AAPG Bulletin
 Copyright ©2008. The American Association of Petroleum Geologists. All rights reserved.
Abstract
The results of exploration in individual plays show that, although discovery sizes are highly variable, their distributions have certain properties useful in assessing undrilled prospects, an example being the upper limit of P99. However, such information rarely forms an integral part of the evaluation of an undrilled prospect. Where they form part of the workflow, though, historical data can help define the natural distributions associated with reservoir properties and help constrain geological and commercial risk.
In evaluating a new prospect, deterministic volumetrics can be calculated for a high case, but the probability of encountering this is, by itself, mostly guesswork; low volumetrics cases are even more difficult to constrain. Consequently, probabilistic methods have become the standard way of dealing with uncertainty in exploration. However, there is a problem in defining the trap size or volume of hydrocarbonbearing gross reservoir (hcbGRV), specifically the distribution defined by the combined cumulative probabilities of the position of seals, reservoirs, and fluid contacts because, prior to drilling, no direct samples of these surfaces are given. Unfortunately, this problem does not have a solution, so we have developed a quality assurance tool that uses deterministic inputs to check the reality of probabilistic outputs. The tool is called “real point resource iteration” (RPRI) and is primarily aimed at improving consistency in volumetrics prediction.
RPRI uses objective criteria to calculate two deterministic cases from which a fulldiscoverysize distribution is created. The results are then iterated with simple statistics and information from historical data. One of the key elements of the technique involves defining standard hcbGRVs based on the depth of the last closing contour relative to the culmination. The method is quick, transparent, and repeatable and helps avoid overoptimism using empirical observations to predict realistic low case volumes. The outputs are analogous to those obtained from probabilistic techniques, meaning they can easily be compared and adjusted. RPRI can also be used to produce maps and reservoir parameters for specific probabilistic outcomes, providing real cases for input to economics calculations and planning.
Manuscript reviewed by special issue editor
Dave Quirk is an exploration geoscientist at Maersk Oil in Denmark and has previously worked for Shell, Oxford Brookes University, Burlington Resources, and Hess Corporation. He received his B.Sc. degree from Liverpool University, U.K., in 1984 and Ph.D. from Leicester University, U.K., in 1988. His current interests include salt tectonics, the geology of the Isle of Man, and risk and uncertainty.
Rick Ruthrauff is a petroleum engineer working on decision analysis at Hess. He has a diverse background in exploration, exploitation, production, reserves, and operations at Hess and Texaco, and one year of LNG projects at El Paso Corporation as a contractor. He received his B.S. degree in chemical engineering from the University of Pittsburgh in 1978.
INTRODUCTION
Finding significant quantities of oil and gas becomes ever more challenging. Nevertheless, there seems to be no shortage of outlines on maps showing prospects and leads in acreage licensed for exploration. Which ones are worth drilling, however, may not be immediately obvious and is the subject of extensive evaluation in exploration companies. One of the key factors in the drilling decision is the potential size of the prize, which, of course, is uncertain at the predrill stage.
This article presents a process aimed at helping improve consistency and predictability in volumetric assessments. It is divided into two parts, addressing the following questions:

How can historical data on discoveries be used to improve volume prediction in exploration?

