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Abstract

Risk and uncertainty are not synonymous (Megill, 1984; Rose, 1987). Risk connotes the threat of loss. Risk decisions weigh the level of investment against four considerations: net financial assets, chance of success/failure, potential gain, and potential loss. The last three considerations must rely on estimates, made under uncertainty, of the range of probabilities that some condition may exist or occur.

Every exploration decision involves considerations of both risk and uncertainty. Risk comes into play in deciding how much we are willing to pay for additional data or mineral interests, considering the high impact of front-end costs on project profitability. Uncertainty is intrinsically involved in all geotechnical predictions about the range of magnitude of the inferred mineral deposit, the chance of discovery, and the cost of finding and developing it. Therefore, once prospects have been identified, the problem in serial exploration decision making is twofold:

  • to be consistent in the way we deal with risk and uncertainty, and

  • to perceive uncertainty accurately and reduce it where possible.

Although extensive scientific and geotechnical work is indeed essential to successful modern petroleum exploration, we must also recognize that nearly all of the parameters required to assign expected monetary value to the exploratory prospect can only be estimates made under substantial uncertainty. Table 1 lists the most significant ones.

Given the importance of responsible estimating, it is quite remarkable that until recently so little effort has been made by most modern oil companies to monitor and improve their geotechnical staff's estimating performance.

Risk, Uncertainty, and Estimating

Risk and uncertainty are not synonymous (Megill, 1984; Rose, 1987). Risk connotes the threat of loss. Risk decisions weigh the level of investment against four considerations: net financial assets, chance of success/failure, potential gain, and potential loss. The last three considerations must rely on estimates, made under uncertainty, of the range of probabilities that some condition may exist or occur.

Every exploration decision involves considerations of both risk and uncertainty. Risk comes into play in deciding how much we are willing to pay for additional data or mineral interests, considering the high impact of front-end costs on project profitability. Uncertainty is intrinsically involved in all geotechnical predictions about the range of magnitude of the inferred mineral deposit, the chance of discovery, and the cost of finding and developing it. Therefore, once prospects have been identified, the problem in serial exploration decision making is twofold:

  • to be consistent in the way we deal with risk and uncertainty, and

  • to perceive uncertainty accurately and reduce it where possible.

Although extensive scientific and geotechnical work is indeed essential to successful modern petroleum exploration, we must also recognize that nearly all of the parameters required to assign expected monetary value to the exploratory prospect can only be estimates made under substantial uncertainty. Table 1 lists the most significant ones.

Given the importance of responsible estimating, it is quite remarkable that until recently so little effort has been made by most modern oil companies to monitor and improve their geotechnical staff's estimating performance. Many organizations, even today, persist in utilizing deterministic estimates—“single-value forecasts.” These are hopelessly inadequate given the wide uncertainties that usually exist and the multiplicity of interactive parameters involved in calculating the chance-weighted after-tax net present worth [Expected Net Present Value (After Tax) = ENPV(AT)] of a typical exploration prospect (Equation 2): 

formula

Table 1

Estimated geotechnical parameters.

Dimensionalthickness, area, volume, depth
Reservoirnet/gross, ϕ (porosity), K (permeability), HC-rec %, GOR, SW, etc.
Well PerformanceIP, % decline, etc.
Geochemical ValuesSR-type, TOC, maturity, composition
Migrationimpedance, dispersal, routes
Trap Integrityseal effectiveness, leakage, flushing, etc.
Timingmigration vs. trap creation
Front-end Costsland, drilling, completion, geotechnical data acquisition, overhead
Discovery Probabilitygeologic chance factors, commercial and economic reserve thresholds
Wellhead Pricelocal vs. international influences, envelope of historical real oil prices
Dimensionalthickness, area, volume, depth
Reservoirnet/gross, ϕ (porosity), K (permeability), HC-rec %, GOR, SW, etc.
Well PerformanceIP, % decline, etc.
Geochemical ValuesSR-type, TOC, maturity, composition
Migrationimpedance, dispersal, routes
Trap Integrityseal effectiveness, leakage, flushing, etc.
Timingmigration vs. trap creation
Front-end Costsland, drilling, completion, geotechnical data acquisition, overhead
Discovery Probabilitygeologic chance factors, commercial and economic reserve thresholds
Wellhead Pricelocal vs. international influences, envelope of historical real oil prices

