COMBINED METHODS IMPROVE RESERVE ESTIMATES

May 1, 1995
Rene Santos, Erwin Ehrl Mobil Erdgas-Erdol GmbH Celle, Germany A comparison of deterministic and probabilistic methods can provide quality assurance for estimating hydrocarbon reserves. Proved reserves would then be calculated both deterministically and probabilistically and the two values compared. Probabilistic methods use stochastic parameters such as a Monte Carlo simulation. On the other hand, deterministic calculations are made with discrete values.
Rene Santos, Erwin Ehrl
Mobil Erdgas-Erdol GmbH
Celle, Germany

A comparison of deterministic and probabilistic methods can provide quality assurance for estimating hydrocarbon reserves. Proved reserves would then be calculated both deterministically and probabilistically and the two values compared.

Probabilistic methods use stochastic parameters such as a Monte Carlo simulation. On the other hand, deterministic calculations are made with discrete values.

If the deterministic value and the probabilistic value agree, then confidence in the reserve calculation is increased. If the two values are very different, the assumptions need to be reexamined.

PROVED RESERVES

Probabilistic methods for calculating proved reserves have several inherent problems. These methods are affected by all the input parameters, including the most likely and maximum values for the parameters.

Proved reserves derived from probabilistic methods are intangible and impossible to "point to on a map." They also may be difficult to reconcile with legal definitions of a proved area. In a probabilistic calculation one cannot back calculate the input parameters associated with the proved reserves. One knows only the end result but not the exact value of any input parameter.

On the other hand, deterministic methods derive proved reserves that are more tangible and explainable. In a deterministic calculation one knows exactly the parameters used in the calculation. However, deterministic methods may sometimes ignore the variability and uncertainty in the input data. Probabilistic methods allow the incorporation of more variance in the data.

Deterministic methods use single-point parameters to obtain reserves.1 2 The result is a single value such as 10 billion cu m.

Some parts of the deterministic calculation of proved reserves are constrained by legal definitions, such as the U.S. Security and Exchange Commission (SEC) definitions for proved area.

CALCULATING RESERVES

To determine reserves, probabilistic methods use stochastic parameters such as a Monte Carlo simulation. The result is a cumulative probability-vs.-reserves curve, for example a 40% probability of producing 10 billion cu m or more.1-4 Proved reserves can be read from this curve at a defined probability but these reserves cannot be tied to a defined proved area.

A hypothetical gas reservoir demonstrates some of the problems inherent in probabilistic methods. Table 1 lists the input parameters required to calculate reserves with a probabilistic method. Each input parameter such as net pay, porosity, etc. has a range of values. Fig. 1 illustrates the probabilistic results (from a PC-based Monte Carlo simulation with 5,000 passes through the data) of a beta distribution with a slope such that the average value, EV, is defined as:

EV = (Min + 4 x Most likely + Max)/6

Other distributions, such as triangular, could have been used. The distribution function will influence the shape of the cumulative probability-vs.-reserves curve.

The graph shows an expected value (EV) of 9.3 billion cu m. The expected value is defined as the statistical average gas reserves. In other words, EV is the best estimate of reserves that one expects to produce from a field.5

To probabilistically compute proved reserves (commonly defined as estimated gas and oil volumes that geologic and engineering data demonstrate with "reasonable certainty" to be produced in the future),6 7 some companies use "last barrel of proved production" probabilities of between 85% and 95% and read proved reserves from a curve such as in Fig. 1.

In the hypothetical example, proved reserves are 5.9 billion cu m if a 90% "probability cutoff" is used to classify reserves as proved. Proved reserves calculated probabilistically are affected both by the magnitude of all parameters in the distributions and by the shape of the distributions. The computed proved reserves change when any of the input parameters (most likely and maximum values as well as minimum values) of the probabilistic computation are changed.

To demonstrate this effect, we increased the most likely drainage area in our hypothetical reservoir by 25% (from 15 sq km to 18.75 sq km), left all other variables unchanged, and recomputed the probabilistic reserves. As expected, the EV (Fig. 2) increased from 9.3 to 10.8 billion cu m. Perhaps unexpectedly, however, proved reserves also increased, from 5.9 to 7.0 billion cu m (a 19% increase).

