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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
PETR 4314
Nodal AnalysisM. Y. Soliman, PhD, PE, NAI
Lecture 5 - The Near-Wellbore Condition; Skin Effects
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Sources of Damage
Drilling
Completion
Production
Injection
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture
5
The Near Well Condition
Damage Characterization
Skin Effects
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Zone of Altered Permeability
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Hawkins formula
w
s
s rr
kks ln1
sk
k
wr
srDamagepenetration
distance
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Hawkins Formula
w
sidealwfs
r
r
kh
qpp ln
2,
w
s
s
idealwfsr
r
hk
qpp ln
2,
w
s
w
s
s r
r
kh
q
r
r
hk
qs
kh
qln
2ln
22
w
s
s r
r
k
ks ln1
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Example 6-1
rw=0.328 ft
Penetration damage = 3ft
What is the skin ifk/ks=5 and 10.
Ifk/ks= 10. What would be the required
penetration damage to provide the same
skin effect as the latter case withk/ks=5?0.328
3.328
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Example 6-1
w
s
s rr
kks ln1
27.9328.0
328.3ln15
s
85.20328.0
328.3ln110
s
0
5
10
15
20
25
0 1 2 3 4
Penetration of Damage, ft
Skin
K/Ks=2
K/Ks=5
K/Ks=10
ftr
er
r
r
s
s
s
s
60
328.0
21.5328.0
ln
328.0ln1585.20
21.5
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Example 6-1
w
s
s r
r
k
ks ln1
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7
skin
permeability of damaged area
Effect of permeability damage
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Example 6-1
w
s
s r
r
k
ks ln1
What is the dominant term in the above equation?
How high can skin get? When?
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Example 6-2
With same skin effects calculated Ex. 6-1,
compare portion of pressure drop due to
damage within the near-wellbore zone vs.
the total pressure drop. AssumeA=640
acres (re=2980 ft)
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Example 6-2
skh
qBpskin 2.141
s
r
r
kh
qBp
w
etotal ln2.141
sr
r
s
sr
r
kh
qB
skh
qB
p
p
w
e
w
etotal
skin
lnln2.141
2.141
504.0
27.9328.0
2980ln
27.9
total
skin
p
p
696.0
85.20328.0
2980ln
85.20
total
skin
p
p
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 5 10 15 20 25
skin
da
magepressuredropasfractionof
totalpressuredrop
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
Pressure Drop in the Near-Wellbore Zone versus in
the Reservoir
ln
ln
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Example 6-3 Skin Factor for Concentric Radial
Damage Zones
ln
ln ln lnp f f
p w f p w
r r rk ks
k r k r r
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Skin Components
pseudopcd sssss
skinEffectivetodueSkinSkin
typermeabiliinchangeactual
damage p.p. &
slant
perfs Rate and phase dependenttotal
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture
5
Skin Components
Non-Darcy Skin
Dqss
Skin due to evolution of gas or condensate
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Field Determination of Non-Darcy Skin
Dqss Which test do you use
to get this graph?
Well Completed Openhole in The Top of The Reservoir
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Skin from Partial Completion and Slant
Papers to read
Cinco, Ramey, and Miller, SPE 5589
Papatzacos, SPERE, SPE 13956, May 1987
Kuchuk and Kirwan, SPE 11676
Besson, SPE 20965
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Equation for Partial Penetration Skin
h
hh
k
k
z
rr
hhh
)/h/(hB)/h/(hA
B
A
h
h
hrh
s
D
H
v
w
wD
wwD
wDDwDD
wD
wD
wDDwD
p
11
2/1
11
2/1
/
431and41
where
1
1
2
ln1
2
ln11
From Papatzacos, SPERE, SPE 13956, May 1987
h
zw
hw
h1
Calculate skin using this equation
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Equation for Partial Penetration Skin
From Papatzacos, SPERE, SPE 13956, May 1987
Effect of vertical permeability
Effect of vertical permeability on skin factor
10
12
14
16
18
20
22
24
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
permeability anistropy, kv/kh
Skin
factor
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Equation for Partial Penetration Skin(Kuchuk and Kirwan - SPE11676)
8204SPERamey,andGringartenbycomputed
point,pressureaveragetheis
log003745.0log05499.009069.0
cossin12
*
2*
*
1
D
wDwDD
v
h
w
wD
w
w
oD
n
pp
z
hhz
k
k
r
hh
h
hb
Dh
bnKbznbn
nbS
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
30
25
20
10
15
5
00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Penetration Ratio; b
P
artialPenetrationSkin;pp
hwD= 50
hwD= 100hwD= 250
hwD= 500
hwD= 1000
hwD= 2500
hwD= 5000
hwD= 10000
Equation for Partial Penetration Skin
(Kuchuk and Kirwan, SPE11676)
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5Deviated Well Skin Effect for Isotropic and
Anisotropic Reservoirs (Besson)
= ln 4cos + cos ln 4 cos = ln 1
4 cos + cos ln211
4cos
= 12 co21 12
is angle from vertical
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
History of perforation
Bullet Guns
Shaped charges
Explosives
Primary detonators
Secondary -
30,000 ft/sec
2-5 million psi
Jet tip is up to 15 million psi
Hydrajetting
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Perforation Skin Effect
