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PET 325
James A.
Craig
Omega 2011
PERFORATION
TABLE OF CONTENTS
 Introduction
 Shaped Charged Perforation
 Explosives
 Perforating Guns
 Perforation Efficiency & Gun Performance
 Well/Reservoir Characteristics
 Calculations
 References
INTRODUCTION
 Objective of perforation is to establish
communication between the wellbore & the
formation.
 This is achieved by making holes through the
casing, cement & into formation.
 The inflow capacity of the reservoir must not
be inhibited.
 Well productivity & injectivity depend
primarily on near-wellbore pressure drop
called Skin.
 Skin is a function of:
 Completion type
 Formation damage
 Perforation
 Skin is high & productivity reduced when:
 Formation damage is severe (drilling &
completion fluids invasion ranges from several
inches to a few feet)
 Perforations do not extend beyond the invaded
 Deep penetration:
 Increases effective wellbore radius
 Intersects more natural fractures if present
 Prevents/reduces sand production by reducing
pressure drop across perforated intervals.
 High-strength formations & damaged
reservoirs benefit the most from deep-
penetrating perforations.
SHAPED CHARGED PERFORATION
 The shaped charge evolved from the WW2
military bazooka.
 Perforating charges consist of:
 A primer
 Outer case
 High explosive
 Conical liner connected to a detonating cord.
 The detonating cord initiates the primer &
detonates the main explosive
 The liner collapses to form the high-velocity
jet of fluidized metal particles that are
propelled along the charge axis through the
well casing & cement & into the formation.
 The detonator is triggered by:
 Electrical heating when deployed on wireline
systems or,
 A firing pin in mechanically or hydraulically
operated firing head systems employed on
tubing conveyed perforating (TCP) systems
 The jet penetrating mechanism is one of
“punching” rather than blasting, burning,
drilling or abrasive wearing.
 This punching effect is achieved by
extremely high impact pressures –
 3 x 106 psi on casing
 3 x 105 psi on formation.
 These jet impact pressures cause steel,
cement, rock, & pore fluids to flow plastically
outward.
0 μsec
4 μsec
9.4
μsec
16.6 μsec
 Elastic rebound leaves shock-damaged rock,
pulverized formation grains & debris in the
newly created perforation tunnels.
 Hence, perforating damage can consist of
three elements:
 A crushed zone
 Migration of fine formation particles
 Debris inside perforation tunnels.
 The crushed zone can limit both productivity
& injectivity.
 Fines and debris restrict injectivity & increase
pump pressure, which:
 Decreases injection volumes
 Impairs placement or distribution of gravel &
proppants for sand control or hydraulic fracture
treatments.
 The extent of perforation damage is a
function of:
 Lithology
 Rock strength
 Porosity
 Pore fluid compressibility
 Clay content
 Formation grain size
 Shaped-charge designs
EXPLOSIVES
 Explosives used in perforation are called
Secondary high explosives.
 Reaction rate = 22,966 – 30,000 ft/s.
 Volume of gas produced = 750 – 1,000 times
original volume of explosive.
 These explosives are generally organic
compounds of nitrogen & oxygen.
 When a detonator initiates the breaking of
the molecules' atomic bonds, the atoms of
nitrogen lock together with much stronger
bonds, releasing tremendous amounts of
 Typical explosives are:
 RDX (Cyclotrimethylene trinitramine)
 HMX (Cyclotrimethylene tetranitramine)
 HNS (Hexanitrostilbene)
 PYX Bis(Picrylamino)-3,5-dinitropyridine
 PS (Picryl sulfone)
 Composition B (60% RDX, 40% trinitrotoluene)
Explosive
Chemical
Formula
Densit
y
(g/cc)
Detonatio
n Velocity
(ft/sec)
Detonatio
n
Pressure
(psi)
RDX Cyclotrimethylene trinitramine
C3H6N6O6 1.80 28,700 5,000,000
HMX Cyclotrimethylene tetranitramine
C4H8N8O8 1.90 30,000 5,700,000
HNS Hexanitrostilbene
C14H6N6O12 1.74 24,300 3,500,000
PYX Bis(picrylamino)-3,5-
