Water Technology and Sciences - November - December, 2014 - page 126

124
Aragón-Aguilar
et al.
,
Comparison of Methodologies to Analyze Decline in the Productivity of Wells
Water
Technology and Sciences.
Vol. V, No. 6, November-December, 2014
(1945) and Fetkovich (1980). Based on this
curve, the properties of the deposit (
kh
/
m
,
f
c
t
h
) are determined using the known
equation for radial diffusion (Faulder,
1996):
kh
μ
=
141.2
B
q
p
q
Dd
ajuste
ln
r
e
r
wa
0.75
(11)
where
k
is the permeability,
h
is the
thickness of the formation, μ is the viscosity
of the fluid,
r
e
is the radial drainage of the
well,
r
wa
is the apparent radius of the well,
q
/
D
p
and
q
Dd
are obtained according to the
fit point of the comparison of the plot of
t
verses
D
p
with the type curve. Storage is
obtained using:
c
t
h
=
0.00633
t kh
μ
0.5
t
Dd
r
wa
2
r
e
r
wa
2
1 ln
r
e
r
wa
0.75
(12)
Where
c
t
is the compressibility of the
formation;
t
and
t
Dd
are determined based
on the fit point of the comparison of the
plot of
t
verses
D
p
with the type curve.
Flow normalization is another method
used to analyze decline in production
(Sanyal, Menzies, Brown, Enedy, & Enedy,
1989). This method is useful to identify
wells that need to be repaired, among
other applications. The method anticipates
the lack of data related to static pressure
and/or flow, which are often not obtained
since a) static pressures are only measured
occasionally when wells are disconnected
from the production system and b) the
head pressure does not remain constant.
The relation between production flow
(
W
) and head pressure (
p
f
) under flow
conditions was developed based on the
empirical equation adapted for gas wells
(Williamson, 1990):
W
=
C p
2
p
f
2
(
)
n
(13)
where
p
is the head pressure under static
conditions;
p
f
is the head pressure under
flow conditions; and
n
is an empirical
parameter often known as the turbulence
factor and ranges from 0.5 to 1. The value
of
C
under initial conditions is determined
by:
C
i
=
W
i
p
i
2
p
fi
2
(
)
n
(14)
At any moment during the productive
life of the well, the above equation can be
used to determine the static pressure (
p
):
p
=
W
C
1
n
+
p
f
2
(15)
This value makes it possible to
continually monitor the behavior of
the well. A well’s production data are
associated with its different opening
diameters, which causes variations in head
pressure, making it difficult to identify a
true trend in the decline of productivity. To
calculate the normalized flow in function
of the changes in the pressure (
p
f
) generated
in a well, Sanyal
et al
. (1989) proposed the
equation:
W
n
=
p
2
p
std
2
(
)
n
p
2
p
f
2
(
)
n
W
(16)
where
W
n
is the normalized production
flow and
p
std
is the standard wellhead
pressure, which is the head pressure at the
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