There are several important observations to be made about this equation. First, in an American-style tax and royalty license, the owners of the producing property usually pay 100% of the costs but receive a reduced proportion—ordinarily from about 70% to 87.5%—of the revenues from production. This reduced proportion is the net revenue interest (NRI); the remainder goes to the royalty owner(s)—generally the landowner. In production-sharing contracts the formula is different, although the general principle still prevails that the operator provides most or all of the capital, especially the exploration investment, but receives only a part of the production revenues. Second, the equation expresses the profit or (loss) as if it were a “lump-sum” payment, whereas it is actually received over a long period of time: a complex net cash-flow stream combining investments, production decline, price fluctuations, expenses (including taxes), and inflation. Third, in order to consider the time value of money, the net cash flows are expressed as a discounted cash-flow stream so the entire venture can be compared with current alternative investments. Wherever a dollar value is expressed as Present Value (PV), it means that the value has been discounted to reflect the time value of money.

Uncertainty attends every item in this ENPV equation except the net revenue interest. These uncertainties are diverse, relating to geology, engineering, law, politics, economics, and acts of God. It is the special professional responsibility of geotechnical staff to estimate the magnitude of reserves, production rates, and costs; to reduce the level of uncertainty as much as possible through sound scientific and technological judgment (and additional investigation, where warranted); and to accurately and consistently convey estimates—as well as uncertainty levels—to management. Otherwise management's investment decisions may be misguided and imprudent. Thus the financial consequences of their geotechnical predictions and estimates constitute a weighty professional responsibility of the geotechnical staff.

Magnitude of Geotechnical Uncertainty

The earth is a coarse filter. Even though petroleum explorationists employ increasingly sophisticated and discriminating technology, our precision in measuring most of the important geotechnical factors and parameters bearing on prospect value is much more limited than many of us care to admit. Technology can reduce, but not eliminate, uncertainty. Moreover, exploration always operates at the cutting edge—the threshold of resolution—so that the potential effectiveness of new tools and concepts is constantly and aggressively being evaluated by applications in new and old exploration theaters. Accordingly, explo-rationists will always have to deal with uncomfortably large uncertainties. Figure 2 shows, by cross-plot, four actual experiences of modern oil companies in attempting to estimate reserves contained in prospects that turned out to be discoveries (Capen, 1992). Figure 15 shows similarly wide uncertainties by a large number of companies exploring in the Norwegian North Sea over an extended period of time.

The cross-plots in Figure 2 express two important attributes of prospect reserves forecasting:

  1. Prevalent optimistic bias of estimates vs. actual outcomes—in cross-plots B, C, and D, most of the outcomes are overestimates (cross-plot A is an unbiased data set). We will address bias later.

  2. Substantial uncertainty, expressed as a characteristic, wide “scatter” of estimates. Given a continuing and substantial number of exploration ventures (repeated trials), statistics offers a practical way to deal with the prevailing large uncertainties that characterize petroleum exploration.

This characteristic, wide “scatter” conveys a profound (if disagreeable) message that petroleum prospectors would do well to absorb: Explorationists cannot predict very well how much oil or gas their successful prospects (= discoveries) will contain. We can generally identify those closures that are too small to contain large volumes, but we cannot forecast how much oil or gas the large closures may contain, often because of unanticipated variations in trap fill-up, reservoir quality, and dip rate.

Stated more pragmatically, we can usually distinguish between a 5-million-barrel (MM bbl) closure and a 50-million-barrel closure, but we cannot distinguish between 3-million and 5-million-barrel closures, or 30-million and 50-million-barrel closures. Moreover, we often cannot tell how much oil may be present in a closure having 50-million-barrel capacity—1 million, 5 million, 20 million, or even 50 million. This basic “fact of life” has profound (and often ignored) implications for explorationists.

