Lecture 6b:

Perforation

Shahid Bahonar University of Kerman

Faculty of Engineering
Department of Petroleum Engineering

Saeid Norouzi
sna.teaching@gmail.com

Semester 2, 1398
1
Industry Testing Procedure for Performance Evaluation of Shape
Charges

API RP43 is applied for depth of penetration and flow efficiency

Section 1: Penetration depth test

The inner casing simulates

the oil well casing and the
concrete between the two
concentric casings is the
target material.

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Procedure:
The concrete target material must be cured for 28 days and must develop a
compressive strength of 4,000psi (which corresponds to 400 psi tensile
strength). A regular gun containing 6 to 8 shots is placed on one side of the
inner casing with zero clearance. Several shots are fired.

Upon completion of firing the concrete is sectioned to determine the

entrance hole diameter and the depth of penetration. 3
Section 2: Laboratory Flow Efficiency Test
Deals with flow test on Berea Sandstone as a target material
The objective of this test is to show that the material can expel the debris
resulting from the penetration process and is able to clean up when
production (backflow) is resumed.

BEREA SANDSTONE
STAINLESS STEEL
CANISTER

ESTABLISH:
1500-PSI WELL
PRESSURE
(9.6 PPG SALT WATER)

CEMENT

SALT WATER
PERFORATE & INFILTER: 1000 PSI
1500-PSI WELL PRESSURE CORE PRESSURE

DP = 500 PSI

BACKFLOW TO STABILIZATION:
1000-PSI WELL PRESSURE 1200 PSI
CORE PRESSURE
(KEROSENE FLOW)

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DP = 200 PSI
Procedure:
• A Berea sandstone core is cemented in a steel container which has the
porosity between 17% to 22% and effective permeability between 150mD
and 300mD.

• The compressive strength of the Berea sandstone should, on an average,

be 6000psi.

• The length of the Berea sandstone should be such that, 5 inches of

unpenetrated sandstone must be remained.

• Prior to the perforation, and after perforation - kerosene is flowed at a

differential pressure of 200psi until a stable flow rate is achieved.

• Then the core flow efficiency is determined according to Darcy’s liner flow
equation.

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 Lo
BEREA CORE
HASSLER UNIT
DETERMINE ORIGINAL ko:

Q om o L o
ko =
A o DPo
AREA , Ao
Qo KEROSENE VISCOSITY mo
CALCULATE PERFORATION
kP FROM TEST:
Q Pm P L P
kP = DPo
A o DPP

CALCULATE CORE FLOW

EFFICIENCY: CORE OF CROSS SECTIONAL AREA
k k k "A" MOUNTED IN CANNISTER,
CFE = P o = P QP
PERFORATED AND KEROSENE
ki ko ki FLOWED, VISCOSITY mP

ki/ko REPRESENTS THE RATIO OF THE EFFECTIVE

PERMEABILITY OF A TARGET CONTAINING AN IDEAL DP = 200 PSI
(DRILLED) PERFORATION (OF THE SAME DEPTH &
DIAMETER AS THE PERFORATED ONE) TO THE ORIGINAL
TARGET PERMEABILITY ko

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Certificate for individual shot record on 3 '' shaped charge 7
Other Perforation Techniques
 bullet perforator,
 hydraulic jet perforator and
 mechanical cutter.

Bullet Perforator
• Bullet guns were the technique of choice until the jet (shaped charge)
perforator was developed in the 1950’s.
• Most bullet guns were manufactured 3 1/4 inch outside diameter or larger
and were effective in penetrating materials with 600 psi compressive
strength and lower.
• Muzzle velocity of the bullet gun could reach up to 4000 ft/sec. It looses
its velocity and energy when the clearance increases. At zero gun
clearance, it is 15% more efficient than that with 0.5 inch clearance (Allen
and Roberts, 1989).

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 (A) (B)
SOFT ROCK HARD ROCK
CASING

CEMENT

GUN GUN

INWARD BULGING JUST

ABOVE AND BELOW
PERFORATION

Typical bullet gun perforator

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Hydraulic jet perforator

• It has been found that the hole

size and the flow efficiency of the
perforation has been greater than
a jet (shaped charge) perforator.

• When pumping rate and

pressure, which is required to
create significant number of holes
per foot, hydraulic jet perforator
has been proven ineffective over
jet (shaped charge) perforator.

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Mechanical cutter

• The application of mechanical

cutters has been limited to
the initiation of horizontal
fractures or other specific
operations.

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 Calculation of Pressure Losses in Perforation Tunnels
Most calculations of pressure loss are based on single phase gas or liquid
flow. Two methods of calculating the pressure loss in perforations were
proposed by:

• McLeod (1983) and

• Karakas and Tariq (1988).

