John SchuylerOil & Gas Consultants International

Aurora, Colo.

Several key issues with the newly revised reserves definitions remain, and further innovation is needed to increase efficiency in probabilistic reserves calculations. In these calculations, probabilities and probability distributions are used to characterize variables used for determining remaining hydrocarbon reserves.

Petroleum property evaluation is undergoing a dramatic change. There is growing awareness and now formal acceptance of applying decision analysis to reserves evaluations by including probabilistic tools and techniques, which have long been available.

With these techniques, companies are able to report, legitimately, somewhat higher proved reserves. This is because traditional techniques understate proved reserves. More importantly, forecasts calculated with probabilities lead to more complete and more accurate evaluations.

Better evaluations support better decisions in transactions, reservoir management, and asset portfolio management.

### Updated reserves definitions

Reserves are those quantities of petroleum that are anticipated to be commercially recoverable from known accumulations after a given date.^{1}These volumes and their associated monetary values are extremely important to the upstream petroleum industry.

In March 1997, the Society of Petroleum Engineers (SPE) and the World Petroleum Congresses (WPC) released new petroleum reserves definitions that superseded the 1987 SPE and WPC separate but similar definitions.

The industry is still interpreting the brief, two page definitions and evaluating how to apply them.

SPE is preparing a book on how to apply the definitions, and the Society of Petroleum Evaluation Engineers (SPEE) is about to issue its updated guidelines.

But disagreement in applying probabilistic methods remains, and more work lies ahead to educate the petroleum community and to enhance the calculation tools.

The major change in the reserves definitions is recognizing the alternate "probabilistic" evaluation approach. This refers to using probabilities and probability distributions to characterize judgments about geological, engineering, and economic inputs. With some input variables represented as distributions, the evaluation model produces probability distribution outputs.

Previously, most companies represented recovery uncertainty by using descriptive word classifications such as "proved," "probable," or "possible."

Deterministic calculations, with every input value singly determined, are still acceptable and may be preferred in some cases.

Probabilistic, or stochastic reserves evaluations are applications of decision analysis. This discipline helps decision-makers choose wisely under conditions of uncertainty.

It centers on a decision policy based on the expected value (EV) concept. EV is simply the probability-weighted average of all possible outcome values.

Decision analysis was introduced in the petroleum industry in the 1960s.^{2 3} Since then, this process has become routine in exploration, and it was natural that the techniques expand into production operations, including reserves assessments.

### Category definitions

Reserves definitions have a long history in the literature. Some of the best papers are those by Cronquist^{4}and Garb.

^{5 6}SPE Transactions Reprint Series No. 3, Oil and Gas Property Evaluation and Reserves Estimates, is the classic historical reference.

Previously, asking engineers "What probability supports a proved classification?" would return answers ranging from 50 to 98%. The new definitions provide unambiguous and consistent numeric confidence levels for proved and other reserves categories. This single pronouncement significantly advances petroleum property evaluation.

Assigning a probability confidence does not necessarily make the judgment more accurate. However, probabilities are explicit, unambiguous, and useful in calculations.

If deterministic methods are used, the term reasonable certainty is intended to express a high degree of confidence that the quantities will be recovered. If probabilistic methods are used, there should be at least a 90% probability that the quantities actually recovered will equal or exceed the estimate.^{1}

The 90% probability volume is commonly referred to as the "P90" volume. Similarly, the confidence levels are P50 for "proved + probable" reserves and P10 for "proved + probable + possible" reserves. These category groupings are often referred to as P1, P2, and P3.

There are many additional conditions as to data quality, and the implications of these. Equating the traditional descriptive words with probabilities is the key change in the 1991 proposed revisions and the new definitions. "Reasonable certainty" is now defined, in regards to probabilistic reserves, to mean a 90% confidence.

### Accurate computations

Many people are attracted to decision analysis in a desire to characterize uncertainty in the evaluation result, for example, the range of reserves or economic values for a property. The process also provides the project team and decision manager with increased insights. A better answer is another key benefit.Decision trees and Monte Carlo simulation are the calculation workhorses of decision analysis. Each has strengths and weaknesses, and often both methods are included in the same analysis. Both techniques, in effect, propagate probability distributions faithfully through the forecasting model.

