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# Production forecasting decline curve analysis

Decline curve analysis (DCA) is a graphical procedure used for analyzing declining production rates and forecasting future performance of oil and gas wells. Oil and gas production rates decline as a function of time; loss of reservoir pressure, or changing relative volumes of the produced fluids, are usually the cause. Fitting a line through the performance history and assuming this same trend will continue in future forms the basis of DCA concept. It is important to note here that in absence of stabilized production trends the technique cannot be expected to give reliable results.

The technique is not necessarily grounded in fundamental theory but is based on empirical observation of production decline.

Three types of declines are observed :

- Exponential
- Hyperbolic
- Harmonic

There are theoretical equivalent to these decline processes. It can be demonstrated that under conditions such as constant well back pressure, equation of fluid flow through porous media under boundary dominated flow are equivalent to exponential decline. However for our purpose it is the empirical nature of this term which has a greater significance since it allows the technique to be applied to multiple fluid streams even ratios!

## Golden rule of decline curve analysis (DCA)

The basic assumption in this procedure is that whatever causes controlled the trend of a curve in the past will continue to govern its trend in the future in a uniform manner

## Decline curve analysis (DCA) history

J.J. Arps collected these ideas into a comprehensive set of equations defining the exponential, hyperbolic and harmonic declines. His work was further extended by other researchers to include special cases. Following section gives a historical perspective of work done on the subject;

- Arps 1945 and 1956.
- Brons 1963 and Fetkovitch 1983 applied constant pressure solution to diffucisivty equation and demonstrated that exponential decline curve actually reflects single phase, incompressible fluid production from a closed reservoir. DCA is more than a empirical curve fit.
- Fetkovitch 1980 and 1983 developed set of type curves to enhance application of DCA.
- Doublet and Blasingame 1995 developed theoretical basis for combining transient and boundary dominated flow for the pressure transient solution to the diffusivity equation.

## Decline curve analysis (DCA) today

The major application of DCA in the industry today is still based on equations and curves described by Arps. Arps applied the equation of Hyperbola to define three general equations to model production declines.

In order to locate a hyperbola in space one must know the following three variables.

- The starting point on Y axis, (qi), initial rate.
- Initial decline rate (Di)
- The degree of curvature of the line (b).

Arps did not provide physical reasons for the three types of decline. He only indicated that exponential decline (b=0) is most common and that the coefficient b generally ranges from 0 to 0.5.

ARPS Equation Insert

Clearly all wells do not exhibit exponential behavior during depletion. In many cases a more gradual hyperbolic decline is observed where rate time performance is better than estimated from exponential solutions implying that hyperbolic decline results from natural and artificial driving energies that slow down pressure depletion. Hyperbolic decline is observed when reservoir drive mechanism is solution gas cap drive, gas cap expansion or water drive. It is also possible where natural drive is supplemented by injection of water gas. The type of decline and its characteristic shape is a major feature of DCA. We shall be talking more about this as we go further. The various types of declines experienced by a well are documented in the **Fig 1 and Fig 2**.

INSERT FIGURE 1 q vs. Time showing various types of declines on Cartesian plot. (b value for hyperbolic curve =0.5) INSERT FIGURE 2 Log q vs. Time showing various types of declines on Semilog plot. (b value for hyperbolic curve =0.5). Note change in shapes of curves.

Observe the change in Shapes of curve from Cartesian to logarithmic; this is very helpful in identification of type of decline.

Two sets of curves are normally used while analyzing production decline.

- Flow rate is plotted against Time:
- Very convenient since it provides future profiles directly.

- Provide recovery estimates at a specific economic limit.
- Able to incorporate impact of intermittent operations that impact production.

INSERT FIGURE 3 Rate verses Time and Rate verses Cum Oil

## References

## Noteworthy papers in OnePetro

## Noteworthy books

Society of Petroleum Engineers (U.S.). 2011. Production forecasting. Richardson, Tex: Society of Petroleum Engineers. WorldCat or SPE Bookstore

## External links

## See also

Production forecasting glossary

Sandbox:Production forecasting building blocks

Sandbox:Production forecasting expectations

Sandbox:Production forecasting flowchart

Sandbox:Production forecasting in the financial markets