2. Decline Curve Analysis
Preliminaries:
MBE analysis yields only G and Gp as a function of p
for gas reservoirs.
Estimation of production rate specially as function of
time is also of great importance
Under natural depletion, the rate normally declines with
recovery
Majority of oil and gas reservoirs show natural
production rate decline according to standard trends
Unless natural trend is interrupted (water injection, well
shut in) the natural decline trend is expected to
continue until abandonment
3. Decline Curve Analysis for Reserve
Estimation
Natural decline trend is dictated by natural drive, rock and
fluid properties well completion, and so on. Thus, a major
advantage of this decline trend analysis is implicit inclusion
of all production and operating conditions that would
influence the performance.
The standard declines ( observed in field cases and whose
mathematical forms are derived empirically) are
Exponential decline
Harmonic decline
Hyperbolic decline
4. Decline Curve Analysis
When the average reservoir pressure decreases with time
due to oil and gas production, this in turn causes the well
and field production rates to decrease yielding a rate time
relation similar to that in the following figure.
Definition of normalized production rate decline, D:
0
/ /
lim
t
dq dt q t
D
q q
5. Decline Curve Analysis
D = continuous production decline rate at time t
(1/time)
If t = years:
Da= annual continuous production decline rate (1/year)
If t = months:
Dm= monthly continuous production decline rate
(1/month)
Unit of q is not important
6. Decline curve models
The general decline curve models is defined according
to their relation with q as follows:
where n is called as the decline exponent
The three standard decline models (usually observed in
field) are defined as follows.
n
i
i
q
D D
q
7. Decline curve models
1. Exponential decline (n=0):
2. Harmonic decline (n=1):
3. Hyperbolic decline
where Di is the initial decline rate
i
i
q
D D
q
tan
i
D D cons t
n
i
i
q
D D
q
8. Decline curve models
exponential rate decline
harmonic rate decline
hyperbolic rate decline
1/
( ) .3
1
i
n
i
q
q t Eq
nD t
( ) .2
1
i
i
q
q t Eq
D t
( ) exp( ) .1
i i
q t q D t Eq
Producing rate during decline period for each
model are (derived in appendix C:
9. Decline curve models
Cumulative production as a function of q for each model
are determined as:
ln( / ) .5
i
p i
i
q
G q q Eq
D
.4
i
p
i
q q
G Eq
D
1 1
1 1
.6
(1 )
n
i
p n n
i i
q
G Eq
D n q q
exponential decline
harmonic decline
hyperbolic decline
10. Decline curve models
Time at abandonment:
If we define the economic limit when the production rate is
qa then the exponential, harmonic and hyperbolic declines
would have the following abandonment times respectively:
1
ln .7
i
a
i a
q
t Eq
D q
1
1 .8
i
a
i a
q
t Eq
D q
1
1 .9
n
i
a
i a
q
t Eq
nD q
15. Graphical Features of Models
For hyperbolic decline no immediate straight form
is obtained, therefore a linear plot which allows us
to determine two parameters namely Di and qi
simultaneously is not available.
In summary : The production plots allows us two
determine the nature of decline and then we can
obtain the decline model parameters.
16. Summary Production Plots
1. A plot of log(q) vs t is
Linear if decline is exponential
Concave upward if decline is hyperbolic (n>0) or harmonic
2. A plot of q vs Np is
Linear if decline is exponential
Concave upward if decline is hyperbolic(n>0) or harmonic
3. A plot of log(q) vs Np is
Linear if decline is harmonic
Concave downward if decline is hyperbolic (n<1) or exponential
Concave upward if decline is hyperbolic with n>1.
4. A plot of 1/q vs t is
Linear if decline is harmonic
Concave downward if decline is hyperbolic (n<1) or exponential
Concave upward if decline is hyperbolic with n>1.
17. Hyperbolic decline analysis
1. Since no wells have declines where n=0 or 1 exactly it is more
appropriate to use a regression technique to determine all
three parameters namley Di, qi and n simultaneously. Two
approaches are suggested by Towler:
An iterative linear regression
Nonlinear regression
Towler also pointed out that linear regression impose more weight
on smaller values of production rates as it involves logs of
variables. Furthermore, the two suggested procedures on linear
regression do not produce equivalent results.
Therefore, he suggests nonlinear regression as a method which
produces repeatable results, and weights the production rates
equally. The steps of regression on an excel sheet is also
provided in Appendix C.
18. Caution for applicability
The emprical decline curve equations assume that the
well/field analyzed is produced at constant BHP. If the
BHP changes, the character of the well's decline
changes.
They also assume that the well analyzed is producing
from an unchanging drainage area (i.e., fixed size) with
no-flow boundaries, If the size of the drainage area
changes (e.g., from relative changes in reservoir rates),
the character of the well's decline changes. If, for
example, water is entering the well's drainage area, the
character of the well's decline may change suddenly,
abruptly, and negatively.
19. Caution for applicability
The equation assumes that the well analyzed
has constant permeability and skin factor. If
permeability decreases as pore pressure
decreases, or if skin factor changes because of
changing damage or deliberate stimulation, the
character of the well's decline changes.
It must be applied only to boundary-dominated
(stabilized) flow data if we want to predict future
performance of even limited duration.
20. Decline Type Curves
Prepare a report explaining Carter decline
curves
Include the solution of exercise 9.5 from the
textbook