Monte Carlo simulation is usually preferred for probabilistic reserves calculations.^{7}

The EV result is often different and more accurate than the deterministic solution, although some may be averse to the adjective "accurate" to describe a decision analysis result.

Accuracy characterizes a condition of having low bias and high precision. In decision analysis, probability distributions represent key uncertain inputs. Of course, most of these inputs are subjective assessments, that is, performed by humans.

If these inputs have poor quality, the calculated results will also be poor. The chief analytic benefit of decision analysis is to ensure the integrity, or accuracy in the calculations.

The improved accuracy results from two effects.

The first is psychological. Judgments about risks and uncertainties are best expressed as probabilities and probability distributions. Distributions allow complete expressions of professional judgments about uncertainties.

The author has witnessed substantial adjustments, or corrections, when people consider the inputs as ranges rather than single-point values.

Note that the best single-point values are not medians (P50s) or modes (most likely points). The mean (EV) is the only objective, meaning unbiased, single-point estimate from a probabilistic forecast.

The author suggests preparing a deterministic base-case projection, where the input variables are set at their EVs. The base case is for reference in discussion, not for decision-making. The consideration of the possibilities often has profound effects on the single-point inputs and base-case solution.

The second effect is mathematical. Probability distributions often interact in counter-intuitive ways as they propagate through the evaluation model calculations.

The value estimate correction, stochastic variance, is the deterministic base-case value less the EV forecast.8 9 Surprisingly, this is a little-known phenomenon.

The solving of a deterministic model with EV inputs does not generally provide an EV solution result. Stochastic variance (which is a recent name for the topic) is the topic that the decision analysis pioneer Paul Newendorp considers his most important paper.^{10}

The term stochastic variance is from the variance analysis performed by cost accountants. It is not to be confused with the variance statistic.

Variance analysis is about explaining the difference between the forecast and actual outcome. Stochastic variance is a component of total variance.

The value of an option (a subsequent decision point) is often a key contributor to stochastic variance. For example, a conventional, deterministic analysis may indicate that a property is marginal, that is to say, net present value (NPV) is approximately zero.

A probabilistic model could and should incorporate decision logic to represent the options to either continue or accelerate production if oil prices increase or to shut-in or plug-and-abandon if prices fall.

Much greater value will be realized from the marginal property if prices rise. At the same time, there is little downside if prices fall. Thus, a more realistic appraisal value will recognize the value of the options.

A deterministic evaluation can be preferred over a probabilistic approach, as evidenced by many practitioners steadfastly applying conventional deterministic methods to evaluating reserves. If there is little uncertainty, the deterministic solution produces essentially the same result with slightly less work. This is especially true for performance-based evaluations.

### Aggregation, correlation

A frequent topic in reserves assessment discussions is aggregation. How should groups of completions, wells, or properties be rolled up? If one considers aggregation into reserves classes, then the deterministic calculation falls short.A common beginner's mistake is to assume that probabilities and probability distributions are independent. This often is not the case. For example, water saturation has an inverse relationship to porosity, and ignoring this relation presents some impossible scenarios. The association between variables is called correlation.

There are several ways to represent dependency relationships in evaluation models. Crafting efficient ways to recognize correlations is likely the greatest challenge in designing software for probabilistic reserves with many properties.

The new definitions only provide this understated warning:

"Because of potential differences in uncertainty, caution should be exercised when aggregating reserves of different classifications."

The same can be said for adding reserves of the same classification.

Adding volume or monetary values for reserves categories does not work except for EVs. It is statistically invalid to add, for example, proved-plus-probable reserves in multiple properties where the volume for each property is determined at the 50% (P50, median) confidence level.

That is, summing P50s does not result in a P50 total.

This caution applies to NPVs as well. Note also that Pxx reserves do not correspond to a Pxx NPV case. The xx is the percentage confidence level. An example of reserves aggregation is shown in the example box.

In this simple example, the correct proved reserves are almost 8% higher using the P90 cutoff. With a large number of properties, the P90 total can be achieved at much lower confidences of the component properties. For proved reserves, the agreed target is 90% confidence at the company or total report level. A back-calculation is needed to determine the common confidence levels at the property levels. In the two-reservoir example, the P90 total gas reserves is realized by summing the P86 levels of each reservoir.