Is there a simple way of checking the validity of probabilistic volumetrics in undrilled prospects?
LESSONS FROM HISTORICAL EXPLORATION DATA
Before discussing the use of historical data, we summarize briefly the statistical theory that will be used in the analyses; more detail can be found in Quirk and Ruthrauff (2006).
Natural Distributions
The central limit theorem (Trotter, 1959) shows that random samples of average values from a natural population, such as porosity in a reservoir, will tend toward a normal distribution around a central mean, equal to the median and mode (Figure 1a). Theoretically and empirically, a normal distribution best represents the uncertainty associated with any new sample of a geological parameter, for example, in a proposed exploration well (Murtha, 2001). A normal distribution can be plotted as a straight line by transformation to a domain known as the cumulative standard normal distribution (Figure 1b) using the formula where v = value belonging to the normal distribution, σ = standard deviation of the distribution, μ = mean of the distribution, and NORMSINV(1 – [Pn/100]) = percentage reverse cumulative probability of the value converted into a standard statistical function known as the inverse of the standard normal distribution (reverse cumulative probability, Pn, means there is an n% chance that any new sample is at least as large as v). The symbols σ and μ are constants representing the slope of the straight line and the intercept of the y axis or median value, respectively.
With a statistically valid number of samples from a normal distribution (typically 20 or more random data points), a natural geological population can be plotted in the cumulative standard normal domain (Figure 2) by distributing the ranked data in equal divisions between 0 and 100% (fractile percentages).
In contrast to normal distributions, values used to represent the size of a prospect, such as recoverable resources, gross rock volumes, areas, barrels per acre foot, and hydrocarbon column heights (for example, Niemann, 1998) are products of natural populations whose multiplicative distributions are skewed so that the mean is larger than the median and the median is larger than the mode (Figure 3a). However, natural logarithms of the values form normal distributions and these are consequently known as lognormal (Aitchison and Brown, 1957). Like normal distributions, any lognormal distribution can be plotted as a straight line in the cumulative standard normal domain (Figures 3b, 4) using the formula Because σ represents the slope of the straight line, it is a function of the difference between the upside and downside of uncertainty and can therefore can be rewritten as f(log_{e}P10/log_{e}P90). Likewise, μ represents the median value or P50, which is equivalent to √(P10/P90). In other words, with values for P10 and P90 (or, for that matter, any other two cumulative probabilities), this formula can easily be solved (Quirk and Ruthrauff, 2006; Figure 3b).
Discovery Size Distributions
The sizes of inplace or recoverable resources discovered in mature plays are lognormally distributed (for example, Figure 5) although some discrimination in the sampling of very small traps is present. Unfortunately, it is easy to produce invalid statistics by wrongly sampling the distribution (Quirk and Ruthrauff, 2006). To avoid this, it is important to (1) include data from only one play; (2) use all discoveries in the play not just commercial fields; and (3) define the lognormal trend only with reliable data, namely, those discoveries constrained by appraisal, development, or production information, although all data are needed to determine fractile percentage and ranking (Figure 6).
We have analyzed more than 100 different plays across the world in this way, and all those with more than 20 discoveries show a good lognormal trend between P99 and P1. To prevent the statistics being biased by extreme upsides, as well as to ensure that the mean of the distribution is similar to the average discovery size, it is recommended that the lognormal trend is truncated at P99 and P1. Empirically, the mean of the distribution between P99 and P1 (mean^{P99–P1}) is generally within 20% of the average discovery size (total recoverable resources discovered divided by number of discoveries) and, unlike the mean for the untruncated distribution, typically has a narrow range of cumulative probability, around P25–P20 (Table 1), equating with a 1in4 to 1in5 chance that a discovery is larger than mean^{P99–P1}, a useful fact for qualitychecking purposes. The untruncated mean is larger than mean^{P99–P1}, sometimes significantly larger.
Quirk and Ruthrauff (2006) have shown that mean^{P99–P1}, the P10 to P90 ratio, the total number of discoveries, and the chance of making a discovery are unique to each play. Nevertheless, most plays show certain common limits to P99, P50, risked mean^{P99–P1}, chance that a discovery is commercial, and total amount of recoverable resource between P99 and P1 (Table 1), some of which can be used as reality checks for estimations of recoverable resource in new prospects. Further analysis shows that exceptions in a positive sense may occur in new plays (less than 20 discoveries) and plays with direct hydrocarbon indicators (DHIs), where small traps have effectively been screened out. Exceptions at the other end of the spectrum occur in certain onshore plays with good infrastructure, where traps significantly smaller than usual have been targeted (Quirk and Ruthrauff, 2006).