McLeod’s method
McLeod treated an individual perforation tunnel as a miniature well with a
compacted zone of reduced permeability around the tunnel.

The compacted zone is believed to be created as a result of the impact of the

shaped charge jet on the formation. For permeability in the compact zone,
McLeod suggested the permeability was:
 10% of the formation permeability, if perforated overbalanced
 40% of the formation permeability, if perforated underbalanced.
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A cross section of McLeod’s perforation flow model is presented in here. The
thickness of the crushed zone is assumed to be 0.5 in. The massive
reservoir rock surrounding a well perforation tunnel renders it feasible to
assume a model of an infinite reservoir surrounding the well of the
perforation tunnel.

Flow into a perforation after McLeod, 1983. 13

 Oil Well Gas Well

p wfs  p wf = aq o2  bq o p 2wfs  p 2wf = aq g2  bq g

1 1
2.30  10 14
B o    
2
o r r 
a=  p c
L2p
Note!
 rc  qo and qg are oil or gas
m o Bo  ln 
 r  flow rate per perforation
 p 
b=
7.08  10 3 L p k p

2.33  1010
o =
k 1p.201
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HW 2:

Sensitivity study of Oil Well Perforations using McLeod’s Method

Make a completions sensitivity study for the following well undergoing
underbalanced perforation:

k = 20 md, 𝑃𝑅 = 3000 psia re = 2000 ft h = 25 ft

hp = 20 ft rp = 0.021 ft Lp = 0.883 ft γg = 0.65
rc = 0.063 ft rw = 0.365 ft APIo = 35º
Bo = 1.2 RB/STB μo = 1 cp

1. Calculate the pressure loss through perforations for shot densities 2, 4,

8, 12, 20 and 24 in the flow rate range from 100 to 1200 STB/day (100,
200, 400, 800, 1200).
2. Plot completion sensitivities q vs. Δp.

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Karakas and Tariq method
McLeod’s method gives fair estimates of pressure loss through perforations.
However the model is not very sophisticated and does not consider effects
such as phasing and spiral distribution of the perforations around the
wellbore.

Karakas and Tariq presented a semi-analytical solution to the complex

problem of three dimensional flow into a spiral system of perforations around
the wellbore. These solutions are presented for two cases:
 A two dimensional flow problem valid for small dimensionless perforation
spacings (large perforation penetration or high shot density). The vertical
component of flow into perforations is neglected.
 A three dimensional flow problem around the perforation tunnel, valid in
low shot density perforations (below 6 shots/feet).

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Karakas and Tariq presented the perforation pressure losses in terms of
pseudoskin. This enabled the modifications of IPR curves to include the
effect of perforations on well performance as follows:

For steady state flow into a perforated well,

2kh( p R  p wf )
Qo =
  re  
mB ln   S t 
  rw  

Where St= total skin factor including pseudoskin due to perforation (obtained
from well test)
k = formation permeability
h = net thickness of formation

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For total skin
S t = S p  S dp

Where Sp= perforation skin factor

Sdp= damage skin factor

The damaged skin factor, Sdp, is the treatable skin component in a

perforated completion. The perforation skin, Sp, is a function of the
perforation phase angle θ, the perforation tunnel length lp, the perforation
shot density ns and the wellbore radius rw. The following dimensionless
parameters are used to correlate the different components of the perforation
skin:

Dimensionless Perforation Height,

h kh
hD = h = 1 / SPF
lp kv
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Dimensionless Perforation Radius,
rp  kv 
r pD = 1  
2h  kh 


Dimensionless Well Radius, rw

rwD =
rw  l p

The calculation of perforation skin is essential to estimate the damage skin.

Karakas and Tariq characterized the perforation skin as:

S p = S h  S wb  S v

Where,
Sh= pseudo skin due to phase (horizontal) effects
Swb= pseudo skin due to wellbore effects (dominant in zero degree phasing)
Sv= pseudo skin due to vertical converging flow effects (negligible in the
case of high shot density; 3D effect)
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  rw 
S h = ln 
 rwe ( ) 

Where rwe(θ) is the effective wellbore radius as a function of phasing

angle (θ) and perforation tunnel length (lp).

rwe ( ) = 0.251l p if θ = 0

rwe ( ) =  rw  l p  Otherwise

 can be obtained using Table 5.2.

Table. 5.2: Values for effective wellbore radius at a given phasing angle.
Perforation Phasing 
180 0.5
120 0.648
90 0.726
60 0.813
45 0.86
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The pseudo skin due to the wellbore can be calculated using the
following empirical relationship:

S wb ( ) = C1   expC2  rwD 

If rwD < 0.5 the wellbore effect can be considered negligible for phasing
smaller than 120o.

Table. 5.3: Values for variable C1 and C1 at a given phasing angle.

