Decline Curve Analysis

Learning Objectives of Lecture 8:

Importance of decline curves Decline curve models Decline curve plots Applications

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

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

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

/ /limt

dq dt q tD

q q

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

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

ii

qD D

q

Decline curve models

1. Exponential decline (n=0):

2. Harmonic decline (n=1):

3. Hyperbolic decline

where Di is the initial decline rate

ii

qD D

q

taniD D cons t

n

ii

qD D

q

Decline curve models

exponential rate decline

harmonic rate decline

hyperbolic rate decline 1/( ) .3

1

in

i

qq t Eq

nD t

( ) .2

1i

i

qq t Eq

D t

( ) exp( ) .1i iq t q D t Eq

Producing rate during decline period for each model are (derived in appendix C:

Decline curve models

Cumulative production as a function of q for each model are determined as:

ln( / ) .5ip i

i

qG q q Eq

D

.4ip

i

q qG Eq

D

1 1

1 1.6

(1 )

ni

p n ni i

qG Eq

D n q q

exponential decline

harmonic decline

hyperbolic decline

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:

1ln .7i

ai a

qt Eq

D q

11 .8i

ai a

qt Eq

D q

11 .9

ni

ai a

qt Eq

nD q

Graphical Features of Models

Cartesian plots yields

Graphical Features of Models

Seilog plots yield

Graphical Features of Models

Cartesian q vs Gp plots yield

Graphical Features of Models

Semilog q vs Gp plots yield

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.

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.

Hyperbolic decline analysis1. 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 whichproduces repeatable results, and weights the production rates equally. The steps of regression on an excel sheet is also

provided in Appendix C.

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.

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.

Decline Type Curves

Prepare a report explaining Carter decline curves

Include the solution of exercise 9.5 from the textbook