
Slopes Analysis: Restricted Growth Theory
LqiAdt
dw
1
LqiRR
E
dt
dp
2
2
16
3
2
2RA
w
R
Epn 16
3
and
Slopes Analysis: Restricted Growth Theory (cont.)
,12
0
,
DtD
DLtL t
tg
tACq
.911=
9/8,
0
DtD
D
td
tg
91.11
2,t
ACq LtL
Clock Time, hh:mm:ss
3700B
ott
om
ho
le P
ress
ure
, p
si
19:00:00 19:20:00 19:40:003300
3500
Bottomhole Pressure From HPF Treatment
3700
Clock Time, hh:mm:ss
Fil
tere
d B
HP
, p
si
19:00:00 19:20:00 19:40:003300
3500
Bottomhole Pressures Corresponding to Width Inflation Intervals
Determining Packing Radius For A Width Inflation Period
Combining the newly developed basic equations:
Or:
91.11
22
2
16
3 2
2 tC
Ri
RR
Em L
0375.025.223
m
iE
tm
CERR L
Estimated Packing Radius With Interpolation
50
40
30
20
10
0
t, min
R,
ft
Packing Radius
0 10 20 30 40 50
Hydraulic Radius
Determining The Final Areal Proppant Concentration
For every time interval, t, determine the mass of proppant entering the fracture.
Assume this mass to be uniformly distributed inside the packing radius corresponding to the given time step.
Obtain the mass of proppant in a “ring” between radius R1 and R2 by summing up (accumulating) the mass of proppant placed during the whole treatment.
Repeat Step 3 for all rings to obtain the areal proppant concentration as a function of radial location R.
14
12
10
8
6
4
2
0
R, ft
c p, l
b/f
t2
0 10 20 30 40 50
Final Areal Proppant Concentration as a Function of Distance From the Perforations
Design Improvement in a Field Program Sizing Pad volume for “generic” design More aggressive or defensive proppant schedule Proppant change (resin coated, high strength) Fluid system modification (crosslinked, foam)
Proppant carrying capacity Leakoff
Perforation strategy changes Forced closure Fiber reinforcement
Field Analysis of Fractured Wells
Case Study of 1000 wells analyzed in Western Siberia
Evaluation of field-derived productivity indexes with the ones designed
Improvement in design
JD; JDtarget and the JDAttainable vs.
reservoir permeability, all wells
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0.01 0.1 1 10 100 1000
Reservoir permeability, md
JD
JD
JDtarget
JDAttainable
2003 and 2004 fracture designs vs. the presumed reservoir permeability
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0.1 1 10 100
Presumed reservoir permeability, md
JD
2004 Design
2003 Design
PI vs. presumed permeability
0
0.5
1
1.5
2
2.5
3
3.5
4
0 5 10 15 20 25 30
Presumed permeability, md
PI,
cu
b.m
/d/a
tm.
2004
2003
Comparison of JDDesign vs. JD from Nprop field-derived JD wells fractured in 2003
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
1 10 100
Presumed permeability, md
JD
2003 JD Design
2003 JD Nprop kpr
2003 JD kpr
Comparison of JDDesign vs. JD from Nprop field-derived JD wells fractured in 2004
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
1 10 100
Presumed permeability, md
JD
2004 JD Design
2004 JD Nprop kpr
2004 JD kpr
Comparison of JD based on Nprop from
pressure matched frac geometry 2003
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80
JD Design
JD
Ix
kp
r
Comparison of JD based on Nprop from pressure matched frac geometry 2004
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80
JD Design
JD
Ix
kp
r
JD based on Nprop from pressure
matched geometry for 2003
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0.1 1 10 100 1000
CfD
JD
Np=100
Np=60
Np=30
Np=10
Np=6
Np=3
Np=1
Np=0.6
Np=0.3
Np=0.1
Ix=1
Np 0.08-0.2
Np 0.2-0.45
Np 0.45-0.8
JD based on Nprop from pressure matched geometry for 2004
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0.1 1 10 100 1000
