127 / 743
Dynamic Data Analysis – v5.12.01 - © KAPPA 1988-2017
Chapte
r 4 – R ate Transient Analysis (RTA)- p127/743
4.B
The old stuff
4.B.1
Arps
Decline Curve Analysis methods, as formalized by Arps in 1945, have been for many years the
conventional technique for analysis and forecasting of well production data. Decline type-
curves are based on an empirical rate-time and associated cumulative-time equation, which
can be expressed in the general form:
q t
q
bD t
i
i
b
1
1
Q t
q
D b
q q t
i
b
i
i
b
b
(
) 1
1
1
where:
q
i
is the initial rate,
D
i
is the decline factor, and
b
a parameter varying between 0 and
1, defining the decline type. Three types are usually considered: hyperbolic, exponential and
harmonic.
Exponential decline,
b
0
It can be shown that the general decline equation tends to an exponential decline when b
tends to 0:
q t
q e
i
D t
i
Q t
q q t
D
i
i
Harmonic decline,
b
1
q t
q
D t
i
i
1
Q t
q
D
q
q t
i
i
i
ln
Hyperbolic decline,
b
0 1,
The expressions are those above.
Decline curve equations are applicable only after the transient part of the response has
ceased, i.e. during boundary dominated flow. A general approach consists in the determination
of the three parameters directly, by non-linear regression. The traditional usage however, is
centered on the use of some specific presentations where linearity is sought after the value of
b has been fixed. Practically, the following scales / linearity can be used:
log( )
q vs t
:
Linear plot if the decline is exponential, concave upward otherwise.
q vs Q
:
Linear plot if the decline is exponential, concave upward otherwise.
log( )
q vs Q
:
Linear plot if the decline is harmonic, concave downward otherwise.