Carter and Morales describe aggregation of 25 gas fields in a disguised but real project.^{11} They first developed reserves distributions for individual fields. Then a matrix of qualitative factors was developed to represent various correlations between properties.

The qualitative factors were transformed into a matrix of correlation coefficients. Using the correlation matrix, the field distributions were aggregated, with a Monte Carlo simulation, into a distribution of total project gas volume.

The resulting P90 proved volume was 9.3% higher than the sum of P90 volumes for the individual properties.

While the analysis lacked detail in quantitatively representing common drivers, their high-level calculation approach may prove to be an excellent balance between assessment effort and quality.

### Proved reserves math

Conceptually, summing proved-plus-probable (P50) reserves of enough properties will provide a total that is greater than the 90% confidence level. This is because the P50 value is slightly conservative, lower than the EV, and a property's unique risks are diluted with diversification.Thus, the portion of reserves classified as proved will increase as properties are aggregated. As such, total proved reserves will increase when properties are purchased by a larger company.

Is this creating value? Most of any real value, if any, in consolidating assets is through organization efficiencies and synergies, not in the aggregation mathematics. Better mathematics in aggregating reserves does not distort or create value, it merely better represents what value is already there.

Portfolio theory recognizes that the error in aggregating reserves at the property or other component level is made worse by simply adding P90 volumes. With a broad mix of properties, the significant correlations include product prices and possibly technology and political risks.

Reservoir risks are diversified away. The relative independence, even negative correlation because of price, to the broader capital markets should make upstream petroleum investments especially attractive to investors.

In the author's conversations with engineers, few have given reserves aggregation much thought. The laws of probability and statistics apply, and the aggregation procedure should be designed accordingly.

### Tools needed

Most companies involved with exploration use at least rudimentary decision analysis. The most common methods are:- Calculating probability of success (ps) with components of geologic success. Most explorationists treat individual adequacy factors, such as source and migration, as separate and independent chance events.
- Using Monte Carlo simulation to calculate a distribution of recoverable gas or oil volumes. This is usually based upon a simulation of a volumetric equation, using distributions for each input variable.
- Calculating prospect value with a single-node probability tree as EMV = EV NPV = ps (discovery value) + (1 - ps) (dry hole cost).

Yet, most people agree that the P90 confidence for proved should be at the company or report level. Note P90 reserves at the property level are sometimes uneconomic and, thus, may be inconsistent with the definition of proved.^{12}

Most often the evaluated volumes are attributed to only one category. This saves some work, although this sacrifices completeness.

Increasingly, different classifications are being assigned to different performance scenarios at the same evaluation unit, such as illustrated in Fig. 1 [27,975 bytes]. For example, a well being analyzed using decline-curve analysis might have three forecasts:

- Proved, using a conservative decline (highest decline rate)
- Proved + probable, for an intermediate case
- Proved + probable + possible, assigned to the volume using an optimistic decline (lowest decline rate).

Cash flow projections are needed for each reserves case. Unfortunately, P90 NPV does not correspond to P90 reserves, and this problem needs to be more fully explored.

Black boxes can lead to trouble. For example, the NPV functions in Excel and Lotus 1-2-3 most often produce the wrong values because the formula's timing assumption is inconsistent with most real projects. Computer models are only approximations to the real system. People should understand what their tools are doing in order to assure that the calculations reasonably represent their beliefs and judgments about the actual situation.

### Current approaches

Most companies and their consultants are using traditional, deterministic methods for calculating and valuing reserves. There are exceptions. Shell Oil Co., for example, has been using probabilistic methods for over three decades for assessing its reserves. And Mobil Corp. has presented its mixed probabilistic and deterministic approach at several recent conferences.^{13}

Many companies are using probabilistic methods in resource assessment. This may be as simple as a volumetric simulation or as sophisticated as stochastic models of geology and reservoirs. More advanced users are carrying the calculations through the economics. Only a few companies are using probabilistic representations for product prices, inflation, technology changes, and country risks.