Perforation Phasing C1 C2
0 (360) 1.60E+01 2.675
180 2.60E-02 4.532
120 6.60E-03 5.32
90 1.90E-03 6.155
60 3.00E-04 7.509
45 4.60E-05 8.791

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It is interesting to note, that for high-shot density and unidirectional
perforations or where Sv is negligible, the perforation skin is independent of
the perforation hole diameter.

Karakas and Tariq (1988) suggested that for a low-shot density or high
dimensionless perforation height, hD, the pseudovertical skin, Sv can be
estimated with the following equation:

S v = 10 a hDb 1 rpD
b

where the coefficients a and b are given by:

a = a1 logr pD   a 2

b = b1 r pD   b2

The constants a1 a1, a2, b1 and b2 may be determined from Table 5.4.
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Table. 5.4: Values for variable a1, a2, b1 and b2 at a given phasing angle.

Perforation
Phasing a1 a2 b1 b2
0 (360) -2.091 0.0453 5.313 1.8672
180 -2.025 0.0943 3.0373 1.8115
120 -2.018 0.0634 1.6136 1.777
90 -1.905 0.1038 1.5674 1.6935
60 -1.898 0.1023 1.3654 1.649
45 -1.788 0.2398 1.1915 1.6392

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 Example - Pseudoskin calculations
Given
lp = 1.25 ft
rw = 0.5 ft
ns = 16

1. Calculate the perforation pseudoskin for 0o phasing.

2. If this well is tested and the total skin calculated from buildup is 4
what is the treatable skin?

Solution:
S p = S h  S wb ( Sv is negligible for 16 shots per foot)

rwe = 0.25  1.25 = 0.31

 r  rw 0.5
S h = ln w  = .466 rwD = = = 0.29
rw  l p 0.5  1.25
 rwe 
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From Table 5.3 C1 = 0.16 C2 = 2.675

S wb = 0.16  exp2.675  0.29  = 0.34

S p = 0.466  0.34 = 0.81

For S t = 4

S t = 4 = S p  S dp

S dp = 4  0.81 = 3.19

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Crushed Zone Effect
For conditions of linear flow into perforations, the effect of a crushed
or compacted zone may be neglected. In the case of 3D flow, an
additional skin due to the crushed zone may be calculated as
follows:

k   rc 
=
h
  1  ln
l k  r 
Sc
p c   p

Where the crushed zone permeability and radius (kc and rc )are
calculated using McLeod’s method.

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For perforations extending beyond the damaged zone - Karakas and Tariq
contended, the total skin equals the pseudoskin due to perforations. That is,

St = S p for l p  ld

The pseudoskin due to perforation is calculated using modified lp and

modified rw as follows:

 kd 
l = l p  1  l d
'
p
 k 

 k 
rw' = rw  1  d l d
 k 

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Type of perforating fluid
• Type of fluid in the wellbore has great influence on perforation
clean-up (Allen and Worzel, 1956).

• Severe reduction in effective permeability due to high differential

pressure which caused by mud invasion.

• Maximum perforation effectiveness can be accomplished only

when compatible fluids are used. A compatible fluid is the one
which is solid free and non reactive to rock matrix and formation
fluids. Acceptable fluids may include:
• 5 to 10% HCl
• 10% acetic acid
• 2% (or more) KCl water
• 2% NH4Cl water
• Clean brines
• Filtered diesel
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Charge Penetration

Depth of penetration as the most important factor in well

deliverability ?
Field results often contradict this!

In reports of small through-tubing guns provided, better production

results obtained compared to larger ones - when the small guns
(shooting one-third to one-half as deep) are fired with differential
pressure toward the wellbore.

This would suggest that well completion conditions are of equal or

even greater importance than penetration in terms of achieving best
well deliverability.

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 Fig. A - Perforation ratio vs. penetration depths for
various shot densities, after Haris,1966..

The Productivity Ratio is defined as the ratio of productivity of ideal

perforations through casing to that of the uncased hole.

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Some important notes from Fig. A are as follows:
1. Four perforations per foot, 5'' to 6'' deep, would yield the same
theoretical flow capacity as the uncased hole.
2. Evidently, the first few inches of penetration are quite important. But
note that beyond about 6'', (Qp/Qr)ss increases only 10% to 12'' of
depth.
3. In terms of capacity of the well to produce, shot density would
appear to be of greater importance than penetration depth. Note
that four perforations per foot, 2'' deep, offer a (Qp/Qr)ss significantly
greater than one perforation per foot with a perforation depth of 12''.

The above would tend to de-emphasize the importance of perforation

depth. However, the data neglects wellbore and perforation damage.
Basically, the objective is to penetrate at least 5'' to 6'' beyond the region
of reduced permeability, when shooting at four shots per foot. Further, the
reduced perforation efficiency resulting from the compacted zone
provides a lower flow rate, which can be compensated by increased
penetration.

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