Transcript HFSC - Petroleum Engineering | College of Engineering

Hydraulic Fracturing
Short Course,
Texas A&M University
College Station
2005
Fracture Dimensions
Peter P. Valkó
Fracture Dimensions
Proppant Placement
Fracture
Dimensions
2
Proppant Placement Concepts
From dynamic width (hydraulic) to propped
width (after frac closes on proppant)
Areal proppant concentration
Added proppant concentration
Max added proppant conc
Proppant (placement) efficiency
Fracture
Dimensions
3
Proppant Transport: Settling
Settling causes problems
proppant efficiency decreases (proppant
leaves pay layer)
screenout danger
No settling in “perfect” transport fluid
Viscosity (rheology) and density
difference
(Foams: visc good, dens: bad)
Fracture
Dimensions
4
Design Logics
 Height is known (see height map)
 Amount of proppant to place is given (from NPV)
 Target length is given (see opt frac dimensions)
 Fluid leakoff characteristics is known
 Rock properties are known
 Fluid rheology is known
 Injection rate, max proppant concentratrion is given
Fracture
Dimensions
5
 How much fluid? How long to pump? How to add
proppant?
Key concept: Width Equation
Fluid flow creates friction
Friction pressure is balanced by injection
pressure
Net pressure is positive
Fracture width is determined by net
pressure and characteristic dimension
(half length or half height)
Fracture
Dimensions
6
The combination of fluid mechanics and
solid mechanics
Two approximations:
Perkins-Kern-(Nordgren)
Vertical plane strain
characteristic half-length ( c ) is half height, h/2
elliptic cross section
Kristianovich-Zheltov - (Gertsmaa-deKlerk)
Horizontal plane strain
characteristic half length ( c ) is xf
rectangular vross section
Fracture
Dimensions
7
Width Equations (consistent units)
Perkins-Kern-Nordgren PKN
 mqi x f 
1/ 4
width: w, wo, wwell,o
viscosity: m
inj. rate (1 wing): qi
half-length: xf
plain-strain
modulus: E'
height: hf
Vf = w(hf x f )
Fracture
Dimensions
8

ww, 0 = 3.27
 E' 
w  0.628ww,0
Kristianovich-Zheltov
Geertsma-De-Klerk KGD
 mqi x
ww = 3.22
 E' h
f

w  0.785ww
2
f
1/ 4




PKN Power-Law Width Equation
With equivalent viscosity at average shear
rate
the maximum width at the wellbore is
ww, 0 = 9.15
1
2n2
ww,0
Fracture
Dimensions
9
 3.98
n
2n2
1  2.14n 


n


n
2n2
K
1
2n2
 qi h1f n x f


E'

n




1
2n2
Power Law fluid
K: Consistency (lbf/ft2)·sn
n: Flow behavior index
Material balance +Width Equation
Vf = w(hf x f )
Vf = w A
2qi
Vi = qi te
xf
Vfe = Vi - Vlost
Average
w(xf)
qi
hf
Fracture
Dimensions
10
A
Lost: spurt +leakoff
Pumping time, fluid volume, proppant
schedule: Design of frac treatments
Pumping time and fluid volume:
Injected = contained in frac + lost
length 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-possibleproppant-added-conc
Fracture
Dimensions
11
Pumping time, slurry volume (1 wing)
1 Calculate the wellbore width at the end of pumping from the
PKN (Power Law version)
ww, 0 = 9.15
1
2n2
 3.98
n
2n2
1  2.14n 


n


n
2n2
K
1
2n2
 q h xf 



E ' 

n 1 n
i
f
1
2n2
2 Convert max wellbore width into average width
we  0.628ww,0
3 Assume a k = 1. 5 and solve the mat balance for inj time,
(selecting sqrt time as the new unknown)
 qi

h x
 f f
4 Calculate injected volume
Fracture
Dimensions
12
5 Calculate fluid efficiency

