ESTIMATING DECLINE CURVES WITH CONFIDENCE

Wayne A. Beninger, Robert H. Caldwell
Scotia Group Inc.
Dallas

The concept of probabilistic reserve estimation is simply a measure of confidence that can be applied to both production performance and volumetric estimation.

The Society of Petroleum Engineers likely will discuss the concept during its annual meeting this week in Dallas.

Extrapolation of production history has long been considered the most accurate and defendable method of estimating remaining recoverable reserves from a well and, in turn, a reservoir.

The purpose of this series of articles is to provide the basis for making a probabilistic link between production performance in the form of decline curve estimates and reserve estimates derived from volumetric calculations.

This article is intended to show the range of answers to be expected from decline curve analysis and to present a way to describe the meaning of the range.

REASONABLE CERTAINTY

Anyone who projects production history knows intuitively that the projection is wrong.

The intent is for the projection to reflect the spirit of the term "reasonable certainty."

In the case of decline curve analysis, the estimator can be more reasonably certain of his projection when there is a large amount of history for the subject well, a thorough understanding of the petrophysics of the reservoir, and an abundance of analogous data.

This however is usually not the case. In fact in many cases the estimator will restrict himself only to the data specific to the subject well.

He will then pick up his pencil and straight-edge, squint through one eye, stick his tongue out the corner of his mouth, and rely on his experience to make a reasonable pick of the decline (the authors wish to thank Dr. Steve Holditch for that observation). This may be on the high side or low side of actual production to be experienced.

RANGE OF POSSIBILITIES

An alternative is to consider the potential range of the correct answer and then attempt to find reasons to support some number within the range.

An example (Fig. 1) illustrates the range from most conservative (exponential projection) to a rather optimistic projection (harmonic). Harmonic decline has been chosen for the purpose of simplicity. The harmonic decline is not restricted by using a constant percentage de cline tail.

A 2.6 fold difference between the extreme picks can be observed, much of it early in the life of the well where there is the greatest impact.

To describe this range, we have chosen to use DECSIM, which is a Monte Carlo based decline curve simulator developed by Scotia Group.

For example purposes, everything is held constant except for the exponent N (for N = 0 the curve is a straight line, for N = 1 the curve is harmonic).

PROBABILISTIC DISTRIBUTION

The result is a distribution that describes the probability associated with remaining levels between the two extremes.

The only additional variable that must be supplied by the estimator is an estimate of the most probable exponent. This can be arrived at by looking at offset wells for an idea of what to expect,

A probabilistic distribution (Fig. 2) of the remaining reserves between the extremes shows the potential variation in the hyperbolic exponent (between 1 and 0 with our decision that the most probable is .7) and shows that based on a random sampling the mean average estimate of remaining reserves is 86,690 bbl of oil. However, the question remains, how much confidence should be put in the estimate?

Fig. 2 can be viewed as a measure of confidence. It shows that there is a 90% probability that the actual reserves are greater than 62,020 bbl. These could be described as proved reserves (i P).

Due to less certainty, it could be further considered that the proved plus probable reserve (2P) estimate could be represented by the median estimate; that is, a 50% probability the actual reserves are greater than the estimate and a 50% probability they are lower. This would suggest that there is a further 24,550 bbl to be recovered from this well if it performs at the median level.

Finally, it could be assumed that the proved plus probable plus possible reserve (3P) estimate could be represented by the 10% confidence value. That is, there is only a 10% probability that the well will perform better than this estimate and a 90% probability that it will perform worse.

Fig. 2 shows this estimate to be 112,280 bbl. Then by difference between the 90th and 50th percentiles we could estimate the possible reserves assigned to this well to be 25,710 bbl.

VALUES CONVERGE

Using this method, an interesting phenomenon is observed as production history accumulates and the uncertainty associated with the decline curve pick decreases. As the range of uncertainty narrows, the values for 1P, 2P, and 3P come closer together (the quantity of probable and possible reserves decreases) to the point where a near certainty situation occurs and all remaining reserves become proved.

Since reserve estimates are based on confidence, it is incumbent on the estimator to use a duplicatable approach that would result in the same answer at some point in the future if the same data are available.

This method provides a reasonable explanation for the potential range of results. As will be shown in the next article in a subsequent issue, the approach carries over into estimates made using volumetric analysis for describing plays and trends.

Copyright 1991 Oil & Gas Journal. All Rights Reserved.