dinitropyridine C17H7N11O16 1.77 24,900 3,700,000
 RDX is the most commonly used explosives
for shaped charges (up to 300 oF).
 In deep wells when extreme temperature is
required & where the guns are exposed to
well temperatures for longer periods of time
HMX, PS, HNS or PYX is used.
 It is important to respect the explosives used
in perforating operations.
 They are hazardous.
 Accidents can occur if they are not handled
carefully or if proper procedures are not
followed.
PERFORATING GUNS
 Perforating guns are configured in several
ways.
 There are four main types of perforating
guns:
 Wireline conveyed casing guns
 Through-tubing hollow carrier guns
 Through-tubing strip guns
 Tubing conveyed perforating guns
Wireline Conveyed Casing Guns
Generally run in the
well before
installing the tubing.
 The advantages of casing guns over the
other wireline guns are:
 High charge performance
 Low cost
 Highest temperature & pressure rating
 High mechanical & electrical reliability
 Minimal debris & minimal casing damage
 Instant shot detection
 Multi-phasing
 Variable shot densities of 1 – 12 spf
 Speed & accurate positioning using
CCL/Gamma Ray
Through-tubing Hollow Carrier Guns
Smaller versions of
casing guns which
can be run through
tubing.
 They have lower charge sizes &, therefore
lower performance, than all other guns.
 They only offer 0o or 180o phasing
 Maximum shot density of 4 spf on the 2-1/8”
OD gun & 6 spf on the 2-7/8” OD gun.
 Due to the stand-off from the casing which
these guns may have, they are usually fitted
with decentralizing/orientation devices.
Through-tubing Strip Guns
Semi-expendable
type guns
consisting of a
metal strip into
which the charges
are mounted.
 Charges have higher performance.
 They also cause more debris, casing
damage & have less mechanical & electrical
reliability.
 They also provide 0o or 180o phasing.
 By being able to be run through the tubing,
underbalance perforating can possibly be
adopted but only for the first shot.
 A new version called the Pivot Gun has
even larger charges for deep penetration.
A Pivot
gun
system
Tubing Conveyed Perforating Guns (TCP)
TCP guns are a
variant of the
casing gun which
can be run on
tubing.
 Longer lengths can be installed.
 Lengths of over 1,000 ft are possible
(especially useful for horizontal wells).
 The main problems associated with TCP are:
 Gun positioning is more difficult.
 The sump needs to be drilled deeper to
accommodate the gun length if it is dropped after
firing.
 A misfire is extremely expensive.
 Shot detection is more unreliable.
PERFORATION EFFICIENCY &
GUN PERFORMANCE
 Optimizing perforating efficiency relies
extensively on the planning & execution of
the well completion which includes:
 Selection of the perforated interval
 Fluid selection
 Gun selection
 Applied pressure differential
 Well clean-up
 Perforating orientation
 API RP 19B, 1st Edition (Recommended
Practices for Evaluation of Well Perforators)
provide means for evaluating perforating
systems (multiple shot) in four ways:
 Performance under ambient temperature &
atmospheric pressure test conditions.
 Performance in stressed Berea sandstone
targets (simulated wellbore pressure test
conditions).
 How performance may be changed after
exposure to elevated temperature conditions.
 Flow performance of a perforation under specific
stressed test conditions
 Factors affecting gun performance include:
 Compressive strengths & porosities of
formations.
 Type of charges used (size, shape).
 Charge alignment.
 Moisture contamination.
 Gun stand-off.
 Thickness of casing & cement.
 Multiple casings.
 It is necessary for engineers to obtain as
much accurate data from the suppliers & use
the company’s historic data in order to be
able to make the best choice of gun.
 Due to the problem of flow restriction, the
important factors to be considered include:
 Hole diameter to achieve adequate flow area.
 Shot density to achieve adequate flow area.