Ranges and Probabilities

The problem is how to express our technical uncertainties realistically, and in a form by which they can be utilized in economic equations and formulae and subjected to subsequent evaluation. The most common convention in use today by modern petroleum corporations involves the formulation of a range of anticipated values for a given parameter, with probabilities— ordinarily 90%, 50%, and 10%—assigned to the values that constitute the range. For example, the geologist may believe there is a 90% chance that the anticipated pay-zone will be more than 10 feet thick, and she may be 50% confident that it will be more than 20 feet thick, but she is only 10% sure that it could be more than 40 feet thick. The same procedure may be applied to any parameter—productive area, reservoir-yield, initial production rate, decline-rate, wellhead price, drilling costs, and the like.

Figure 2

Geotechnical estimates of prospect reserves; modified after Capen, 1992.

Figure 2

Geotechnical estimates of prospect reserves; modified after Capen, 1992.

However, such estimates cannot be pulled out of the air! They must rely on objective considerations of all relevant data, especially maps, cross sections, geophysical data, borehole log interpretations, analogous production records, and the like. Moreover, geotechni-cal professionals must arrive at a final distribution for each parameter by repeated iterations—making trial estimates, examining the implications of various values in the distribution, determining through credibility checks and reality checks that the distribution makes sense, comparing it with analog data, considering the independently derived opinions of other pro-fessionals, and adjusting it repeatedly until finally becoming comfortable with all the estimates in the distribution, as constituting a “best fit” to the facts.

Table 2

Biases affecting judgments under uncertainty (modified after Rose, 1987).

Biases in Estimating under Uncertainty

Bias is a more serious problem in geotechnical forecasting than is the characteristic wide uncertainty. If the exploration company's decisionmakers consistently receive biased estimates concerning prospect value, their investment decisions will be correspondingly flawed, leading to suboptimal economic performance of the company's exploration portfolio. The stockholder will suffer. Table 2 lists the most signifi-cant biases observed in modern exploration companies (Rose, 1987).

For the exploration company, three of these biases are especially dangerous.

Overconfidence

This bias typically leads to excessively narrow ranges: Technical specialists think they know more than they really do, so they tend naturally to set predictive ranges that correspond to a confidence significantly less than the ranges they think they are setting. A common result is that, for prospect reserves forecasts, the anticipated “low-side” reserves prediction is too large and the projected “high-side” prediction is too small. The common operational symptom of the problem is that prospectors experience frequent surprises on reserve sizes of discoveries (Capen, 1976), as well as many other geotechnical parameters. Figure 2 indicates that the real ranges of new-field wildcat prospect reserves uncertainties are commonly about two orders of magnitude (powers of 10) at about the 90% confidence level.

Conservatism

This bias commonly leads to underestimates because professionals, fearing criticism if results are disappointing, may think it is worse to overestimate a project than to underestimate it. The psychology of an unexpected upward revision in project profitability is much more pleasant than a disappointing downward revision. In fact, however, either error may result in a loss to the investor (Rose, 1987). Overestimates result in overinvesting in projects, whereas underestimating may cause the firm to invest too little, or even decline to invest. Either result is a loss.

Overoptimism

This form of motivational bias leads to overestimates because of perceived career or economic self-interest on the part of the professional. The most common example in exploration is prospectors inflating estimates of prospect reserves or probability of success in order to “sell the deal” and get the prospect drilled (Rose, 1987).

Lognormality

Basis

Statistics is routinely taught to students by employing the “normal” distribution—the well-known symmetrical “bell-shaped” curve. Even though students of mathematical statistics have long known the significance of the Central Limit Theorem, the lognormal distribution in petroleum science has only gained wide acceptance—and more importantly, routine analytical application—during the past decade.

The Central Limit Theorem states that distributions resulting from the natural addition of independent random variables will be “normal”—that is, a frequency distribution will tend to take the form of the familiar “bell-shaped” curve, in which the vertical axis is ordinarily expressed as a percent of the total, and the hori-zontal axis is an arithmetic scale expressing some variable such as dimension or value (Figure 3a). Another convention for presenting the same data is the cumulative probability distribution, in which the vertical axis is 0-100% and the horizontal axis displays a dimensional variable, using an arithmetic scale (Figure 3b). The power of the cumulative probability distribution is that, conceptually at least, it represents the full universe of all possible outcomes—100%—and probability is expressed as a cumulative percent of some outcome “equal to or less than” or “equal to or more than” a particular value1. Thus the cumulative probability distribution is especially useful as a predictive tool.