 t  2κ C


L

t  (we  2S p )  0
Vi  qite
V
h x w
e = fe  f f e
Vi
Vi
Nolte’s power law proppant schedule:
1
e
x
 dx 
C/C e
1
0
y
=xe
Area  (1  f pad )
fpad
0
Fracture
Dimensions
13
1
e
1
1
1 e
Nolte's proposition:
select fpad=e
slurry
0
1
1 e
x
1
1
V/Vi
Area 
1 e
1 e
M  ce  Vi
1 e
M  ce  Vi 
1 e
Proppant schedule calculation
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
1  e
e
1  e
Vpad  eVi
t pad  ete
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
Fracture
Dimensions
14
clean fluid” (mass/clean-fluid-volume)
M
eVi
 t  t pad
c  ce 
t t
 e pad
cadded 




c
1
c
 propp
e
Gross and Net Height
2qi
Vi = qi te
Vfe = Vi - Vlost
2D design: hf is given
A
hf
hp
Fracture
Dimensions
15
rp= hp /hf
Lost: spurt +leakoff
Ex_2: Frac Design
Pay: 45 ft
Gross: 67.5 ft
(Gross = hf)
Proppant mass (2wing) = 100,000 lbm is available
2/3 will go to pay layer
Slurry injection rate (2qi) = 30 bpm
Created fracture height is 67.5 ft
E' = 2.08 106 psi
Power Law rheology:
K' = 0.022 lbf/(ft2 sec0.63) and n' = 0.63
Leakoff coefficient (w.r.t. perm zone) CL,p = 0.003 ft/min1/2
Spurt loss is negligible
Fracture
Dimensions
16
Blender can do max 12 ppga
Fracture
Dimensions
17
Proppant mass for (two wings), lbm
Sp grav of proppant material (water=1)
Porosity of proppant pack
Proppant pack permeability, md
Formation permeability, md
Permeable (leakoff, net) thickness, ft
Well Radius, ft
Well drainage radius, ft
Pre-treatment skin factor
Fracture height, ft
Plane strain modulus, E’ , psi
Slurry injection rate (2 wings, liq+prop), bpm
Rheology, K' (lbf/ft2)×sn'
Rheology, n'
Leakoff coefficient in perm layer, ft/min0.5 0.003
Spurt loss coefficient, Sp, gal/ft2
100,000
2.65
0.35
60,000
0.5
45
0.328
3000
0
67.5
2.08×106
30
0.0220
0.63
0
Ex_2 Proppant placement efficiency is 66.7%
The fracture height is 1.5 times the pay layer thickness,
therefore approximately 66,700 lbm proppant will be
placed into the pay (2 wings).
The mass of proppant in one wing will be 50,000 lbm
from which 33,300 lbm will be in the pay layer.
Fracture
Dimensions
18
Ex_2 Modified Target
Proppant mass placed (2 wing), lb
Proppant in pay, (2 wing) lb
Proppant number, Np
Dimensionless PI, JDact
Dimensionless fracture cond, CfD
Half length, xf, ft
Propped width, wp, inch
Post treatment pseudo skin factor, sf
Folds of increase of PI
Fracture
Dimensions
19
100,000
66,700
0.117
0.48
1.6
718
0.115
-6.3
4.0
Ex_2 Input in Consistent Units (SI)
n'  0.63
K '  1.053 Pa  s0.63
M1w, pay  33,333lbm  15,120 kg
E'  2.08106 psi  1.4361010 Pa
M1w  50,000lbm  22,680kg
hp  45 ft  13.72 m
h f  67.5 ft  20.57 m
rp  0.6667
x f  718ft  219m
 0.00264979m3 /s 
3
qi  15 bpm  
  0.03975m /s
l bpm


CL , p
Fracture
Dimensions
20
 0.0393495m/s0.5 
ft
4
0.5
 0.003


1
.
18

10
m/s


min0.5 
l ft/min0.5

Ex_2 Modified (Apparent) Leakoff Coefficient
is 2/3-rd of CL,p
The fracture height is 1.5 times the pay layer
The apparent leakoff coefficient will be only
CL = 0.667 CLp = 0.787×10-4 m/s0.5
Fracture
Dimensions
21
Ex_2 Pumping time, slurry volume (1 wing)
1 Calculate the wellbore width at the end of pumping from the
PKN (Power Law version)
ww, 0 = 9.15
1
2n2
 3.98
n
2n2
1  2.14n 


n


n
2n2
K
1
2n2
 q h xf 




E
'


ww,0 = 0.0102m  0.402in.
2 Convert max wellbore width into average width
we  0.628ww,0
we = 0.0064m  0.252in.
Fracture
Dimensions
22
n 1 n
i
f
1
2n2
Ex_2 Pumping time, slurry volume (cont’d)
3 Assume a k = 1. 5 and solve the mat balance for inj time,
 qi