 Shot phasing, Penetration, Debris removal.
Hole Size
 The hole size obtained is a function of the
casing grade & should be as follows:
 Between 6 mm & 12 mm for natural completions.
 Between 15 mm & 25 mm in gravel packed
completions.
 Between 8 mm & 12 mm if fracturing is to be
carried out & where ball sealers are to be used.
Shot Density
 Shot density is the number of holes specified
in shots per foot (spf).
 An adequate shot density can reduce
perforation skin & produce wells at lower
pressure differentials.
 Shot density in homogeneous, isotropic
formations should be a minimum of 8 spf but
must exceed the frequency of shale
laminations.
 A shot density greater than this is required
where:
 Vertical permeability is low.
 There is a risk of sand production.
 There is a risk of high velocities & hence
turbulence.
 A gravel pack is to be conducted.
 Note: Too many holes can weaken the
casing strength.
Shot Phasing
 Phasing is the radial distribution of
successive perforating charges around the
gun axis.
 Simply put, phasing is perforation orientation
or the angle between holes.
 Perforating gun assemblies are commonly
available in 0o, 180o, 120o, 90o & 60o
phasing.
Carrier gun
arrangement
 The 0o phasing (all shots are along the same
side of the casing) is generally used only in
small outside-diameter guns.
 60o, 90o & 120o degree phase guns are
generally larger & provide more efficient flow
characteristics near the wellbore.
 Optimized phasing reduces pressure drop
near the wellbore by providing flow conduits
on all sides of the casing.
 Providing the stand-off is less than 50mm,
180o or less, 120o, 90o, 60o is preferable.
 If the smallest charges are being used then
the stand-off should not be more than 25mm.
 If fracturing is to be carried out then 90o and
lower will help initiate fractures.
Effect of
centralizatio
n
Penetration
 In general, the deeper the shot the better, but
at the least it should exceed the drilling
damage area by 75mm.
 However, to obtain high shot density, the
guns may be limited to the charge size which
can physically be installed which will impact
penetration.
WELL/RESERVOIR CHARACTERISTICS
 Pressure differential between a wellbore and
reservoir before perforating can be described
by:
 Underbalanced
 Overbalanced
 Extreme overbalanced (EOB)
Underbalanced Perforating
 Reservoir pressure is substantially higher
than the wellbore pressure.
 Adequate reservoir pressure must exist to
displace the fluids from within the production
tubing if the well is to flow unaided.
 If the reservoir pressure is insufficient to
achieve this, measures must be taken to
lighten the fluid column typically by gas lifting
or circulating a less dense fluid.
 The flow rates & pressures used to exercise
control during the clean up period are
intended to maximize the return of drilling or
completion fluids & debris.
 This controlled backflush of perforating
debris or filtrate also enables surface
production facilities to reach stable
conditions gradually.
 Standard differential pressure ≈ 200 – 400
psi.
 Differential pressures up to 5,000 psi in low
Overbalanced Perforating
 Perforating when the wellbore pressure is
higher than the reservoir pressure.
 This is normally used as a method of well
control during perforating.
 The problem with this method is it introduces
wellbore fluid into the formation causing
formation damage.
 Use clean fluid to prevent perforation
plugging.
 Use of acid in carbonates.
Extreme Overbalanced Perforating
 The wellbore is pressured up to very high
pressures with gas (usually nitrogen).
 When the perforating guns are detonated the
inflow of high pressure gas into the formation
results in a mini-frac, opening up the
formation to increase inflow.
CALCULATIONS
 A mechanism to account for the effects of
perforations on well performance is through
the introduction of the perforation skin effect,
sp in the well production equation.
 For example, under steady-state conditions:
 