A special type of cumulative probability graph paper has been developed on which the vertical probability axis is symmetrical around the 50% probability, with complementary probability intervals (40-50% and 50-60%; 30^0% and 60-70%, etc.) that are equal but of increasing spans upward and downward (Figure 4a). Maximum and minimum probabilities are 1% and 99%, rather than 0% and 100%. The horizontal axis is arithmetic. The special property of the cumulative probability graph is that a cumulative probability distribution that is perfectly normal will plot as a straight, sloping line.

Figure 3

(a) A symmetrical (normal, bell-shaped) fre-quency distribution on a regular coordinate graph. (b) A cumulative probability distribution on a regular coordinate graph. (c) A lognormal frequency distribution on a semi-log graph. (d) A lognormal frequency distribution on a regular coordinate graph. (e) A lognormal cumulative probability distribution on a log probability graph.

Figure 3

(a) A symmetrical (normal, bell-shaped) fre-quency distribution on a regular coordinate graph. (b) A cumulative probability distribution on a regular coordinate graph. (c) A lognormal frequency distribution on a semi-log graph. (d) A lognormal frequency distribution on a regular coordinate graph. (e) A lognormal cumulative probability distribution on a log probability graph.

The Central Limit Theorem also provides that distributions resulting from the natural multiplication of independent random variables will be “lognormal”— that is, the frequency distribution will tend to form a symmetrical “bell-shaped” curve where the horizontal axis is logarithmic (Figure 3c). When a lognormal distribution is plotted as a frequency curve on a regular coordinate graph (i.e., arithmetic scale), it takes the form of a severely right-skewed frequency curve (Figure 3d). Another special type of graph paper has also been developed for plotting “cumulative log probability,” in which the vertical axis is the cumulative probability scale, as described in the preceding paragraph, whereas the horizontal axis is a logarithmic scale. A cumulative probability distribution that is perfectly lognormal will appear as a straight, sloping line (Figure 3e). Figure 4b shows a cumulative log probability graph; note that maximum and minimum values on the vertical probability scale are 1% and 99%, and the horizontal axis is a log scale.

Figure 4a

Cumulative probability graph; note vertical axis is nonlinear probability scale, whereas horizontal axis is arithmetic scale.

Figure 4a

Cumulative probability graph; note vertical axis is nonlinear probability scale, whereas horizontal axis is arithmetic scale.

Figure 4b

Cumulative log probability graph; note vertical axis is nonlinear probability scale, whereas horizontal axis is logarithmic scale.

Figure 4b

Cumulative log probability graph; note vertical axis is nonlinear probability scale, whereas horizontal axis is logarithmic scale.

So natural multiplication of independent, random variables yields lognormal distributions. Most important geotechnical parameters involved with oil and gas occurrence are lognormal (Megill, 1984; Capen, 1984, 1992). Geoscientists who are aware of the prevalence of lognormality (and who constrain their estimates in the expectation of lognormality) will tend to make better predictions of most parameters having to do with oil and gas reserves (Rose, 1996c). A few petroleum parameters are exponential; fewer still are normal. Predictions of all such parameters should be constrained by the expected form of the distribution.

Field-size Distributions

Distributions of reserve sizes (projected ultimate recoveries) in fields in a given trend, play, or basin show a pronounced tendency to follow a conventional lognormal pattern:

  • just a few very small fields,

  • a great many small fields,

  • a handful of medium-size fields, and

  • a very few very large fields

The reason, of course, why field-size distributions (FSDs) are lognormal is that the parameters controlling field size are multiplicative: Field Area χ Average Net Pay Thickness χ Hydrocarbon Recovery Factor = Field Reserves. Several attributes of FSDs are noteworthy. First, they typically shift toward smaller sizes as exploration progresses (Figure 5a). Second, where many small fields (1,000 to 100,000 BOE [barrels of oil equivalent]) are included, the FSD may depart from a straight line on a cumulative log probability graph, taking a concave form at the lower end (Figure 5a), because of incomplete sampling of smaller fields. Such smaller accumulations may be incompletely represented in the population of discovered fields because of economic and technological censoring:

  1. anomalies recognized to be small may therefore not be drilled;

  2. discoveries recognized to be very small by testing may not be completed for production; and

  3. small anomalies may not be visible geotechni-cally, and therefore never drilled.

