Fracture Design Hydraulic Fracturing Hydraulic Fracturing Short Course, Short Course, Texas A&M University Texas A&M University College Station College Station 2005 2005 Fracture Design Fracture Design Fracture Dimensions Fracture Dimensions Fracture Modeling Fracture Modeling Peter P. Valkó Peter P. Valkó
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2Source: Economides and Nolte: Reservoir Stimulation 3rd Ed.
FractureDesign
3
Frac Design Goals
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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
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Hydraulic Fracturing Design and Evaluation
Why do we create a propped fracture?
How do we achieve our goals?
Data gathering
Design
Execution
Evaluation
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Fractured Well Performance
Relation of morphology to performance
Streamline view
Flow regimes, Productivity Index, Pseudo-
steady state Productivity Index, skin and
equivalent wellbore radius
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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
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Principle of least resistance
Horizontal fracture Vertical fracture
Least Principal Stress Least Principal Stress
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Mismatch (Choked fracture)
Typical mismatch situations:
Horizontal well with a transverse vertical
fracture
Vertical well intersecting a horizontal
fracture
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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
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Longitudinal Vertical Fracture -Horizontal well
H,maxxf
H,min
H,min
Can it be done?
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Transverse Vertical Fractures - Horizontal Well
H,maxHydraulic Fracture
H,maxD
xf
H,min
Radial converging flow in frac
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Fracture Morphologysource: Economides at al.: Petroleum Well Construction
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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?
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Prod Eng 101
Transient vs Pseudo-steady state
Productivity Index
Skin
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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
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Hawkins formula
w
s
s r
r
k
ks ln1
skk
wrsrDamage
penetration distance
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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
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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
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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
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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
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Fully penetrating vertical fracture: Relating Performance to Dimensions
wp
2xf
h2Vfp
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Dimensionless fracture conductivity
Dimensionless fracture conductivity
f
ffD kx
wkC
2 xf
w
fracture conductivity
no name
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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
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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
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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