141.2 ln
e wf
e
p
w
kh P P
q
r
B s
r



  
  
  
 Karakas and Tariq (1988) have presented a
semi-analytical solution for the calculation of
the perforation skin effect, which they divide
into components:
 The plane-flow effect, sH
 The vertical converging effect, sV
 The wellbore effect, swb
 The total perforation skin effect is then:
p H V wbs s s s  
The Plane-flow Effect
 rw = wellbore radius (ft).
 r’w(θ) = effective wellbore radius (ft). It is a
function of the phasing angle θ.
 lperf = length of perforation (ft)
 
ln w
H
w
r
s
r 
 
    
 
 
for 0
4
for 0
perf
w
o w perf
l
r
a r l





  
  
 Constant ao depends on the perforation
phasing.
a1a2a1b2b1c2c
The Vertical Converging Effect
1
10a b b
V D Ds h r

 1 2log Da a r a  1 2Db b r b 
1
2
perf V
D
perf H
r k
r
h k
 
   
 
1
shot density
perfh 
perf H
D
perf V
h k
h
l k

 a1, a2, b1 & b2 are obtained from the table
above.
 kH = horizontal permeability
 kV = vertical permeability
 rperf = radius of perforation (ft)
 sV is potentially the largest contributor to sp.
The Wellbore Effect
 c1 & c2 are obtained from the table above.
 1 2expwb wDs c c r 
 
w
wD
perf w
r
r
l r


REFERENCES
 Gatlin, C.: “Drilling Well Completion,”
Prentice-Hall Inc., New Jersey, 1960.
 ENI S.p.A. Agip Division: “Completion Design
Manual,” 1999.
 Halliburton: “Petroleum Well Construction,”
1997.
 Ott, W. K. and Woods, J. D.: “Modern
Sandface Completion Practices Handbook,”
1st Ed., World Oil Magazine, 2003.
 Schlumberger: “Completions Primer,” 2001.
 Golan, M. and Whitson, C. H.: “Well
Performance,” 2nd Ed., Tapir, 1995.
 Karakas, M. and Tariq, S.: “Semi-Analytical
Productivity Models for Perforated
Completions,” paper SPE 18271, 1988.
 Clegg, J. D.: “Production Operations
Engineering,” Petroleum Engineering
Handbook, Vol. IV, SPE, 2007.
 Bellarby, J.: “Well Completion Design,” 1st
Ed., Elsevier B.V., 2009.

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Petroleum Production Engineering - Perforation