Figure 5a

Field-size distributions change as play matures.

Figure 5a

Field-size distributions change as play matures.

Figure 5b

Economic truncation causes convex curve at lower end of field-size distributions.

Figure 5b

Economic truncation causes convex curve at lower end of field-size distributions.

When FSDs are truncated at the low end to eliminate fields that are noncommercial, the resulting dis-tribution typically fits a straight, sloping line, but in the lower part (the P99%-P80% sector), the FSD has a characteristic convex shape at the lower end as a consequence of the arbitrary elimination of the small part of the sample (Figure 5b). FSDs of trends in economi-cally demanding regions, such as the North Sea or deep Gulf of Mexico, where only larger discoveries qualify for platform installation, have already been severely truncated at the lower end by such minimum economic requirements. Parent distributions in such areas contain very many uncompleted accumulations, ordinarily reported as “shows,” many of which were not even tested. If such a trend were located onshore, however, many such “shows” would have been completed as small fields. This point is elaborated further on page 80 and in Appendix F.

Construction of FSDs sheds great light on exploration of most trends and basins. They are recognized as an indispensable tool by most modern companies, serving as “reality checks” and giving essential perspective on proposed exploration ventures.

Calculating the Mean of Lognormal Distributions

Statistically, the best single representation of a log-normal distribution is the mean, or average. Because events in the low-probability end of the distribution have disproportionately much greater “weight” than in the high-probability part, the arithmetic mean of a lognormal distribution typically increases as sample size (n) increases. The statistical mean assumes a continuous distribution; that is, that n = °° and characteristically represents the largest possible mean value. On the other hand, if we simply calculate the arithmetic average of a lognormal distribution composed of a small number of values (say n = 6, or n = 10), that mean will be smaller than the statistical mean.

A practical problem with use of the statistical mean in exploration forecasting is that extremely low-probability events (less than P1%), which have extremely large values, contribute to the mean. But such events are sufficiently unlikely that we are justified in treating them as “geologically impossible.” By truncating such distributions above P1%, the resulting mean values are more realistic.

A widely used alternative is Swanson's Mean (Megill, 1984), which works well for (1) n values consistent with exploration experience (i.e., most trends do not contain an infinite number of fields), (2) distributions truncated at the upper end, beyond P1%, and (3) distributions of low to moderate variance, including distributions truncated toward the low end by economic threshold requirements. Appendix A illustrates and reviews various techniques for calculating the mean of a lognormal distribution.

Techniques for Improving Geotechnical Estimates

Exploration staffs can learn to improve their geo-technical estimating performance by using at least seven techniques (Table 3).

Geotechnical Analog Models

Since about 1950, geoscientists have increasingly developed and used “analog models”—exceptionally well-documented and well-understood examples of various “type” geologic situations—to anticipate dimensions, patterns, and associations of newly encountered (and therefore poorly documented) counterpart geologic phenomena. The first such models were strati-graphic. One example is the very well-known carbonate facies-complex of the middle Permian Guadalupean shelf-margin of west Texas and New Mexico (Newell et al., 1953; Pray, 1988). Another is the modern delta of the Mississippi River feeding into the Gulf of Mexico (Fisk, 1954; Coleman and Prior, 1982). Stratigraphers familiar with such models can often make far-reaching and insightful forecasts about newly encountered geologic situations, even though very little prospect-specific data exist. Now we also have structural models, such as the balanced structural models used to resolve and interpret seismic lines in complex thrusted terranes. Engineers routinely set up models of reservoir behavior. Economic models predict economic trends, given certain technologic and market developments. Such models effectively widen our conceptual and predictive ranges by providing flexible templates and characteristic associations that would never have been available to someone using only traditional geologic or economic principles. However, experienced geoscientists and engineers have learned that utilizing models too literally can lead to predictive errors; the lesson is to maintain flexibility in interpreting new geology based on analog models.