 hf xf

 t  (2  1.5 CL) t  (w e )  0

x t
The positive root of the quadratic equation is
x = 43.4 s0.5 therefore the injection time is te = 43.42 s
= 31.4 min.
4 Once the injection time is known, calculate the
injected slurry volume (1 wing)
Vi  qi  t e  75.0 m3  2,649ft3  19,810gallon
Fracture
Dimensions
23
Ex_2 Efficiency
Volume of 1 wing at end of pumping:
Vfe  x f  hf  we  28.8 m
3
5 Fluid efficiency:
e 
Fracture
Dimensions
24
V fe
Vi
 0.385  38.5 %
Ex_2 Proppant concentration at end of pumping
M1w 22,680 kg
kg
lbm
ce 

 788 3  49 3
3
Vfe
28.8m
m
ft
This concentration is mass proppant per volume of
slurry.
We want this to be the proppant concentration
everywhere in the fracture at the end of pumping.
This should be the proppant concentration in the last
injected slurry stage.
Fracture
Dimensions
25
In terms of added proppant to clean liquid this is
1133 kg added to 1 m3 clean liquid, 70.8 lbm added to
1 ft3 clean fluid that is 9.3 ppga (lbm proppant added
to 1 gallon clean fluid)
Ex_2 Proppant schedule
Nolte exponent e 
Pad
Propp
concentration
1  e 1  0.385

 0.445
1  e 1  0.385
Vpad  eVi  0.445 75.0 m3  82.8 m3
t pad  e  te  0.445 31.5 min  14.0 min
 t  t pad
c  ce 
t t
 e pad