Differences between plays in many of the key metrics such as P99, mean^{P99–P1}, and the P10 to P90 ratio are related primarily to the range of size in individual traps, true also at different stages in the maturity of a single play as the bigger prospects are commonly drilled first.
Exploration Risk
One of the more sobering statistics to come out of the analysis of historical data is that, on the average, only a little more than half of all discoveries are commercial in a typical exploration play (Figure 7; Table 1). In other words, although small subeconomic discoveries are never sought, they are an inescapable reality of exploration and therefore need to be acknowledged in prospect evaluations (Capen, 1992).
Quirk and Ruthrauff (2006) have shown that very small discoveries are avoided during the early stages of exploration in some successful frontier plays because, initially, only the biggest features are selected, i.e., P99 for certain immature plays can be significantly larger than usual, also reflected in a smaller P10 to P90 ratio (Figure 8; Table 1). The flip side of exploring new plays is that the geological risk is generally much higher, although sometimes when a new play in a proven basin is identified, the best of both worlds can ensue (for example, Doré and Robbins, 2005).
Although the size of discoveries decreases over time, the discovery rate in many plays does not change significantly (see Figure 9), which may in part explain why the industry seems to be relatively good at estimating the chance of geological success in proven fairways (for example, Otis and Schneidermann, 1997).
All in all, it appears that it is important for exploration companies to invest at least as much technical effort in volumetrics evaluation as they do in risk assessment (cf., Hesthammer and Boulaenko, 2005).
METHODS OF CALCULATING PROSPECT RESOURCES
Background
Exploration programs usually underperform because of overoptimistic assessments of the size of prospects (Rose, 1987; Capen, 1992; Campbell, 2001; Rose et al., 2003). Uncertainty is an inescapable part of exploration, but with realistic predrill assessments, there would be an equal chance that a prospect improves or deteriorates with additional data and further interpretation. Instead, volumes estimated for an exploration prospect usually decrease over time as technical work continues, rarely increasing. Does exploration fail to deliver on predictions because uncertainty in the subsurface is so great or because evaluation processes tend to have a bias toward highside models? In either case, this section of the article aims to show that, although the potential ranges of geological properties in undrilled targets may at first seem dauntingly large, realistic assessments of prospect size are achievable using a systematic quality control process.
Our experience is that volumetric assessments of the same predrill prospect made by different interpreters and by different companies commonly vary by more than a factor of two, despite internal quality assurance processes. The problem seems to revolve around a few human characteristics: (1) a subjective approach to probabilities, (2) an inclination toward the optimistic, (3) a preference for narrow rather than broad ranges, and (4) a tendency to stick with and embellish single scenarios. The latter two points are in part compounded by ever improving technology and increasing amounts of data that may lead to a certain degree of overconfidence in one particular model. Despite advances in seismic imaging and sophisticated stochastic analyses, the degree of uncertainty involved in subsurface prediction is such that relatively simple concepts and wide distributions generally describe prospects best because they contain fewer biases and encompass the greatest range of possibilities.
Reliable exploration decisions depend on evaluations that are internally consistent and objective, deliver what they predict (based on a valid number of tests), are valued correctly, and have been conducted efficiently and in a timely manner. Assuming this is true, then the straightforward question “how big is the prospect?” is valid, but as will be discussed now, the preferred answer is “there is a probability of X% that a discovery will contain at least Y million barrels of oil (or gas equivalent).”
Probabilistic versus Deterministic Volumetric Estimations
Exploration volumetrics can be estimated either deterministically or probabilistically (Kaufman, 1963; Smith, 1970; Davidson and Cooper, 1976; Megill, 1984; Capen, 1992; Murtha, 2001). Advantages and disadvantages of each method are summarized in Table 2, the main differences being that probabilistic techniques attempt to incorporate uncertainty into the analysis using distributions as inputs, with the apparent drawback that the outputs are somewhat removed from real cases, whereas deterministic techniques use actual geologicalengineering scenarios but without a simple means of calculating the chance of finding a certain size of resource.
Despite the ascendance of probabilistic methods in resource estimations, it commonly appears that the estimated range in prospect size is biased to the upside (Capen, 1992; Rose, 2001), with the downside effectively truncated (Figure 10), such that exploration programs frequently underperform (Rose, 1987; Campbell, 2001). Indications that the probabilistic evaluation of a new prospect may be problematic include the following:

The distribution of potential recoverable resource is symmetric (mean^{P99–P1} ≈ P50) instead of lognormal (skewed) as should result from the multiplication of geological distributions.

Mean resource is greater than the historic average for the play, assuming that the largest traps were targeted first (Root and Drew, 1979).

P99 is larger than historical data supports.

Most of the distribution is economic, assuming that similar commercial conditions prevail over time.
In fact, the common observation that smaller than expected volumes are encountered in an exploration well can be caused by a multiplicity of reasons (Figure 11). Generally, only in cases where a prospect has a large unequivocal DHI and a high degree of seismic resolution are very small discoveries avoidable.
Disappointing drilling outcomes can lead to a lack of confidence in probabilistic volumetrics among decision makers whereas deterministic techniques can more easily be related to a geological model and a map. Hence, it is useful if probabilistic and deterministic techniques are not treated as mutually exclusive.
The Fundamental Difficulty in Assessing Prospect Size
Although probabilistic methods have been adopted by most oil companies, it is still possible to introduce overoptimism by biasing realistic input ranges with unrealistic distribution models. For reservoir parameters, statistical information from existing well data can serve as a useful guide (for example, Figure 2). However, the main and mostly unspoken issue in exploration is that there are no direct samples of geological populations defining trap size, specifically the volume of gross hydrocarbonbearing reservoir. The probabilities and distributions of surfaces defining the top and base of the reservoir interval and the position of hydrocarbon contacts are unknown, a problem compounded by uncertainties in the accuracy and precision of seismic picks, seal position relative to reservoir top, depth conversion, and oil or gas versus mixed charge (Figures 12, 13). In other words, hydrocarbonbearing gross rock volume (hcbGRV) is not only highly uncertain but also unconstrained in probabilistic terms, leading to significant differences in the mode, median, and mean values associated with trap size. This issue is serious because variance in this parameter usually has a far larger effect on prospect size than any specific reservoir property, as will be shown below.
Example of Sensitivity of Prospect Evaluation to Trap Size
To illustrate the trap size problem, a series of probabilistic volumetric calculations were run for the same nonDHI oil prospect (V) illustrated in ⇓⇓Figure 14. The top and base of the reservoir interval are clearly imaged on highquality 3D seismic data, and 21 wells have already tested the play, meaning that reservoir parameters are relatively well constrained (for example, Figure 14c), and the presence of a gas cap is considered unlikely.
A base case Monte Carlo simulation was run on prospect V assuming a lognormal distribution for hcbGRV. On the most likely depth map (Figure 14a), the contour representing maximum closure, here called the last closing contour or LCC, was taken to correspond to P5 hcbGRV (Figure 14b) based on the average of a poll of 20 interpreters (the range was actually P50 to P0.5). A P90 hcbGRV was defined by a contour one third of the depth between culmination and the LCC, again based on the average choice of 20 interpreters. Normal distributions were used for all reservoir parameters with P90 and P10 values based on statistical information from existing wells in the play (for example, Figure 14c).
Note that depth contours are used here as a convenient way of referring to different potential sizes of trap fill so that changes shown in, say, the cumulative probability of LCC represent variations in the distribution of gross rock volume lying above the hydrocarbon water contact, be these because of differences in the interpretation of seismic reflections, time to depth conversions, amount of charge, thickness or lateral extent of the gross interval, position of the top seal relative to the top of the reservoir, capacity of the seals, or likelihood of stratigraphic trapping (Figures 11, 12, 14b).
The mean^{P99–P1} probabilistic outcome for the base case in prospect V was a recoverable resource of 46.4 million bbl. Individual changes were then made to the input distributions or cumulative probabilities of either hcbGRV or a single reservoir parameter to show its relative importance in quantifying the size of the prospect (see Table 3).
The biggest change in prospect size from the base case occurs with a switch in the model of trap size or hcbGRV from lognormal to another type of distribution (Table 3). Thus, using the same contours to define P5 hcbGRV and P90 hcbGRV, a normal distribution produces a mean^{P99–P1} recoverable resource almost twice that of the base case (84.8 million bbl compared to 46.4 million bbl) and a smaller P10 to P90 ratio (23 versus 43); a triangular distribution shows an even bigger difference. Furthermore, if the probability associated with a depth contour is changed, even if only slightly, a significant change in the resultant recoverable resource occurs. For example, the difference in the mean between assuming that LCC represents P1 and assuming that LCC represents P10 is 38.0 million bbl (from 29.2 million bbl to 67.2 million bbl). In contrast, changes in distributions of reservoir parameters make no more than 15% difference (Table 3).
Considering the entire distributions represented in Table 3, the biggest relative difference in probabilistic estimations occurs in lowside cases, for example, the variation between the smallest and largest P90 value is five times, whereas the range in P10 and mean values is only three times, the extremes once more associated with differences in trap size (or hcbGRV). The main effect this has is on the chance of discovering an economic field size, apparently much lower in a probabilistic evaluation using a lognormal distribution of hcbGRV than other distributions documented in Table 3.
Although the depth of the contour corresponding to P50 hcbGRV varies relative to culmination by no more than ±23%, the recoverable resource differs by a factor of 0.6 smaller to 1.9 larger than the base case. This is because a small change in depth has a much larger effect on hcbGRV (Figure 14b), a fact that cannot be avoided, but one that may be overlooked, usually out of necessity, there being no statistics to constrain the probabilistic values associated with trap size.