Multiple Working Hypotheses and Maps

T.C. Chamberlin's (1931) classic paper emphasizes the importance in scientific investigations of the conscious identification and evaluation of independent, multiple working hypotheses. To the exploration mind, it offers a disciplined method to widen predictive ranges because it forces the investigator to systematically construct and evaluate alternative interpretations of incomplete data sets. In its simplest practical form, it requires the prospector to make several possible maps of various prospect parameters, showing optimistic, intermediate, and pessimistic possible cases, or various possible structural or depositional interpretations of the geotechnical data.

Table 3

Ways to improve accuracy and build confidence in estimating.

1.USE OF GEOTECHNICAL MODELS AS ANALOGS
2.USE OF MULTIPLE WORKING HYPOTHESES AND MAPS
3.INDEPENDENT MULTIPLE ESTIMATES
“Delphi Rounds”
Team Exploration
Peer and Committee Reviews
Technical Subcommittees in Joint Ventures
4.“NATURE'S ENVELOPES”
Lognormality
Known Ranges of Parameters Plausibility Checks
5.“REALITY CHECKS”
Field-size Distributions
Historical Record
Comparisons with Worldwide Databases
Iteration and Tests for Reasonableness
6.PROPER STATISTICAL PROCEDURES
7.PRACTICE AND COMPARISON OF PRIOR PREDICTIONS WITH OUTCOMES
1.USE OF GEOTECHNICAL MODELS AS ANALOGS
2.USE OF MULTIPLE WORKING HYPOTHESES AND MAPS
3.INDEPENDENT MULTIPLE ESTIMATES
“Delphi Rounds”
Team Exploration
Peer and Committee Reviews
Technical Subcommittees in Joint Ventures
4.“NATURE'S ENVELOPES”
Lognormality
Known Ranges of Parameters Plausibility Checks
5.“REALITY CHECKS”
Field-size Distributions
Historical Record
Comparisons with Worldwide Databases
Iteration and Tests for Reasonableness
6.PROPER STATISTICAL PROCEDURES
7.PRACTICE AND COMPARISON OF PRIOR PREDICTIONS WITH OUTCOMES

Independent Multiple Estimates

When we are estimating under uncertainty, the consideration and reconciliation of independent multiple estimates of the parameter yields forecasts that are generally less biased and closer to reality than the more orthodox procedure of devoting more time, money, and technology to additional study by a single investigator. Modern exploration firms accomplish this by organizational means, such as multidisciplin-ary exploration teams, peer reviews of emerging projects, formal prospect review by a centralized exploration risk committee, or structured iterative estimating procedures called “Delphi Rounds.” Exploration joint ventures provide a practical way to achieve similar balance among participating partners who interact through technical subcommittees.

Nature's Envelopes

Most geologic and engineering variables involved in petroleum occurrence and production are distrib-uted lognormally; similarly, our estimates of such parameters are also distributed lognormally. A few are distributed exponentially; fewer still are distributed normally. By understanding the probable distribution of a given parameter, we can make estimates that honor and are constrained by the expected distribution. Such “natural envelopes” lead to reduced bias and more realistic predictive ranges. Another natural envelope is provided by the known natural ranges of parameters. For example, we know that the largest known hydrocarbon recovery factor is about 1200 barrels per acre-foot (bbl/af); also, any oil reservoir yielding less than about 50 bbl/af is likely to be physically unresponsive. All geotechnical predictions should be made in observance of such natural envelopes. By projecting distributions out to the extremes, provisional P1% and P99% values may be checked to see if such large or small values are plausible; that is, do they con-stitute values that, when honoring available data, represent credible extreme high-side and low-side values?2 If such extreme values are not plausible, the distribution must be shifted until they are.

Reality Checks

Once a preliminary estimate has been made, it should be tested repeatedly against known examples to ensure reasonability and obtain a best-fit. FSDs provide such a “reality check” against which prospect reserves estimates can be compared. The historical drilling record can provide a basis for evaluating estimates of discovery probability. Comparison of predicted prospect parameters against parameters measured in fields of similar type in the trend or basin, or against worldwide databases, can help evaluate those predictions. Comparison of the prospect's reserves variance against observed variance of analogous prospect types also provides useful reality checks (see p. 26).

