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Dynamic Data Analysis – v5.12.01 - © KAPPA 1988-2017
Chapte
r 4 – R ate Transient Analysis (RTA)- p129/743
Exponential decline is widely used because of the simplicity of the associated graphical
methods. It leads to conservative reserves estimates. Besides, it can be demonstrated that
exponential decline is the late time behavior of a constant pressure production in a closed
reservoir, with a slightly compressible fluid assumption.
The equation governing the PSS behaviour is:
bq mQ p
With
w i
p p p
Q
= cumulative production
q
: instantaneous production rate
and
t
Nc
m
1
Differentiating the two terms of the equation with respect to the time:
dt
dq
b
dt
dQ
m
dt
pd
Under constant production well pressure conditions
dt
dq
b
dt
dQ
m
dt
pd
0
We have
q
dt
dQ
Therefore
q
b
m
dt
dq
or
dt
b
m
q
dq
dt
b
m
q
dq
or
cst
t
b
m
q
ln
)
exp(
cst
t
b
m
q
that can be written
)
exp(
t
b
m
i
There are many situations however, where the general hyperbolic decline is more adequate.
This is the case in solution gas drive reservoirs.
In our opinion, and given the power of the non-linear regression, it is better to try and
determine all three parameters, including b, systematically.