CfD
JD
Np=100
Np=60
Np=30
Np=10
Np=6
Np=3
Np=1
Np=0.6
Np=0.3
Np=0.1
Ix=1
Np 0.08-0.2
Np 0.2-0.45
Np 0.45-0.8
Np 0.8-2.0
Np2.0-4.5
Hydraulic Fracturing
Deviations from IdealityAdvanced Concepts
Fracturing High-Rate Gas Wells
Non-Darcy flow reduces fracture flow capacity substantially
However, fracturing is a major way to reduce non-Darcy effects in an unfractured wells and provide well stimulation
(Ref. Economides et al. World Oil, Oct., 2002)
Reduction of Fracture Conductivity
Re
,, 1 N
kk nf
ef
vk
N nf ,Re
Effective Fracture Permeability
Reynolds Number
anfk
bx
)()101(
,
8 a and b are constantsof the proppant
Example of Fracture Design for Gas Well
Proppant mass for (two wings), lbm 150,000
Sp grav of proppant material 2.65
Porosity of the proppant pack 0.3
Formation permeability, md 0.5
Permeable (leakoff) thickness, ft 150
Well Radius, ft 0.30
Well drainage radius, ft 800
Pre-treatment skin factor 10.0
Fracture height (gross) , ft 400.0
Nominal (Darcy) proppant pack permeability, md 200,000
Additional Information Needed for Non-Darcy Calculations
Gas Specific Gravity (air=1) 0.71
p avg (psia) 4000
pwf (psia) 1500
(cp) 0.015
T (R) 580
Z 0.91
Coefficients for the Cooke correlation ( 20/40 mesh sand)
a 1.54
b 110,470
Design Procedure in UFD
Assume a Reynolds number Calculate the effective proppant permeability Calculate the Proppant Number. Obtain the
maximum possible productivity index JD,max and the optimum dimensionless fracture conductivity, CfD,opt . Determine fracture dimensions.
From the productivity index and drawdown determine the actual production rate, which in turn is used to obtain the Reynolds number.
Design Iteration 1
Proppant Number, Nprop 1.288
Dimensionless PI, JD, opt 1.06
Optimal dimensionless fracture cond, CfD,opt
3.0
Optimal half length, xf,opt, ft 464
Optimal propped width, wopt, inch 0.042
Post treatment pseudo skin factor, sf -6.20
Assume NRe = 0, thus kf,e = 200,000 md
Design Iteration 1
Bg = 0.0283 (ZT / pfrac) = 0.0283 (0.91) (580) / 1500 = 0.00997 res ft3/SCF
= 0.076 g/Bg lbm/ft3 = 1.22 g/Bg kg/m3 = 86.9 kg/m3
v = (0.00997)(96,960)(1000)/(24)(3600)(400)(0.042/12)(2) = 4 ft/sec = 1.22 m/s
MSCF/d 96,960 (1.06)R) 580cp)(0.91)( 1424(0.015
)psi) (1500psi) ft)[(4000 md)(150 (0.5
1424
)( 2222
Dwfave J
ZT
ppkhq
Design Iteration 1
a
fk
b
)(108 75,800 1/m
NRe = (75,800) (1.97 X 10-10) (1.22)(86.9) / (0.015 X10-3) = 106
Design Iteration 2
Assume NRe = 9, thus kf,e = 20,000 mdProppant Number, Nprop 0.1288
Dimensionless PI, JD, opt 0.50
Optimal dimensionless fracture cond, CfD,opt
1.6
Optimal half length, xf,opt, ft 200
Optimal propped width, wopt, inch 0.097
q = 45,740 MSCF/d, v = 0.25 m/s, NRe = 22
Design Iteration 3
Assume NRe = 15, thus kf,e = 12,500 mdProppant Number, Nprop 0.0756
Dimensionless PI, JD, opt 0.444
Optimal dimensionless fracture cond, CfD,opt
1.6
Optimal half length, xf,opt, ft 157
Optimal propped width, wopt, inch 0.124
q = 41,000 MSCF/d, v = 0.174 m/s, NRe = 15
Design Pumped
Efficiency, , % 44.9
Pumping time, te, min 47.7
Pad pumping time, tpad, min 18.1
Max added proppant concentration, lb per gal clean fluid
10.0
Design Pumped
0
5
10
15
20
25
30
0 10 20 30 40 50 60
Pumping time, min
Liqu
id in
ject
ion
rate
, bpm
012345678910
ca, l
bm p
rop
adde
d to
ga
llon
liqui
d
Constants a and b in Cooke’s correlation
Prop Size a b 8 to 12 1.24 17,423 10 to 20 1.34 27,539 20 to 40 1.54 110,470 40 to 60 1.60 69,405
Applying The Firoozabadi And Katz Correlation for Non-Darcy Flow
k
k c vk
app
1
1 0 2
.
c q
h
c
hq c qa a g
2 2 0
k
k c qwk
app
f
f
1
1 00 2.