Proper Statistical Procedures

Predictions of prospect parameters should be made using 80% confidence ranges, which calls for estimating high-side (P10%) and low-side (P90%) cases. Special attention should be given to the mean and median values in all parameter distributions. Because the mean reserves case is the expected outcome of every prospect, the economic viability of the mean must be assessed, so the key cash-flow model required is ordinarily based on the mean reserves case. Nevertheless, it may also be important to carry out discounted cashflow (DCF) analyses on the P90%, P50%, and P10% reserves cases, especially for large-potential, costly exploration prospects. This is especially true where the relationship between project reserves and project net present value (NPV) is not constant, such as with production-sharing contracts where the host country takes an increasing percent as field reserve-size increases, or in offshore projects where “step-functions” may be introduced because of varying costs for offshore production facilities. For such situations, what is needed is the mean of NPVs of all reserves outcomes, rather than the NPV of only the mean reserves case. Mode, or “most likely,” is a widely misunderstood statistical term that commonly leads to overoptimistic reserves forecasts, and its use by geotechnical and economic staff should be discouraged. Many explorationists say “most likely” when they are really thinking about an average, median, or “best guess” value. Accordingly, I recommend that “most likely” be expunged from use in forecasting or estimating.

Practice and Comparison of Prior Predictions with Outcomes

Discussion, justification, and refinement of geotech-nical estimates among professional staff provides an excellent way to clarify, standardize, and improve their ability to make sound and consistent estimates of prospect parameters. In addition, disciplined comparison of predictions with actual outcomes provides objective feedback as to individual, team, and organizational performance in predicting prospect parameters. This requires systematic recording of predictions and periodic review of actual outcomes over a year or more in order to acquire an adequate sample and to observe the result of learning as expressed by continual improvement in predictive performance. Commonly, this requires persistence, strong management encouragement, and monitoring, if it is to produce a permanent change in organizational values and professional behavior (Rose, 1987). Companies such as Chevron (Otis and Schneidermann, 1997), Amoco (McMaster and Carragher, 1996), Unocal (Alexander and Lohr, 1998), and Santos (Johns et al., 1998), have published compelling accounts about the improvement of exploration performance through such methods.

1Statisticians seem to prefer the “equal to or less than” convention, arguing that it honors statistical notation, and it seems to be easier for people to associate large probabilities with large values, and small probabilities with small values. However, it is not incorrect to express cumulative probabilities as “equal to or greater than.” The writer, after initially being influenced by the statisticians, has come to strongly prefer the “greater than” convention, which is used in this book. Most oil companies have increasingly come to use the “greater than” convention, recognizing four compelling reasons:
  • The exploration expression of reserves is thereby made compatible with the traditional expression of “proved reserves,” as an expression of high confidence in the presence of some specified conservative reserves value, or more;

  • Explorationists, being keenly aware that oil companies are particularly interested in large discoveries, naturally prefer to focus on the potential for large reserves—thus the “or more” expression is more natural and appropriate;

  • It eliminates the disturbing possibility that statistically naîve decisionmakers may be seduced into believing there is a 90% probability of finding the high-side (P90%) outcome or more, rather than only a 10% chance; and

  • Commercial truncation is directly expressed as the proportion of the reserves distribution that is of commercial size or larger, rather than as the (1-Pc [probability of commercial success]) expression required by the < convention.

2Although a few international companies have adapted P5%–P50%–P95% as consistently used parameters, most utilize P10% and P90%, primarily because of early published work by Megill involving applications of Swanson's Rule (see Appendix A), and because estimators seem to be more comfortable with a generally used convention such as a 10% confidence than with a smaller confidence such as 5%. Experience suggests that subjective probability estimates become increasingly tenuous at extreme probability levels (Boccia, 1996).

Figures & Tables

Figure 2

Geotechnical estimates of prospect reserves; modified after Capen, 1992.

Figure 2

Geotechnical estimates of prospect reserves; modified after Capen, 1992.

Figure 3

(a) A symmetrical (normal, bell-shaped) fre-quency distribution on a regular coordinate graph. (b) A cumulative probability distribution on a regular coordinate graph. (c) A lognormal frequency distribution on a semi-log graph. (d) A lognormal frequency distribution on a regular coordinate graph. (e) A lognormal cumulative probability distribution on a log probability graph.