  • 1. PET 325 James A. Craig Omega 2011 PERFORATION
  • 2.
  • 3. TABLE OF CONTENTS  Introduction  Shaped Charged Perforation  Explosives  Perforating Guns  Perforation Efficiency & Gun Performance  Well/Reservoir Characteristics  Calculations  References
  • 4. INTRODUCTION  Objective of perforation is to establish communication between the wellbore & the formation.  This is achieved by making holes through the casing, cement & into formation.  The inflow capacity of the reservoir must not be inhibited.
  • 5.  Well productivity & injectivity depend primarily on near-wellbore pressure drop called Skin.  Skin is a function of:  Completion type  Formation damage  Perforation  Skin is high & productivity reduced when:  Formation damage is severe (drilling & completion fluids invasion ranges from several inches to a few feet)  Perforations do not extend beyond the invaded
  • 6.
  • 7.  Deep penetration:  Increases effective wellbore radius  Intersects more natural fractures if present  Prevents/reduces sand production by reducing pressure drop across perforated intervals.  High-strength formations & damaged reservoirs benefit the most from deep- penetrating perforations.
  • 8. SHAPED CHARGED PERFORATION  The shaped charge evolved from the WW2 military bazooka.  Perforating charges consist of:  A primer  Outer case  High explosive  Conical liner connected to a detonating cord.
  • 9.  The detonating cord initiates the primer & detonates the main explosive  The liner collapses to form the high-velocity jet of fluidized metal particles that are propelled along the charge axis through the well casing & cement & into the formation.
  • 10.  The detonator is triggered by:  Electrical heating when deployed on wireline systems or,  A firing pin in mechanically or hydraulically operated firing head systems employed on tubing conveyed perforating (TCP) systems
  • 11.
  • 12.  The jet penetrating mechanism is one of “punching” rather than blasting, burning, drilling or abrasive wearing.  This punching effect is achieved by extremely high impact pressures –  3 x 106 psi on casing  3 x 105 psi on formation.  These jet impact pressures cause steel, cement, rock, & pore fluids to flow plastically outward.
  • 15.
  • 16.  Elastic rebound leaves shock-damaged rock, pulverized formation grains & debris in the newly created perforation tunnels.  Hence, perforating damage can consist of three elements:  A crushed zone  Migration of fine formation particles  Debris inside perforation tunnels.
  • 17.
  • 18.
  • 19.  The crushed zone can limit both productivity & injectivity.  Fines and debris restrict injectivity & increase pump pressure, which:  Decreases injection volumes  Impairs placement or distribution of gravel & proppants for sand control or hydraulic fracture treatments.
  • 20.  The extent of perforation damage is a function of:  Lithology  Rock strength  Porosity  Pore fluid compressibility  Clay content  Formation grain size  Shaped-charge designs
  • 21. EXPLOSIVES  Explosives used in perforation are called Secondary high explosives.  Reaction rate = 22,966 – 30,000 ft/s.  Volume of gas produced = 750 – 1,000 times original volume of explosive.  These explosives are generally organic compounds of nitrogen & oxygen.  When a detonator initiates the breaking of the molecules' atomic bonds, the atoms of nitrogen lock together with much stronger bonds, releasing tremendous amounts of
  • 22.  Typical explosives are:  RDX (Cyclotrimethylene trinitramine)  HMX (Cyclotrimethylene tetranitramine)  HNS (Hexanitrostilbene)  PYX Bis(Picrylamino)-3,5-dinitropyridine  PS (Picryl sulfone)  Composition B (60% RDX, 40% trinitrotoluene)
  • 23. Explosive Chemical Formula Densit y (g/cc) Detonatio n Velocity (ft/sec) Detonatio n Pressure (psi) RDX Cyclotrimethylene trinitramine C3H6N6O6 1.80 28,700 5,000,000 HMX Cyclotrimethylene tetranitramine C4H8N8O8 1.90 30,000 5,700,000 HNS Hexanitrostilbene C14H6N6O12 1.74 24,300 3,500,000 PYX Bis(picrylamino)-3,5- dinitropyridine C17H7N11O16 1.77 24,900 3,700,000
  • 24.  RDX is the most commonly used explosives for shaped charges (up to 300 oF).  In deep wells when extreme temperature is required & where the guns are exposed to well temperatures for longer periods of time HMX, PS, HNS or PYX is used.
  • 25.  It is important to respect the explosives used in perforating operations.  They are hazardous.  Accidents can occur if they are not handled carefully or if proper procedures are not followed.
  • 26. PERFORATING GUNS  Perforating guns are configured in several ways.  There are four main types of perforating guns:  Wireline conveyed casing guns  Through-tubing hollow carrier guns  Through-tubing strip guns  Tubing conveyed perforating guns