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
Misalignment
Proppant Slugs
Well Orientation
S - shaped
Fracture Orientation: Perforation Strategy (After Dees, SPE 30342)
max max
From overbalanced perforation
From underbalanced perforation
Fracture Face Skin Effect
Damaged Zone
xf
ws
kf
ks
Effect of Fracture Face Skin
fs
s
ssf xhk
wqB
kkp
4
11 1
ffsff s
hk
qBp
21
1
2 sf
sff k
k
x
ws
ff
sD
D
sJ
J
0
11
Dimensionless Productivity Index Including Fracture Face Skin Effect
Fracture Choke Skin
xf
Damaged Zone
kf kck
xs
xf xs
kck
Damaged Zone
ws w kf
Effect of Choke Skin
Production Impairment in Gas-Condensate Reservoirs (SPE 64749)
rgMrgIrg kffkk )1(
bc
aN
f/1)(1
1
here a and b are parameters which are 1.6E-3 and 0.324, respectively, and Nc, is the capillary number which is defined by
Weighted average of immiscible and miscible relative permeability curves:
pk
Nc
Hydraulic Fracturing
Acid Fracturing
Acid Fracturing
Acid is injected at a rate high enough to generate the pressure required to fracture the formation.
Differential etching occurs as the acid chemically reacts with the formation face.
Areas where the rock has been removed and kept open are highly conductive to hydrocarbon flow after the fracture closes.
In general: no proppant
(Fracture Acidizing)
As a general guideline, it is used on formations with >80% hydrochloric acid solubility. (??)
Low permeability carbonates (< 20 md) are the best candidates for these treatments because of the differential permeabilities between the "fracture conductivity" and the matrix of the rock.
Fluid loss to the matrix and natural fractures can be better controlled in lower permeability formations.
The Closed Fracture Acidizing (CFA)
Existing fractures in the formation. The fractures can be natural, previously created fractures, or fractures hydraulically induced just prior to the CFA treatment.
Pumping acid at low rates below fracturing pressure into a fractured well. The acid preferentially flows into areas of higher conductivity (fractures) at low rates for extended contact times, resulting in enhanced flow capacity.
Performance Prediction
Fracture conductivity, created dynamic width, created dissolved width
Width from stochiometry and material balance
Etched pattern Stress and strength (Nierode
and Kruk) limit: 5000 psi
Newtonian Flow of Fluid (Slot Flow) Darcy’s Law
2
12
w
u
L
p avg
Darcyu
kL
p
12
3wkw
Equivalent Permeability of Empty Fracture
Equivalent Conductivity of Empty Fracture
12
2wk
Acid Fracturing
“Ideal” width
Ideal permeability (in consistent units)
Realistic kfw from Nierode and Kruk (rock embedment stress)
area Fracture
dissolvedrock of Volumew i
12
wk
2
id
Nierode and Kruk
Input ideal width wi (in.) rock embedment stress Srock (psi) closure stress (psi)
Output kfw in md-ft
psi 20,000 S if 10)ln28.08.3(
psi 20,000 S if 10)ln3.19.13(
1047.1
rock3
2
rock3
2
47.271
12
rock
rock
i
Cf
SC
SC
wC
eCwk
Controlling Fluid Loss
Pumping a high viscosity preflush ahead of the acid solution, or controlling the densities of the preflush, acid, and overflush fluids used in the treatment.
One technique uses nonacid phases containing fluid-loss control additives pumped at intervals during the treatment to re-establish fluid loss control.
Another technique uses a high viscosity preflush ahead of the acid solution.