These examples underline the dominant effect that hcbGRV has relative to other parameters in prospect volumetrics and the difficulties one has in assigning or qualitycontrolling distributions and cumulative probabilities of hcbGRV. In comparison, differences caused by distributions and probabilities of reservoir parameters are relatively minor and are easily checked against statistics from geological data for the play or from analogs. In other words, trap size models are commonly the key reason for discrepancies in the size of individual prospects between different interpreters and different companies, a situation commonly evident in farmin situations. Certain distributions of hcbGRV produce more positive results than others (Table 3), but unfortunately, it cannot be verified which assumptions are best nor is it possible to determine directly whether probabilities assigned to depth contours are reasonable. With this in mind, individual companies do need to standardize their approach in trap size definition to ensure that evaluations of recoverable resources are relatively consistent across a portfolio of prospects.
Quality Control Using a Different Volumetrics Approach
Noncommercial discoveries commonly occur when the exploration model fails because of one or more negative outcomes (Figure 11), the combined chances of which are difficult to predict. It is therefore virtually impossible to calculate the probability of low case volumes directly. Instead, probabilistic techniques attempt to deal with the problem by randomly sampling a range of values, including downsides. However, as shown above, consistency is difficult to achieve, and the outputs are more difficult to visualize without referring to specific deterministic cases. Therefore, in an effort to constrain the standard probabilistic estimates, a quality control tool has been developed that combines both volumetrics techniques, creating a full probabilistic distribution by extrapolation from specific deterministic highside cases. The constructed distribution is then checked and iterated using historical information, particularly to improve the lower half of the distribution.
An advantage of the technique is that it partially sidesteps the issue of assigning a distribution to hcbGRV, providing an independent check on probabilistic methods where an assumption on the distribution has to be made. The method originally arose from the realization that, while a reliable way of quantifying uncertainty is needed, most people actually have a deterministic mindset, often thinking in specific scenarios instead of broad ranges. Hence, it was found useful to integrate deterministic calculations with the probabilistic methodology in the form of a quality control tool, overcoming some of the disadvantages of either technique when used alone (Table 2).
REAL POINT RESOURCE ITERATION
As has been shown previously, the sizes of discoveries in individual plays tend to form lognormal distributions and so too should the probabilistic range in potential size of recoverable resource in an undrilled prospect (Capen, 1992; Murtha, 2001; Quirk and Ruthrauff, 2006). Furthermore, lognormal distributions can be defined with only two values of known probability. Therefore, if two sizes of recoverable resource can be determined, each with a specific cumulative probability, then the entire distribution can be reconstructed (for example, Figure 15). This idea has been developed into a volumetric estimation technique called real point resource iteration (RPRI) (Table 4).
Two requirements have to be met before the idea can be successfully applied. The first is ensuring that different interpreters define input values in a consistent way, particularly concerning volume of potential hydrocarbonbearing rock. The second is assigning and standardizing the cumulative probability of specific deterministic outputs, a process that involves extensive testing of different probabilistic and deterministic volumetrics in a variety of exploration prospects.
RPRI Applied to Structural Prospects
Interpreters can usually come close to agreeing on two depths in a structural trap (1) the culmination, crest, or highest point of the trap and (2) the last closing contour (LCC, maximum closure, or apparent spill point). Even with different interpretations and depth conversions, the area enclosed by LCC and the difference in height between this and the culmination (i.e., the closure height) rarely vary more than ±25% between interpreters. Therefore, one way of consistently defining the size of the trap is to use the LCC on the most reasonable depth map. In the case of a prospect where the top seal is a distance above the top reservoir, the chance that a discovery is so small that only the waste zone contains hydrocarbons can be accounted for in the prospect risk; also the depth of LCC should be defined by the spillpoint at the base of the top seal (Figure 12). In prospects where the height of the hydrocarbon column is limited by seal effectiveness instead of structural closure, the maximum reasonable column height defines the LCC, and in prospects with unequivocal DHIs, the maximum reasonable outline of the DHI should be used.
With culmination and LCC identified, there are various ways of standardizing contours to define hcbGRV, which can then be used as inputs to deterministic base cases. We have tested many different trap size scenarios in deterministic and probabilistic models and have found that simple assumptions tend to give fairly consistent results. One that works well for a structural prospect is a contour lying at five ninths (56%) the vertical distance from culmination to LCC to define an hcbGRV called P50 hcbGRV (⇓Figure 16). This appears to imply that a uniform probability of encountering a hydrocarbon water contact between culmination and a contour 10% deeper than LCC is present. However, it is actually just a convenient way of standardizing how uncertainty is dealt with in the size of a hydrocarbonbearing trap caused by variations in the amount of fill, top, or base of reservoir, etc., which, on an empirical basis, produces volumetrics that are reasonably consistent in a large spectrum of undrilled structures. In other words, the standard contours are not based on any particular assumed distribution of potential gross pay, but instead P50 hcbGRV serves as a suitable median point for trap volume defined by two fairly unequivocal reference points: culmination and LCC.