  • 27. Wireline Conveyed Casing Guns Generally run in the well before installing the tubing.
  • 28.  The advantages of casing guns over the other wireline guns are:  High charge performance  Low cost  Highest temperature & pressure rating  High mechanical & electrical reliability  Minimal debris & minimal casing damage  Instant shot detection  Multi-phasing  Variable shot densities of 1 – 12 spf  Speed & accurate positioning using CCL/Gamma Ray
  • 29. Through-tubing Hollow Carrier Guns Smaller versions of casing guns which can be run through tubing.
  • 30.  They have lower charge sizes &, therefore lower performance, than all other guns.  They only offer 0o or 180o phasing  Maximum shot density of 4 spf on the 2-1/8” OD gun & 6 spf on the 2-7/8” OD gun.  Due to the stand-off from the casing which these guns may have, they are usually fitted with decentralizing/orientation devices.
  • 31. Through-tubing Strip Guns Semi-expendable type guns consisting of a metal strip into which the charges are mounted.
  • 32.  Charges have higher performance.  They also cause more debris, casing damage & have less mechanical & electrical reliability.  They also provide 0o or 180o phasing.  By being able to be run through the tubing, underbalance perforating can possibly be adopted but only for the first shot.  A new version called the Pivot Gun has even larger charges for deep penetration.
  • 34. Tubing Conveyed Perforating Guns (TCP) TCP guns are a variant of the casing gun which can be run on tubing.
  • 35.  Longer lengths can be installed.  Lengths of over 1,000 ft are possible (especially useful for horizontal wells).  The main problems associated with TCP are:  Gun positioning is more difficult.  The sump needs to be drilled deeper to accommodate the gun length if it is dropped after firing.  A misfire is extremely expensive.  Shot detection is more unreliable.
  • 36. PERFORATION EFFICIENCY & GUN PERFORMANCE  Optimizing perforating efficiency relies extensively on the planning & execution of the well completion which includes:  Selection of the perforated interval  Fluid selection  Gun selection  Applied pressure differential  Well clean-up  Perforating orientation
  • 37.  API RP 19B, 1st Edition (Recommended Practices for Evaluation of Well Perforators) provide means for evaluating perforating systems (multiple shot) in four ways:  Performance under ambient temperature & atmospheric pressure test conditions.  Performance in stressed Berea sandstone targets (simulated wellbore pressure test conditions).  How performance may be changed after exposure to elevated temperature conditions.  Flow performance of a perforation under specific stressed test conditions
  • 38.  Factors affecting gun performance include:  Compressive strengths & porosities of formations.  Type of charges used (size, shape).  Charge alignment.  Moisture contamination.  Gun stand-off.  Thickness of casing & cement.  Multiple casings.
  • 39.  It is necessary for engineers to obtain as much accurate data from the suppliers & use the company’s historic data in order to be able to make the best choice of gun.  Due to the problem of flow restriction, the important factors to be considered include:  Hole diameter to achieve adequate flow area.  Shot density to achieve adequate flow area.  Shot phasing, Penetration, Debris removal.
  • 40.
  • 41. Hole Size  The hole size obtained is a function of the casing grade & should be as follows:  Between 6 mm & 12 mm for natural completions.  Between 15 mm & 25 mm in gravel packed completions.  Between 8 mm & 12 mm if fracturing is to be carried out & where ball sealers are to be used.
  • 42. Shot Density  Shot density is the number of holes specified in shots per foot (spf).  An adequate shot density can reduce perforation skin & produce wells at lower pressure differentials.  Shot density in homogeneous, isotropic formations should be a minimum of 8 spf but must exceed the frequency of shale laminations.
  • 43.  A shot density greater than this is required where:  Vertical permeability is low.  There is a risk of sand production.  There is a risk of high velocities & hence turbulence.  A gravel pack is to be conducted.  Note: Too many holes can weaken the casing strength.
  • 44. Shot Phasing  Phasing is the radial distribution of successive perforating charges around the gun axis.  Simply put, phasing is perforation orientation or the angle between holes.  Perforating gun assemblies are commonly available in 0o, 180o, 120o, 90o & 60o phasing.
  • 46.