Vendors of petroleum economics software have been adding decision analysis capabilities to their products. Perhaps the easiest approach has been to link the economics program to Microsoft Excel. Then, one of the decision trees (such as DATA, DPL, or Precision Tree) or Monte Carlo simulation (such as @RISK or Crystal Ball) add-in packages can be used to add the probabilistic capabilities.

Several companies (such as Economic Analysis Systems, Merak Projects, and OGRE Partners) have or are developing their own integrated computer routines for simulation or decision tree calculations.

Tools are available today to support probabilistic methods in reserves assessments. Individual fields and small portfolios can be accommodated easily with software from several vendors. Efficiently aggregating large numbers of properties with correlations is a capability requiring further development work in software and procedures.

### Continuing progress

Without a doubt, better tools will evolve to minimize the apparent extra effort involved in probabilistic reserves assessments. Computer instruction cycles are cheap, and much of the work can be done by automation. Once the education and tools are in place, probabilistic reserves assessments may require little additional human time.Better evaluations of reserves will foster additional management improvements.

Techniques for probabilistic reserves are useful also for assessing prospects and plays. Portfolio analysis, another prominent topic at the SPE meetings, is based upon probabilistic methods. Improved reserves assessments can be expected to advance practices for managing properties and other assets.

### References

- Society of Petroleum Engineers and World Petroleum Congresses, "Petroleum Reserves Definitions," March 1997.
- Grayson, C.J. Jr., Decisions Under Uncertainty: Drilling Decisions by Oil and Gas Operators, Harvard University, Boston, 1960.
- Newendorp, P.D., and Root, Paul J., "Risk Analysis in Drilling Investment Decisions," JPT, 1968, p. 579.
- Cronquist, C., "Preserves and Probabilities-Synergism or Anachronism?," JPT, 1991, p. 1258.
- Garb, F.A., "Assessing Risk in Estimating Hydrocarbon Reserves and in Evaluating Hydrocarbon-Producing Properties," JPT, June, 1998, p. 765.
- Garb, F.A., "Oil and Gas Reserves Classification, Estimation, and Evaluation," JPT, March 1985, p. 373.
- Schuyler, J.R., and Hochanadel, S.M., "Simulation demonstrates economics of Minnelusa polymer floods," OGJ, May 27, 1991, pp. 90-93.
- Schuyler, J.R., "Decision Analysis in Projects: Stochastic Variance," PM Network, July 1995, p. 11.
- Schuyler, J.R., Decision Analysis in Projects, Project Management Institute, Upper Darby, Pa., 1997.
- Newendorp, P.D., and Quick, A.N., "The Need for More Reliable Decision Criteria for Drilling Prospect Analyses," SPE Paper No. 16318, SPE Hydrocarbon Economics and Evaluation Symposium, Dallas, Mar. 2-3, 1987.
- Carter, P.J., and Morales, E., "Probabilistic Addition of Gas Reserves within a Major Gas Project," SPE Paper No. 50113, Asia Pacific Oil & Gas Conference and Exhibition, Perth, October 1998.
- Wright, J.D., panel discussion, SPEE, Denver, Apr. 14, 1999.
- Nangea, A.G., and Hunt, E.J., "An Integrated Deterministic/Probabilistic Approach to Reserves Estimation: An Update," SPE Paper No. 38803, SPE Annual Technical Conference and Exhibition, San Antonio, Oct. 5-8, 1997.

### Bibliography

- Schuyler, J.R., "Probabilistic Reserves Lead to More Accurate Assessments," SPE Paper No. 49032, revised Nov. 3, 1998.
- Schuyler, J.R., "Review of Common Methods," at the SPE Applied Technology Workshop on Probabilistic Assessment of Reserves, Dallas, Mar. 24-25, 1999.
- Schuyler, J.R., "Aggregation and Correlation," panel report to the Society of Petroleum Evaluation Engineers, Denver, Apr. 14, 1999.

### The Author

John R. Schuyleris a consulting petroleum evaluation engineer in Aurora, Colo. Since 1990, he has presented over 130 industry short courses about risk and economic decision analysis, most in affiliation with OGCI. He holds BS and MS degrees from the Colorado School of Mines and an MBA from the University of Colorado.

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