Nonetheless, in the method described in Table 4, the implicit assumption is that LCC delineates an hcbGRV close to the maximum potential trap size and that the distribution is not significantly skewed. Before using RPRI, a company would need to define its own standard contours, cumulative probabilities, and distributions according to its own models. The one suggested here is no better or no worse than many other assumptions on hcbGRVs or closure areas but has the advantage that it is simple to apply, thus facilitating consistency.
After defining LCC and P50 hcbGRV, the next step is to define at least two standard deterministic values of recoverable resource. The most straightforward to calculate is a P50 volume, which is simply the product of P50 input parameters (Murtha, 2002). In this case, P50 hcbGRV is used for trap size, and P50 reservoir properties can easily be estimated from statistical analysis of wells in the fairway (for example, Figure 14c) or, in an immature play, from analogs. The result of multiplying these deterministic inputs is a median recoverable resource, here called deterministic P50 (DP50), which may be of marginal economic value based on the previous observation that only about half of the discoveries are large enough to have been economic before drilling (Figure 7).
A second calculation can be made for a highside recoverable resource case, which is often the commercial justification for exploration. For simplicity, it has been assumed that the product of P50 hcbGRV and P10 reservoir parameters produces a deterministic resource number that is approximately equivalent to a probabilistic P5 value, termed “deterministic P5” or DP5, an unlikely size of discovery but still feasible. We have made numerous tests of this calculation and have found that DP5 generally falls in the range P10 to P1 when similar inputs are used in probabilistic volumetrics, so the assumption that the DP5 is similar to probabilistic P5 is valid based on empirical evidence.
With these two deterministic values, equivalent to P50 and P5, a full distribution can be constructed in the cumulative standard normal domain (Figure 15). However, as a check, it is useful to determine a third recoverable resource lying somewhere between DP50 and DP5, a size of discovery that is not unreasonable if the original exploration model holds true. In this respect, multiplying LCC hcbGRV with P50 reservoir parameters empirically produces a result that lies somewhere close to P20 in reliable probabilistic estimations and is therefore called deterministic P20 (DP20). DP20 is usually fairly close to the mean^{P99–P1} resource value for the prospect as this commonly has a cumulative probability somewhere between P35 and P20 (Table 5).
Note that although the discussion here concentrates on volumetrics determined by the product of standard hcbGRVs and the appropriate net to gross ratio, the calculations can instead be made using areas enclosed by the contours associated with P50 hcbGRV and LCC hcbGRV multiplied by the P50 or P10 net reservoir thickness and P50 or P10 shape factor. In fact, we strongly recommend that volumetric estimations for any prospect should try both methods to check for inconsistencies (Table 5). It is straightforward to resolve any differences with RPRI but usually difficult when only pure probabilistic methods are used.
Reality Checks on Volumetrics Results
Now that a distribution can be calculated using RPRI, reality checks can be made similar to those listed in Table 5, based mostly on analyses of discovery sizes from different plays made by Quirk and Ruthrauff (2006). In particular, as the lowside part of the curve has been created by extrapolation from highside cases, one needs to check that P99 is reasonable. The importance of historical data in this quality check (QC) process comes from the fact that any new discovery belongs to a discovery size distribution for that play. A large untested trap may legitimately have a P99 value higher than the historical value for the play, but it should be checked that the smallest discoveries in the distribution were made on proportionally smaller prospects.
Usually, one or two iterations of the parameters used to calculate DP50 and DP5 are required before the results are in line with the checks shown in Table 5, such as reviewing the probability of reservoir net to gross or the exact depth of LCC. Parameters such as P99, mean^{P99–P1}, cumulative probability of mean^{P99–P1}, and the chance that a discovery is commercial are important to check for consistency and identify possible exceptions. Note that DHIconstrained prospects, frontier plays, and onshore targets close to infrastructure may fall outside the usual constraints because of different exploration selection and sampling criteria.
RPRI Example
⇓Figure 17 is a worked example of the methodology, prior to quality checking, applied to the structural prospect shown in ⇑⇑Figures 14 and ⇑16. P50 hcbGRV and LCC hcbGRV were defined as described above and in Table 4a, P50 and P10 reservoir parameters were estimated using statistics from the 21 wells that have tested the play, and the minimum economic field size was based on a preliminary estimate. The initial results showed some inconsistencies when reality checks were made, specifically P99 appeared too large compared to historical data from the play, the chance of making an economic discovery seemed too high and the probability of DP20 was too low. Therefore, the inputs and results were iterated such that LCC was picked 25 m shallower, the depth of the culmination was better constrained resulting in a slight change in P50 hcbGRV, minor adjustments were made in reservoir parameters, and a new minimum economic field size was calculated based on engineering scenarios for DP50, DP20, and DP5 (Figure 18a). The final results are shown in Figure 18b, where all checks and QCs are satisfied.