  • 47.  The 0o phasing (all shots are along the same side of the casing) is generally used only in small outside-diameter guns.  60o, 90o & 120o degree phase guns are generally larger & provide more efficient flow characteristics near the wellbore.  Optimized phasing reduces pressure drop near the wellbore by providing flow conduits on all sides of the casing.
  • 48.  Providing the stand-off is less than 50mm, 180o or less, 120o, 90o, 60o is preferable.  If the smallest charges are being used then the stand-off should not be more than 25mm.  If fracturing is to be carried out then 90o and lower will help initiate fractures.
  • 50. Penetration  In general, the deeper the shot the better, but at the least it should exceed the drilling damage area by 75mm.  However, to obtain high shot density, the guns may be limited to the charge size which can physically be installed which will impact penetration.
  • 51. WELL/RESERVOIR CHARACTERISTICS  Pressure differential between a wellbore and reservoir before perforating can be described by:  Underbalanced  Overbalanced  Extreme overbalanced (EOB)
  • 52. Underbalanced Perforating  Reservoir pressure is substantially higher than the wellbore pressure.  Adequate reservoir pressure must exist to displace the fluids from within the production tubing if the well is to flow unaided.  If the reservoir pressure is insufficient to achieve this, measures must be taken to lighten the fluid column typically by gas lifting or circulating a less dense fluid.
  • 53.  The flow rates & pressures used to exercise control during the clean up period are intended to maximize the return of drilling or completion fluids & debris.  This controlled backflush of perforating debris or filtrate also enables surface production facilities to reach stable conditions gradually.  Standard differential pressure ≈ 200 – 400 psi.  Differential pressures up to 5,000 psi in low
  • 54.
  • 55. Overbalanced Perforating  Perforating when the wellbore pressure is higher than the reservoir pressure.  This is normally used as a method of well control during perforating.  The problem with this method is it introduces wellbore fluid into the formation causing formation damage.  Use clean fluid to prevent perforation plugging.  Use of acid in carbonates.
  • 56.
  • 57.
  • 58. Extreme Overbalanced Perforating  The wellbore is pressured up to very high pressures with gas (usually nitrogen).  When the perforating guns are detonated the inflow of high pressure gas into the formation results in a mini-frac, opening up the formation to increase inflow.
  • 59. CALCULATIONS  A mechanism to account for the effects of perforations on well performance is through the introduction of the perforation skin effect, sp in the well production equation.  For example, under steady-state conditions:   141.2 ln e wf e p w kh P P q r B s r            
  • 60.  Karakas and Tariq (1988) have presented a semi-analytical solution for the calculation of the perforation skin effect, which they divide into components:  The plane-flow effect, sH  The vertical converging effect, sV  The wellbore effect, swb  The total perforation skin effect is then: p H V wbs s s s  
  • 61. The Plane-flow Effect  rw = wellbore radius (ft).  r’w(θ) = effective wellbore radius (ft). It is a function of the phasing angle θ.  lperf = length of perforation (ft)   ln w H w r s r             for 0 4 for 0 perf w o w perf l r a r l           
  • 62.  Constant ao depends on the perforation phasing. a1a2a1b2b1c2c
  • 63. The Vertical Converging Effect 1 10a b b V D Ds h r   1 2log Da a r a  1 2Db b r b  1 2 perf V D perf H r k r h k         1 shot density perfh  perf H D perf V h k h l k 
  • 64.  a1, a2, b1 & b2 are obtained from the table above.  kH = horizontal permeability  kV = vertical permeability  rperf = radius of perforation (ft)  sV is potentially the largest contributor to sp.
  • 65. The Wellbore Effect  c1 & c2 are obtained from the table above.  1 2expwb wDs c c r    w wD perf w r r l r  
  • 66.
  • 67. REFERENCES  Gatlin, C.: “Drilling Well Completion,” Prentice-Hall Inc., New Jersey, 1960.  ENI S.p.A. Agip Division: “Completion Design Manual,” 1999.  Halliburton: “Petroleum Well Construction,” 1997.  Ott, W. K. and Woods, J. D.: “Modern Sandface Completion Practices Handbook,” 1st Ed., World Oil Magazine, 2003.
  • 68.  Schlumberger: “Completions Primer,” 2001.  Golan, M. and Whitson, C. H.: “Well Performance,” 2nd Ed., Tapir, 1995.  Karakas, M. and Tariq, S.: “Semi-Analytical Productivity Models for Perforated Completions,” paper SPE 18271, 1988.  Clegg, J. D.: “Production Operations Engineering,” Petroleum Engineering Handbook, Vol. IV, SPE, 2007.  Bellarby, J.: “Well Completion Design,” 1st Ed., Elsevier B.V., 2009.