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Dynamic Data Analysis – v5.12.01 - © KAPPA 1988-2017
Chapte
r 4 – R ate Transient Analysis (RTA)- p131/743
In the above figure the left region of the curves (green to blue) corresponds to the transient
part of the response. On the right hand side, are the Arps decline curves (red to yellow). Note
the legend on the left: the red Arps curve is for an exponential decline (b=0), the last yellow
curve is for a harmonic decline (b=1).
The Fetkovich type-curve displays dimensionless values q
Dd
, Q
Dd
versus t
Dd
as defined below.
The dimensionless variables can be expressed in terms of the Arps decline curve parameters,
or in terms of the transient response parameters. The duality is due to the composite nature of
the type-curve showing once again a merge of a theoretical closed reservoir response, and the
empirical Arps stems.
All the following equations are in Oil Field Units.
Time
Decline curve dimensionless time:
t
D t
Dd
i
Dimensionless time:
t
rc
k
t
wt
D
2
0002637
.0
Related by:
t
t
r
r
r
r
Dd
D
e
w
e
w
1
2
1
1
2
2
ln
Rate
Decline curve dimensionless rate:
q
q t
q
Dd
i
Dimensionless flow rate, oil:
q oil
q t B
kh p p
D
i
w
1412.
And the equivalent expression for gas is:
q gas
Tq t p
T kh m p m p
D
sc
sc
i
w
50300
; with
m p
pdp
Z
p
( )
2
0
q
Dd
and
q
D
are related by:
q q
r
rw
Dd
D
e
ln
1
2
Cumulative production
Decline curve dimensionless cumulative:
Q
Q t
Npi
Dd
Where N
pi
defines the ultimate recovery.