The exercise helped constrain probabilistic analyses of the same prospect (Table 3) such that the base case using a lognormal distribution of hcbGRV appears to be too pessimistic, primarily because it significantly skews the distribution of trap size. Thus, the P50 depth contour is significantly shallower than in other distributions, which in turn has a disproportionately negative effect on recoverable resource.
Table 6 compares three of the probabilistic analyses from Table 3 with the resource estimations from RPRI (⇑Figure 18). Within the range P90–P10, RPRI provides resource numbers lying somewhere between probabilistic analyses using a lognormal distribution of hcbGRV and those using a symmetrical distribution such as normal or uniform. Both P99 and P1 are larger in the RPRI example than in the probabilistic analyses, but they do fall in the range of current statistics for the play (P99 of 1.8 million bbl) and P1 values estimated using other hcbGRV assumptions (Table 3). Further fine tuning of the RPRI estimation is possible, but as a quality checking of the probabilistic analyses, it is adequate as is.
Depending on which assumptions are recommended in a company for resource estimation of exploration prospects, an interpreter may wish to review probabilistic inputs on the basis of a comparison of the outputs with RPRI results, particularly if this helps think about the depth contours used to define trap size. The advantage of using RPRI is that the quality assurance process can be applied quickly and at an early stage in the evaluation.
Application of RPRI to Other Situations
RPRI can also be applied to stratigraphic or poorly imaged prospects and those with an unequivocal DHI using adaptations to the way hcbGRVs are calculated (Table 4b, c).
In the case of a stratigraphic prospect or poorly imaged prospect, the interpreter can decide on a reasonable maximum depth below which it is unlikely hydrocarbons are trapped because of seal constraints, closure limits, or dry wells. This maximum contour can then be used as an equivalent to LCC, and thereafter, other contours associated with hcbGRVs can be calculated in the same way as those of a structural prospect. Thus, the P50 hcbGRV may be defined by the contour 56% of the depth between culmination and LCC. Using P50 hcbGRV, LCC hcbGRV, and estimates of P50 and P10 reservoir parameters, then DP50, DP20, and DP5 can be calculated as before (Table 4). Usually, the mean size of such a prospect can be large (albeit balanced by a lower chance of success), so the definition of what is a reasonable maximum depth needs to be objective, not optimistic.
In a prospect with an unequivocal DHI, the recommended RPRI procedure to standardize trap size is slightly different. Assuming it is robust and well resolved, then the absolute shallowest possible contour for the anomaly (DHI minimum) can be defined and treated in the same way that the culmination is in a structural prospect. With the same logic, a reasonable maximum outline for the DHI equates with the LCC, and thereafter, P50 hcbGRV is determined from the outline or contour equivalent to a depth halfway between the DHI minimum and LCC. From these, DP50 and DP5 resources can be calculated in the same way as structural and stratigraphic prospects (Table 4). It has, however, proved more difficult to get consistency in DP20, probably because the distribution is so much narrower, so it is not used by us in DHIdefined prospects.
We have not tested RPRI on many DHIs and improvements may emerge in the method to define trap size probabilities (cf., Citron and Rose, 2001). For example, with the method described in Table 4c, it is sometimes difficult to build realistic lowside cases on DHIdefined prospects without severely reducing P50 reservoir parameters such as net to gross, hydrocarbon saturation, and recovery factor, during the iteration process. One reality check that helps improve confidence in the results is to compare the yield parameter million barrels per km^{2} (or bcf per km^{2}) for the DP50 resource estimation to that of discoveries in the same play or analogs and then iterate where it is necessary to get results consistent with the historical information (Table 5).
Similar probabilities have purposely been used in Table 4a–c to keep things as simple as possible while remaining aligned with results from pure probabilistic techniques. It is worth reiterating that enough latitude is present in RPRI for different assumptions in probabilities to be used so long as consistency is maintained. The essence of the technique is to produce a minimum of two standard deterministic volumetric calculations with agreed probabilities that can then be used to construct an entire prospect size distribution (Figure 15) for quality controlling results from pure probabilistic techniques (Table 6). The validity of any probability or distribution can be tested by repetition and comparison with other estimations on many prospects and by reality checks against historical data (Table 5).
So far, we have discussed the application of RPRI to recoverable resources, but it is also possible to use the technique for calculating inplace volumes, leaving consideration of recovery for later when dealing with specific discovery scenarios. The disadvantage of this approach is that it is more difficult to integrate uncertainty in recovery when it forms part of a separate step. We prefer to calculate inplace volumes as an intermediate stage in the RPRI process to help build engineering scenarios before a final recoverable resource calculation is completed similar to that outlined in Table 4.
Advantages of RPRI
Should RPRI replace pure probabilistic techniques? RPRI produces distributions of recoverable resource for a prospect by extrapolation from realistic highside cases and helps develop discipline in the way the sizes of prospects are defined. One benefit of this is that maps and reservoir parameters specific to any probability of recoverable resource are a direct and transparent product, meaning scenarios are available on which economics and commercial decisions can be based. However, the assumptions made to get these are still assumptions, even if the results are consistent. Furthermore, it is not difficult to standardize ways of defining inputs to probabilistic estimates. All things considered, RPRI is better applied as a control instead of a replacement for other techniques.
To summarize, using RPRI as a check on probabilistic outputs leads to the following advantages:

It incorporates some of the advantages of deterministiconly techniques (Table 2).

It can be easily understood, is straightforward to apply, and does not require extra training or highly prescriptive corporate rules (Table 4).

It helps interpreters focus on parts of the prospect model that they have most confidence in whilst allowing them to check other more subjective calls on probabilistic distributions and probabilities (Figures 17a, 18a).

It fosters consistency in prospect evaluations by standardizing the way uncertainty is dealt with, particularly in the size of hcbGRV (⇑Figure 16).

It mitigates against overoptimism by statistically accounting for lowside outcomes (Figure 15) and formalizing the integration of reality checks into volumetric assessments (Figures 17b, 18b).

It makes it easy to iterate results and allows for quick resolution of differences between volumetrics calculated using gross reservoir times net to gross and volumetrics calculated using area times net reservoir.

It helps build real maps and reservoir data for direct use in engineering studies, project decisions, commercial analysis, and in selecting well locations (⇑Figures 16, ⇑18).

It allows individual prospects in a portfolio to be quality checked rapidly (Table 5) and can be used to produce specific cases for peer review.

It facilitates rapid construction of probabilistic resource distributions from limited data, for example, during farmin evaluations (Figure 15).

It can easily be integrated with other procedures such as economics programs.

It produces a limited number of standard measures of size for each prospect (Figure 18b).
Expanding on point 7, because of the fact that simple distributions can be created from deterministic input values, it is possible to backcalculate standard parameters for any cumulative probability or size of recoverable resource. This means that a simple map and reservoir properties can be produced for specific probabilistic cases for engineering, economics, and planning purposes such as a minimum economic field development (Figure 19). This process is more complex with pure probabilistic evaluations, as any specific volume or probability can be associated with numerous potential scenarios.
One further advantage of RPRI is that the validity of predictions can easily be checked by using postdiscovery volumetrics to backcalculate predrill probabilities and parameters to compare with what was actually found in a successful well. In the long run, this should help improve predictions in probabilistic volumetrics, particularly in a play likely to be tested multiple times.
Comparison of RPRI with Probabilistic Estimations
Several hundred RPRI calculations have been run by the authors in a wide range of different play types and matched directly against probabilistic volumetrics produced from similar input values (for example, Table 6). The results are comparable, particularly with respect to highside resource numbers (for example, mean^{P99–P1}, DP20P20, and DP5P5). However, a difference is usually detected in the lowside volumes such that P99 calculated from RPRI lies somewhere between probabilistic P99 and probabilistic P90, and the P10 to P90 ratio is consequently smaller. The main reason for the discrepancy is that, even if hcbGRV is fixed with the same LCC and culmination constraints, the trap size distributions assumed in the two approaches are usually different. The difference is regarded as insignificant but nonetheless underlines the importance of using reality checks such as historical P99 for the play in question. It also shows that it is worth experimenting with different distributions and probabilities before RPRI is adopted as a standard qualitychecking tool.
Here, it is worth noting that RPRI can be applied in a slightly different way using only one deterministic value, such as DP5, to fix the upside and historical P99 for the play to fix the downside. This method can be applied rapidly in meetings or farmin situations as a quick check on resource numbers. However, with more time, it is still recommended that at least one other deterministic number is calculated, for example, DP50, to ensure that consistency is present in the trap size and reservoir parameters estimated specifically for the prospect.
This article does not advocate that existing volumetric methodologies are dropped in favor of RPRI, but in an exploration company looking to improve its predictions of prospect size, it is recommended that certain standard deterministic calculations are made for quality check probabilistic estimates. Alternatively, in companies that have not adopted probabilistic techniques, RPRI can be used to attach probabilities to deterministic numbers.
Examples of Successful RPRI Application
Although still in its early stages, two companies are currently testing its application. It is too early to report an improvement in the accuracy of prediction, but there is certainly more confidence in the consistency of resource assessments in prospect portfolios where RPRI has been used.
In summary, and to answer a question posed previously in the article, provided that the uncertainty is dealt with in a simple and transparent way and then rigorously crosschecked against historical data, consistent and reliable estimates of the sizes of future exploration discoveries should indeed be possible.
CONCLUSIONS
From the analysis of exploration discovery data in individual plays, several useful constraints can be applied to prospect evaluations:

All plays with more than 20 discoveries show lognormal distributions of discovered volumes

Most of these plays show predictable upper limits to P99 recoverable resource

Most of these plays also show similar cumulative probabilities of minimum economic field size and of mean resource between P99 and P1 (mean^{P99–P1})
Because of the inherent uncertainties in assessing the distribution of hcbGRVs in undrilled prospects, there is value in having a quality control tool for probabilistic resource estimates. We observe that information from deterministic models can help constrain the upside end of a resource distribution and historical data can help constrain the downside. A distribution of recoverable resource can be constructed for any prospect using two deterministic values of known probability (for example, P50 and P5) with a method known as RPRI. Statistical information is used to check the validity of the lower half of the distribution, which is iterated where necessary. The main application of RPRI is in obtaining consistency in the evaluation of prospect size. It is simple and quick to apply and helps avoid overoptimism. One particular advantage of the technique is that real maps and specific reservoir information are tied directly to cumulative probabilities of recoverable resource, of use in predrill commercial analysis and postdrill review.
Acknowledgments
The authors thank the many colleagues at Maersk Oil, Hess, and other organizations who have contributed to the ideas developed in this article, in particular Matt Docherty, Kenneth Nielsen, Lene Madsen, Danny Schwarzer, Tim Tranter, Ross Ensley, Mark Parsley, Tim Cordingley, Steve Massie, Dave Burnett, Phil Cox, John O'Connor, Christopher Tiratsoo, John Boucher, David Boote, Dan Tearpock, Pete Rose, Gary Citron, and Jim Murtha. We acknowledge Craig Smalley's many suggestions and help in improving the article. We are grateful to Maersk Oil and Hess for support in publishing the work although the opinions expressed here are solely those of the authors.
 Manuscript receivedJune 4, 2008.