The increase in proved reserves resulting from an increase in the most likely values for any of the parameters is an integral feature of the probabilistic method. All input parameters affect the calculated value of proved reserves in a probabilistic sense, without regard to any external constraints on specific variables. Table 2 summarizes the effect of this increase on most likely drainage area, EV, and proved reserves.

Probabilistically calculated proved reserves also change when the minimum or maximum drainage area changes, although these changes are not as dramatic as when most likely values change.

Fig. 3 shows how the calculated proved reserves (determined with a 90% probability cutoff) change with increases in the minimum, most likely, and maximum values for the drainage area. For the hypothetical gas reservoir, a 25% increase in the most likely drainage area results in a 19% increase in proved reserves.

Even in a small gas field where the lowest known gas (LKG) defines the minimum drainage area in the reservoir (the deterministic "proved area" according to some legal definitions), the "probabilistic proved reserves" would increase with increases in the drainage area.

A deterministic calculation of proved reserves, in contrast, would be unaffected by the estimate of the "most likely" drainage area. Instead of rejecting a probabilistic approach for proved reserves computation, the authors suggest independently computing reserves both deterministically and probabilistically and comparing the two results. The results could be compared by using a range of defined probabilities for proved reserves, such as 85%-95% shown by the hatched area in Fig. 4.

If the proved reserves calculated from the deterministic method fit within the defined probability range, the estimate would be assumed valid.

The deterministic proved reserves might, however, intersect the probability curve outside the defined probability range. Fig. 4 shows a hypothetical example in which the deterministic proved reserves (7.6 billion cu m) have an associated last barrel probability of only 70%.

If the deviation from the defined probability range is very high, then one of the following may be true:

  • The deterministic proved reserves are too optimistic/pessimistic.
  • Incorrect input parameters/distributions have been used for the probabilistic calculation.
  • The premises for the two calculations are radically different.

The complete set of input parameters for both the probabilistic and the deterministic calculations should be reviewed and the results reconciled.

This procedure will lend more confidence to reserve determinations because two different methods (probabilistic and deterministic) have been applied independently and both yielded consistent results.

ACKNOWLEDGMENTS

The authors thank the management of Mobil Erdgas-Erdol GmbH for permission to prepare and publish the article. We would also like to thank A.G. Nangea, C.L. McMichael, J.A. Patricelli, A.G. Pollin, and S.N. Salzman from Mobil Exploration & Producing Technical Center and H. Jahnke from MEEG for their helpful suggestions and comments.

Authors' note: The authors want to state that all opinions in this article are those of the authors and do not represent Mobil Oil Corp.'s procedures for calculating reserves.

REFERENCES

1. Guidelines for Application of the Definitions for Oil and Gas Reserves, Monograph Series, SPE, Houston, 1988.

2. Smith, P.J., and Buckee, J.W., "Calculating In-Place and Recoverable Hydrocarbons: A Comparison of Alternative Methods," Paper No. SPE 13776, SPE Hydrocarbon Economics and Evaluation Symposium, Dallas, Mar. 14-15, 1985.

3. Behrenbruch, P., Turner, G.J., and Backhouse, A.R., "Probabilistic Hydrocarbon Reserves Estimation: A Novel Monte Carlo Approach," Paper No. SPE 13982, SPE Offshore Europe Conference, Aberdeen, Sept. 10-13, 1985.

4. Cronquist, C., "Reserves and Probabilities-Synergism or Anachronism?" JPT, October 1991, pp. 1,258-64.

5. Daniel, W.W., and Terrell, J.C., Business Statistics - Basic Concepts and Methodology, Second Edition, Houghton Mifflin Co., 1979.

6. DeSorcy, G.J., "Estimation Methods for Proved Recoverable Reserves of Oil and Gas," Proceedings 10th World Petroleum Congress, Bucharest, 1979, p. 269.

7. Keith, D.R., Wilson, D.C., and Gorsuch, D.P., "Reserves Definitions-An Attempt at Consistency," Paper No. SPE 15865, SPE European Offshore Petroleum Conference, London, Oct. 20-22, 1986.

Copyright 1995 Oil & Gas Journal. All Rights Reserved.