e
 t

 14.0 

kg

 788 3   min
m  31.5  14.0 




0.445
This is kg proppant in 1 m3 of slurry
Convert it “propp-added-to-clean”
Fracture
Dimensions
26
cadded 
c
1
c
 propp
Ex_2 Stages at end of pumping (after PWC)
9 6 to 9 lb/gal
lb/gal
3 to 9 lb/gal
Fracture
Dimensions
27
2 to
9 lb/gal
Proppant
Settling
1 lb/gal
concentrated
to 9 lb/gal
t
Liq_rate (2w) Cum_liq Propp Cum Propp
min
bpm
gal
ppga
lbm
0.00
30.00
0
0.00
0
Fracture
Dimensions
28
14.16
14.94
15.73
16.51
17.30
18.09
18.87
19.66
20.45
21.23
22.02
22.81
23.59
24.38
25.17
25.95
26.74
27.52
28.31
29.10
29.88
30.67
31.46
30.00
28.06
27.15
26.50
25.98
25.53
25.13
24.77
24.44
24.13
23.84
23.56
23.30
23.05
22.82
22.59
22.37
22.16
21.95
21.75
21.56
21.37
21.19
17836
18763
19660
20535
21393
22236
23066
23884
24692
25489
26276
27054
27824
28585
29339
30085
30824
31556
32281
33000
33712
34418
35118
0.00
1.53
2.33
2.92
3.42
3.87
4.28
4.67
5.03
5.38
5.72
6.04
6.36
6.66
6.96
7.26
7.54
7.83
8.11
8.38
8.66
8.93
9.19
0
1,416
3,501
6,057
8,994
12,260
15,816
19,637
23,700
27,990
32,491
37,193
42,085
47,158
52,405
57,818
63,392
69,121
74,999
81,023
87,188
93,490
99,925
xf
wave
ft
inch
0.0 0.000
434.9
450.1
465.0
479.6
493.9
507.9
521.7
535.3
548.7
561.8
574.8
587.5
600.1
612.6
624.8
636.9
648.9
660.7
672.4
683.9
695.3
706.6
717.8
0.216
0.219
0.221
0.223
0.225
0.227
0.229
0.231
0.232
0.234
0.236
0.237
0.239
0.240
0.242
0.243
0.245
0.246
0.247
0.249
0.250
0.251
0.252
Ex_2 Proppant Roadmap
35
10
9
25
7
6
20
5
15
4
3
10
2
5
1
0
0
0
10
20
Pumping time, min
Fracture
Dimensions
29
30
40
gallon liquid
8
ca, lbm prop added to
Liquid injection rate, bpm
30
Stages
Stage design (Injected fluid and proppant amount and rate, for two wings)
Stage
Pad
Fracture
Dimensions
30
Start
End
min
min
0
21.9
Stage
Added
Proppant
Concentr
ppga
0
1
1
2
2
3
3
4
5
5
7
6
9
Stage
Slurry
Volume
gallon
Stage
Proppant
Mass
Cum
Liq
Cum
Propp
gallon
lbm
lbm
0
150,000
Design Outcome
Constraints allow optimum placement of
the given amount of proppant
Some improvement is necessary
Consider higher quality proppant
Better fluid loss control
Better rheology
Larger allowable proppant concentration
Fracture
Dimensions
31
Optimum placement is not possible with
traditional method: consider tip screenout
design
Additional Concerns During Design
Fracture
Dimensions
32
Tip Screenout vs. Near-well Screenout
Screenout in the near-wellbore region:
Proppant cannot enter to the main body of
the fracture (oftentimes in Austin chalk)
Screenout at tip: Length control
Two concepts:
Enough width for a single proppant
Enough width for the actual number of proppant
grains
Fracture
Dimensions
33
Width to accept proppant
At the end of pad stage the created width
has to be at least 2-3 times the proppant
diameter
At the end of pumping the proppant
reaches only that part which has a width at
least 2-3 times the proppant diameter
Propped length less than hydraulic length
Fracture
Dimensions
34
Width ratio criterion
Considering material coordinate,
Accounting for fluid loss
Calculate ratio of (Dry width) to (Dynamic
width)
Criterion: cannot exceed critical value
(about 0.5)
Fracture
Dimensions
35
Net Pressure Prediction (PKN)
 Net pressure is proportional to width
 Width from width equation (PKN)
 Convert it to pn
 Basic uses:
E'
pn 
ww,0
2h f
 Feedback to height containment
 Hydraulic horsepower calculation
Fracture
Dimensions
36
Hydraulic Horsepower
Energy: (Power)  (Time)
Power = (Pumping Pressure) (Injection rate)
(Pumping Pressure) =
Minimum Stress + Net Pressure + Friction Losses Hydrostatic Pressure
Friction Losses : in tubulars, through perforations
and possibly in near wellbore tortuous flow path
Fracture
Dimensions
37
On-site Tuning of Design
During Job Execution
Fracture
Dimensions
38
Main Tasks During Execution
Fracture
Dimensions
39
 Zonal Isolation, Cement Integrity
 Perforation strategy
 Pumping through tubing, casing, both
 Safety considerations: wellhead, casing, tubing
 Formation breakdown and Step rate test
 Calibration test (Minifrac)
 Pad and Proppant schedule tuning
 Pumping
 Monitoring: Tip screenout - near-well/well screenout
 Flush
 Forced closure
 Cleanup
Perforation and Execution Strategy
For thin layer: Perforate the whole interval
For thick or multilayer formation
Danger: non uniform coverage
Solution: Ball sealers, Limited entry or Staged
 Limited entry
Few perforations in small groups
High perforation friction loss
Uniform coverage
Fracture
Dimensions
40
Staged (from bottom to top)
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
Dimensions
41
Introducing…
HF2DPKN
Fracture
Dimensions
42
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
Fracture
Dimensions
43
 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.
Input Parameters cont'd




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.
Fracture
Dimensions
44
Input Parameters cont'd
 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
Fracture
Dimensions
45
 The spurt loss in the permeable layer. Outside the
permeable layer the spurt loss is considered zero. See the
Input Parameters, cont'd
 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, Cont Damage Mech, etc.)
Fracture
Dimensions
46
Summary
 Keep in mind the goals
 Allocate resources according to significance
 Realize need for compromise:
 Limited data
 Limited understanding of physics
 Sensitivity to the uncertainty in data
 Find the optimum complexity of model
 Do sensitivity analysis
 Make decisions top - down
Fracture
Dimensions
47
Computer Exercise 2-1: Medium perm
design example
Fracture
Dimensions
48
Computer Exercise 2-2: Tight gas
design example
Fracture
Dimensions
49
Computer Exercise 2-3: High perm
Frac&pack example
Fracture
Dimensions
50