ACIDS
Hydrochloric (HCl) Acetic (CH3COOH) Formic (HCOOH) Hydrofluoric (HF)
Fracturing Horizontal Wells
Longitudinal Similar to vertical well but with multiple
stages potential increases Transverse
Multiple transverse treatments
Basis of Design
The PI of a fractured vertical well is used to evaluate the attractiveness of the multiple transverse fracture
Unified Fracture Design is adapted with shape factors to account for elongated drainage shapes
Traditional perforating methods if applied will lead to failure. New methods using abrasive jets are preferred
Necessary isolation methods can impact execution time and cost
Design Procedure for Vertical Well, Vertical Fracture
Determine the amount of proppant reaching the target layer
Determine the proppant number and the optimum fracture conductivity
Determine appropriate fracture dimensions
Calculate injection time and proppant schedule to deliver the optimum fracture dimensions.
Np for Elongated Drainage
Square Drainage
Const4
22
e
fffDx kx
wxkCI
r
pf
pe
pff
e
fffDxprop kV
Vk
hkx
whxk
kx
wxkCIN
24422
2
Elongated Drainage
hyxV eeres
e
efDx
ef
ef
ee
ff
res
pfp y
xCI
xx
xx
hykx
whxk
kV
VkN 2
42
88.30A
ppe
CNN
Fluid Flow For Transversely Fractured Horizontal Well
rw
2xf
w
rw
2xf
Fluid flow from reservoir into fracture Fluid flow from fracture into wellbore
PI of Transversely Fractured Horizontal Well
]2
)2
[ln(
wf
c r
h
wk
khs
cDV
DTH
sJ
J
)
1(
1
Multiple Transverse Fractures Intersecting a Horizontal Well
min max
W
rw
min max
W
rw
min max
W
rw
Vertical vs Horizontal Performance Comparison
Proppant Mass, lbs
x e (ft) y e (ft) N p C fD x f (ft) J D
100,000 1640 1640 0.0696 1.60 171 0.43
200,000 1640 1640 0.1391 1.64 239 0.50
300,000 1640 1640 0.2087 1.71 287 0.55
Number of Fracs
x e (ft) y e (ft) N p C fD x f (ft) J DTH
2 1640 820 0.1391 1.62 170 0.65
4 1640 410 0.2782 1.42 182 1.17
5 1640 328 0.3478 1.20 198 1.34
Number of Fracs
x e (ft) y e (ft) N p C fD x f (ft) J DTH
2 1640 820 0.4173 1.75 283 0.94
4 1640 410 0.8347 1.55 301 1.73
5 1640 328 1.0434 1.33 325 2.02
Vertical Well
Horizontal Well100,000 lbs
Horizontal Well300,000 lbs
Production Forecast
0
2000
4000
6000
8000
10000
12000
14000
16000
0 50 100 150 200 250 300
t , days
q, S
TB
/day
Vertical
Horizontal - 4 fracs
0
2000
4000
6000
8000
10000
12000
14000
16000
0 50 100 150 200 250 300
t , days
q, S
TB
/day
Vertical
Horizontal - 4 fracs
Artificial lift required
Planning and Execution Considerations
The notion of fracturing a horizontal well transversely has to be considered BEFORE the well is drilled
Horizontal section must be drilled along the minimum horizontal stress;
Casing, completion and all mechanical elements that go into the well must be able to sustain the pressures and injection rates required for the treatment(s);
Two major decisions need to be taken: a) Method of perforation b) Method of isolation between individual treatments
Method of Perforation
The only suitable method for “perforation” is by abrasive jet cutting tools
It is the only tool that offers large, clean and deep holes and in close spacing.
Traditional guns will require as much as 3 ft to place the required number of perforations for the fracture treatment; this length, in turn, may cause tortuosity or even multiple fracture initiations.
Tortuosity will result in extra fracturing pressure that, many times, might not be available, and the fracture may not initiate.
Example of jet cutter tool with 6 holes longitudinally disposed, 180° phased in a 4” section
Example of jet cutter tool with 4 holes radially disposed, 90° phased
Abrasive Jet Cutter
Method of Isolation Between Individual Treatments
Choices: drillable (composite) coiled tubing conveyed electrically set, or pump-through, hydraulically set bridge plugs. The selection will impact both the operations schedule and the cost.
