Page 203 - Introduction to Petroleum Engineering

190 WELL COMPLETIONS
Before perforating a well, petroleum engineers are responsible for several design
decisions. They first need to determine what zone or zones will be perforated. That
decision depends on results from mud and open‐hole logs plus experience in neigh-
boring wells. They must also consider perforation hole size and length of penetration,
number of shots per foot, angular phasing (e.g., 30, 60, 90, or 180°) between adjacent
shots in the spiral of charges mounted in the gun, and gun length. Service companies
have fired charges and measured penetration length and hole diameter for many rock
samples. Service company personnel can provide support for estimating penetration
length and hole diameter for a specific formation with its unique mechanical
properties.
In 1997, Brooks published a method for predicting productivity of a perforated
vertical well as a function of perforation penetration length L , perforation tunnel
p
diameter d , formation damage length L , number of shots per foot n, the ratio of
d
p
horizontal to vertical permeability k /k , and the skin s of the perforations. Just a
v
p
h
portion of that method is described here. Brooks proposed a dimensionless
description of perforations N :
pd
N
N pd = pd1 (10.8)
N pd2
with
p (
L − ) 32 12
/
/
L nd
N = d p (10.9)
pd1 k ( k ) 58
/
h / v
p (
11+
=
N pd2 ( s + )    s + 1)    (10.10)
p
 N pd1 
Brooks concluded that N pd ≥ 100 is an efficiently perforated well. For N pd < 100,
efficiency of the perforation design can be increased by increasing penetration length
and shot density. For N pd < 10, the perforation design is very inefficient. Brooks’
correlation for dimensionless productivity efficiency N is
pe
− (
038
.
.
N = 0971 exp − ( 057 N pd )) (10.11)
.
pe
This correlation is shown in Figure 10.1. Use of Brooks’ method is demonstrated in
the following examples.
Example 10.3 Brooks’ Dimensionless Perforation Description, N
pd
Calculate N for the following values: perforation penetration length
pd
L = 16 in.; perforation tunnel diameter d = 04 in.; formation damage length
.
p
p
L = 5 in.; number of shots per foot n = 4 shots/ft; the ratio of horizontal to
d
vertical permeability k k = 5; and the perforation tunnel skin s = 5.
/
h v p