Perforating Gun
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
The Perforation Process
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Shaped-Charge Perforator
Explosive
Liner
Case
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Events in Perforation Cleanup
Cement
Jet
Crushed Sandstone
Undamaged Sandstone, k
Debris
Crushed Zone, kpd
Berea SandstoneCasing
Conical LinerExplosive
Shaped Charge
Explosion
After
Perforating,
Before Flow
After Flow
A
B
C
D
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Schematic of Sources of Damage Around Wellbore and Perforation
Cement
Casing
Charge and Core Debris
Pulveration Zone
Grain Fracturing Zone
Compacted
Zone
Undamaged
Permeability k
Wellbore Damaged
Permeability k d
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Deep-Penetrating (DP) Charge(1 of 5)
A
Formation
t = 0
Casing
Fluid Gap
Carrier
Conical Liner
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Deep-Penetrating (DP) Charge(2 of 5)
B
Liner Collapsesto Form Jet
t = 6 x 10-6t = 6 x 10-6 secsec
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Deep-Penetrating (DP) Charge(3 of 5)
C
Jet PenetratesCarrier
Later Stages of LinerCollapse Produce
Slower-Moving Slug
t = 9 x 10-6
sec
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Deep-Penetrating (DP) Charge(4 of 5)
Jet
Slug
t = 1.1 x 10-5
sec
DD
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Deep-Penetrating (DP) Charge(5 of 5)
E
Stretching Jet
Penetrates
Formation
t = 2 x 10-5
sec
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Deep-Penetrating Charges (DP)
Liner geometry isconical; a long, thin, stretching jet is
formed.
Penetration is relatively deep and the hole diameter is small.
Peak collapse pressure at the centerline reaches
approximately29 million psi.
Jet tip velocity can be as high as 26,000 ft/s.
20% of the liner forms the fast-moving jet; the
remaining 80% constitutes a slower-moving slug.
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Big-Hole (BH) Charge(1 of 5)
AA
Formation
t = 0
Casing
Fluid Gap
Carrier
Parabolic Liner
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Big-Hole (BH) Charge(2 of 5)
BB
Liner CollapseLiner Collapse
and Inversionand Inversion
t = 1 x 10t = 1 x 10-5
secsec
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Big-Hole (BH) Charge(3 of 5)
CC
Relatively
Slow-Moving Jet
Concentration
of Material
t = 1.5 x 10-5
sec
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Big-Hole (BH) Charge(4 of 5)
t = 2.3 x 10-5
sec
Jet
Expansion
Slug
Slowly
StretchingJet
D
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Big-Hole (BH) Charge(5 of 5)
E
Large Hole
in Casing
Small Holein Carrier
t = 5 x 10-5
sec
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Big-Hole Charges (BH)
Liner geometry isparabolic or hemispherical; a massive,
slower-moving jet is formed. Penetration is relatively shallow, but a large entrance hole is
created in the casing.
Jet tip velocities are around 13 to 20,000 ft/s.
The jet represents 60 to 80% of the liner mass; the
remaining 20 to 40% constitute the slug.
The annular gap between gun and casing is especially
important for jet development with BH charges, thusgun
centralization isrecommended.
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Perforations Created using shaped charges
TCP or wireline
Skin factor / well productivity depends on:
Number of perforations
Length and diameter of the perforations
Phase angle (distribution)
Underbalance, overbalance or extreme overbalance
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Types of Perforation
Underbalanced
Balanced Slightly Overbalanced
Extreme Overbalance Perforation
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Underbalanced PerforatingUnderbalanced Perforating
Perforating with the pressure in the wellbore lower
than formation pressure.
At the instant of perforating, the pressure differential
causes fluid to flow, which helps clear the tunnel wall
from crushed rock, debris, and explosive gases.
The amount of underbalance required depends upon
the formation fluid type and reservoir permeability.
Higher underbalance is required in gas wells.
A few hundred psi may be sufficient for high-
permeability formations such as Berea. Optimized underbalance is necessary to avoid formation
collapse or stuck pipe.
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Formation Permeability vs. Minimum Underbalance (Oil Zone)
Total Underbalance, psi
100
1000
100
10
1
0.1
0.01
1000 10,000
Acid d id not imp rov e pro duc tion
Acid d id i mpr ove p roduc tion
FormationPermeability,md
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Formation Permeability vs. Minimum Underbalance (Gas Zone)
100
1000
Total Underbalance, psi
100
10
1
0.1
0.01
1000 10,000
Acid Did Not Im prove Produ ct ionAcid Did Improve Produc tion
Problems
Stuck
Packer
Casing
Collapse
Fo
rmationPermeability,md
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Extreme Over-Balance
A near-wellbore stimulation technique in whichtubing is pressurized to high overbalance levelsusing compressible gases, usually Nitrogen (over asmall pad of liquid).