Using an e-line CT would require first to switch CT reel from the previous pumping operation to an e-line reel. This is the major reason that a pump-through, hydraulically set bridge plug might be preferred.
On the other hand, using an e-line coil tubing allows the operator to also run a CCL locator for greater accuracy for the exact location of the bridge plug.
Four sets of operations to be executed
1. Fracture Isolation2. Fracture Placement3. Fracture Clean-Up4. Post Fracture Flow-Back and Testing
The first three sets are repeated for each additional fracture treatment; the fourth is to be performed after all fracture treatments have been placed.
The isolation method selected will impact both the operations schedule and the cost.
Execution Procedure
1) 1) Fracture isolationFracture isolation
2) 2) Fracture PlacementFracture PlacementMinifrac
(Diagnostic Fracturing Tests)Fracturing Job
3) 3) Fracture CleanFracture Clean--UpUpClean-Up Hole
(+ Possible Lift) With CTWell Test
Each Fracture Placement Requires a Loop of Each Fracture Placement Requires a Loop of these 3 Main Tasks. Besides, the final Taskthese 3 Main Tasks. Besides, the final Task
4) 4) Post Fracturing Post Fracturing Milling-Out BP and
Clean-Up Hole With CTWell Test of the Commingle
Multi-Fractured Horizontal Drain
Hydraulically Setting BP + Pressure Test
Abrasive Cutting
Clean-Up Fracturing Fluids
1) 1) Fracture isolationFracture isolation
2) 2) Fracture PlacementFracture PlacementMinifrac
(Diagnostic Fracturing Tests)Fracturing Job
3) 3) Fracture CleanFracture Clean--UpUpClean-Up Hole
(+ Possible Lift) With CTWell Test
Each Fracture Placement Requires a Loop of Each Fracture Placement Requires a Loop of these 3 Main Tasks. Besides, the final Taskthese 3 Main Tasks. Besides, the final Task
4) 4) Post Fracturing Post Fracturing Milling-Out BP and
Clean-Up Hole With CTWell Test of the Commingle
Multi-Fractured Horizontal Drain
Hydraulically Setting BP + Pressure Test
Abrasive Cutting
Clean-Up Fracturing Fluids
Execution Procedure (Pump through hydraulically set bridge plug)
Dummy Run
With CT
1) 1) Fracture isolationFracture isolation
2) 2) Fracture PlacementFracture PlacementMinifrac
(Diagnostic Fracturing Tests)Fracturing Job
3) 3) Fracture CleanFracture Clean--UpUpClean-Up Hole
(+ Possible Lift) With CTWell Test
Each Fracture Placement Requires a Loop of Each Fracture Placement Requires a Loop of these 3 Main Tasks. Besides, the final Taskthese 3 Main Tasks. Besides, the final Task
4) 4) Post Fracturing Post Fracturing Milling-Out BP and
Clean-Up Hole With CTWell Test of the Commingle
Multi-Fractured Horizontal Drain
Electr. Setting BP + Pressure Test
Abrasive Cutting
Clean-Up Fracturing Fluids
Dummy Run
With CT
1) 1) Fracture isolationFracture isolation
2) 2) Fracture PlacementFracture PlacementMinifrac
(Diagnostic Fracturing Tests)Fracturing Job
3) 3) Fracture CleanFracture Clean--UpUpClean-Up Hole
(+ Possible Lift) With CTWell Test
Each Fracture Placement Requires a Loop of Each Fracture Placement Requires a Loop of these 3 Main Tasks. Besides, the final Taskthese 3 Main Tasks. Besides, the final Task
4) 4) Post Fracturing Post Fracturing Milling-Out BP and
Clean-Up Hole With CTWell Test of the Commingle
Multi-Fractured Horizontal Drain
Electr. Setting BP + Pressure Test
Abrasive Cutting
Clean-Up Fracturing Fluids
Execution Procedure(Electrically set bridge plug)
Summary
Increasing role of evaluation Integration of reservoir engineering,
production engineering and treatment information
Cost matters Expensive 3D and P3D models do not
substitute thinking Still what we want to do is increasing JD
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