Figure 3

(a) A symmetrical (normal, bell-shaped) fre-quency distribution on a regular coordinate graph. (b) A cumulative probability distribution on a regular coordinate graph. (c) A lognormal frequency distribution on a semi-log graph. (d) A lognormal frequency distribution on a regular coordinate graph. (e) A lognormal cumulative probability distribution on a log probability graph.

Figure 4a

Cumulative probability graph; note vertical axis is nonlinear probability scale, whereas horizontal axis is arithmetic scale.

Figure 4a

Cumulative probability graph; note vertical axis is nonlinear probability scale, whereas horizontal axis is arithmetic scale.

Figure 4b

Cumulative log probability graph; note vertical axis is nonlinear probability scale, whereas horizontal axis is logarithmic scale.

Figure 4b

Cumulative log probability graph; note vertical axis is nonlinear probability scale, whereas horizontal axis is logarithmic scale.

Figure 5a

Field-size distributions change as play matures.

Figure 5a

Field-size distributions change as play matures.

Figure 5b

Economic truncation causes convex curve at lower end of field-size distributions.

Figure 5b

Economic truncation causes convex curve at lower end of field-size distributions.

Table 1

Estimated geotechnical parameters.

Dimensionalthickness, area, volume, depth
Reservoirnet/gross, ϕ (porosity), K (permeability), HC-rec %, GOR, SW, etc.
Well PerformanceIP, % decline, etc.
Geochemical ValuesSR-type, TOC, maturity, composition
Migrationimpedance, dispersal, routes
Trap Integrityseal effectiveness, leakage, flushing, etc.
Timingmigration vs. trap creation
Front-end Costsland, drilling, completion, geotechnical data acquisition, overhead
Discovery Probabilitygeologic chance factors, commercial and economic reserve thresholds
Wellhead Pricelocal vs. international influences, envelope of historical real oil prices
Dimensionalthickness, area, volume, depth
Reservoirnet/gross, ϕ (porosity), K (permeability), HC-rec %, GOR, SW, etc.
Well PerformanceIP, % decline, etc.
Geochemical ValuesSR-type, TOC, maturity, composition
Migrationimpedance, dispersal, routes
Trap Integrityseal effectiveness, leakage, flushing, etc.
Timingmigration vs. trap creation
Front-end Costsland, drilling, completion, geotechnical data acquisition, overhead
Discovery Probabilitygeologic chance factors, commercial and economic reserve thresholds
Wellhead Pricelocal vs. international influences, envelope of historical real oil prices
Table 2

Biases affecting judgments under uncertainty (modified after Rose, 1987).

Table 3

Ways to improve accuracy and build confidence in estimating.

1.USE OF GEOTECHNICAL MODELS AS ANALOGS
2.USE OF MULTIPLE WORKING HYPOTHESES AND MAPS
3.INDEPENDENT MULTIPLE ESTIMATES
“Delphi Rounds”
Team Exploration
Peer and Committee Reviews
Technical Subcommittees in Joint Ventures
4.“NATURE'S ENVELOPES”
Lognormality
Known Ranges of Parameters Plausibility Checks
5.“REALITY CHECKS”
Field-size Distributions
Historical Record
Comparisons with Worldwide Databases
Iteration and Tests for Reasonableness
6.PROPER STATISTICAL PROCEDURES
7.PRACTICE AND COMPARISON OF PRIOR PREDICTIONS WITH OUTCOMES
1.USE OF GEOTECHNICAL MODELS AS ANALOGS
2.USE OF MULTIPLE WORKING HYPOTHESES AND MAPS
3.INDEPENDENT MULTIPLE ESTIMATES
“Delphi Rounds”
Team Exploration
Peer and Committee Reviews
Technical Subcommittees in Joint Ventures
4.“NATURE'S ENVELOPES”
Lognormality
Known Ranges of Parameters Plausibility Checks
5.“REALITY CHECKS”
Field-size Distributions
Historical Record
Comparisons with Worldwide Databases
Iteration and Tests for Reasonableness
6.PROPER STATISTICAL PROCEDURES
7.PRACTICE AND COMPARISON OF PRIOR PREDICTIONS WITH OUTCOMES

Contents

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