Stored energy in gas is released upon the perforatingevent, resulting in a formation fracture.
This methods used to bypass, rather than remove,perforation tunnel damage.
Creates short fractures during the perforation process
Propellant has been also used
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Gas and/or Liquid Pumping
Compressed Gas
in Wellbore
TCP Gun
Liquid or Gas over
Perforation Interval
Pay Zone
Damaged Zone
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Overbalance Pressure vs. Depth
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
1,000 3,000 5,000 7,000 9,000 11,000 13,000 15,000
Depth, ft
OverbalancePressure
Applied,pbh-
pres,psi
OverbalancePressureApplied,pbh
-pres,psi
Excess Overbalance Pressure vs. Depth
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Applied Wellbore Pressure Gradient vs. Depth
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
1,000 3,000 5,000 7,000 9,000 11,000 13,000 15,000
Depth, ft
AppliedPressureGradient,pbh
/D
,psi/f
AppliedPressureGradient,pbh
/D,psi/ft
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Perforation Skin Variables
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD,
PE, NAI - Lecture 5
Effect of Shot Density and Perforation Length on Productivity Ratio
ProductivityRatio
Perforation Length ( in)
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0 3 6 9 12 15
12-in. Wellbore
Diameter 0.4-in. Perf.
Diameter
No Crushed Zone
No Damaged Zone
No Turbulence
SPF
16
8
4
SPF
16
8
4
90Phasing
0 Phasing
Open Hole
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Effect of Perforation Diameters and Length on Production Ratio
ProductivityRatio
Perforation Length ( in)
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0 3 6 9 12 15
4 SPF
No Crushed Zone
No Damaged ZoneNo Turbulence
Perf. Diameter
0.55 in.
0.40 in.
0.15 in.
90Phasing
0Phasing
Perf. Diameter
0.55 in.
0.40 in.
0.15 in.
18
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Effect of Wellbore Damage on Productivity Ratio
ProductivityRatio
Perforation Depth, inches
0
No PerforationDamage
Shots Per
Foot
8
4
2
1.2
1.0
0.8
0.6
0.4
0.2
0
2 4 6 8 10 12 14 16 18
8 Inch Deep Drilling
kDamage With = 0.2
kdd
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Perforation Skin Components
wbVHp ssss
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Calculation of SH
)(ln
w
wH
r
rs
perf
perf
4
lra
l
r
w
w
for 0
for 0
Usually negative why?
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Calculation of SV
V
H
perf
perf
Dk
k
l
hh
H
V
perf
perf
Dk
k
h
rr 1
2
b
D
b
D
a
V rhs110
21 log araa D 21 brbb D
SPFhperf
1
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Calculation of Swb
wperf
wwD
rl
rr
wDrc
wb ecs2
1
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Near Well Damage and Perforations
ss
wwss
perfperf
wperfppppdsperf
sperfp
s
dp
w
s
s
pd
rk
krrr
k
kll
rlssssrl
rlsk
kss
r
r
k
ks
1and1
:andatevaluatediswhere,)(,For
for)(ln1)( 0
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Discussion Topics
Effect of perforation length and diameter
Effect of SPF
Effect of phasing
Production
Fracturing
Effect of vertical permeability
Effect of centralization
Deep penetration or big hole?
Common Well Completion
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Horizontal Well Damage
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Horizontal Skin Effect
1
3
4
1
1ln1
max,
2
2
max,
w
H
w
H
anis
eqr
a
r
a
Ik
ks
v
hani
k
kI
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Damaged Permeability
vHkkk
svsHs kkk ,,
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Skin Effect and Well Performance Comparison with an
Undamaged Vertical Well
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Horizontal Well Skin Effect Damage Penetration and
Severity of Damage
Why does it take a
significant damage to
seriously affect HW
performance?
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Hydrajetting
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PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
7/23/2019 PETR 4314 L05
38/39
PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
Bernoulli's equation
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
02 2
sc
f
cc
dWDg
dLuf
g
ududz
g
gdp
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39/39
PETR 4314 Fall 2015
M. Y. Soliman, PhD, PE, NAI
Lecture 5What does Hydrajetting do?
After creating a cavity; jet pump principle is applied
Jet creates a small vacuum pulling fluid into the cavity Applying momentum and mass balance equations one may
calculate the increase in pressure as fluid mix.
PETR 4314 Fall 2015, M. Y. Soliman, PhD, PE, NAI - Lecture 5
exitentry pAAQpAAQ
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