Copyright 2000, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the 2000 SPE Annual Technical Conference andExhibition held in Dallas, Texas, 1–4 October 2000.

This paper was selected for presentation by an SPE Program Committee following review ofinformation contained in an abstract submitted by the author(s). Contents of the paper, aspresented, have not been reviewed by the Society of Petroleum Engineers and are subject tocorrection by the author(s). The material, as presented, does not necessarily reflect anyposition of the Society of Petroleum Engineers, its officers, or members. Papers presented atSPE meetings are subject to publication review by Editorial Committees of the Society ofPetroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paperfor commercial purposes without the written consent of the Society of Petroleum Engineers isprohibited. Permission to reproduce in print is restricted to an abstract of not more than 300words; illustrations may not be copied. The abstract must contain conspicuousacknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O.Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.

Abstract

Probabilistic methods have introduced inconsistentinterpretations of how to apply these methods whilecomplying with reserve certification guidelines. The objectiveof this paper is to present and discuss some pitfalls commonlyencountered in the application of probabilistic methods toevaluate reserves. Several Regulatory Guidelines that shouldbe followed during the generation of recoverable hydrocarbondistributions are discussed. An example also is given tounderstand the evolution of reserve categories as a function ofprobabilities.

Most of the conflicting reserve interpretations can beattributed to the current SPE/WPC reserve definitions wherereserve categories are expressed in terms of probabilities ofbeing achieved. For example, proved reserves are defined asthose hydrocarbon volumes with at least a 90 percentprobability of being equaled or exceeded (P-90).Unfortunately, these definitions alone fall short as guidance onhow to derive the distributions from which these percentileswill be calculated. A simple example of this problem is thederivation of an exploratory prospect hydrocarbon resourcedistribution. While a P-90 can be calculated from thisdistribution, no proved reserves should be assigned to theprospect until it has actually been drilled and proveneconomical.

Introduction

In 1997 new reserve definitions were drafted and introducedby the SPE and the World Petroleum Congress (WPC). For thefirst time, these reserve definitions included some language to

address the increased interest in probabilistic analysis toestimate hydrocarbon reserves.

Proved reserves were defined, in part, as those volumes ofrecoverable hydrocarbons with “... a high degree of confidencethat the quantities will be recovered. If probabilistic methodsare used, there should be at least a 90% probability that thequantities actually recovered will equal or exceed theestimate.” This definition implies that satisfying the P-90criteria is sufficient to define proved reserves. We will discusslater in this paper why defining proved reserves as the P-90 ofany distribution is not always appropriate. Also, thedefinitions do not specify at what level the evaluator shouldapply the P-90 test (i.e. is it at the field level or the totalportfolio level).

Probable reserves were then described in the SPE/WPCdefinitions as those recoverable hydrocarbon volumes that “...are more likely than not to be recoverable. In this context,when probabilistic methods are used, there should be at leasta 50% probability that the quantities actually recovered willequal or exceed the sum of estimated proved plus probablereserves.”

Possible reserves were defined as those recoverablehydrocarbon volumes that “... are less likely to be recoverablethan probable reserves. In this context, when probabilisticmethods are used, there should be at least a 10% probabilitythat the quantities actually recovered will equal or exceed thesum of estimated proved plus probable plus possiblereserves.”

The United States Securities and Exchange Commission(SEC) does not recognize probable and possible reserves. TheSEC’s guidelines for reporting proved reserves are set forth inits Regulation S-X, Rule 4-10 and subsequent clarifyingbulletins. In Regulation S-X, Rule 4-10 there are no guidelinesfor the interpretation of probabilistic analysis. The Regulationdefines proved reserves as those recoverable hydrocarbonvolumes with “... reasonable certainty to be recoverable infuture years from known reservoirs ...”

Both the SPE/WPC and SEC proved reserve definitions haveseveral other requirements that are usually applicable to

SPE 63202

Adapting Probabilistic Methods to Conform to Regulatory GuidelinesHerman G. Acuña, SPE, and D.R. Harrell, SPE, Ryder Scott Company Petroleum Consultants L.P.

2 H. G. ACUÑA, D. R. HARRELL SPE 63202

deterministic methods that may conflict with probabilisticanalysis if not properly incorporated. Evaluators of reservesshould exercise caution when using probabilistic methods toensure compliance with the definitions of reserves adopted bythe SEC and the SPE/WPC. Caution is required because thereare certain situations where indiscriminate application ofprobabilistic methods may produce results that are inconsistentwith the reserve definitions. For example, the SEC definitionof proved reserves does not explicitly recognize the use of theprobabilistic method, and in no way allows for theprobabilistic method to be used in such a manner as to violateany term of that definition.

In this paper, we will first present a short definition ofprobabilistic analysis and the risks and benefits of using thistechnique. Next, we will address some significantshortcomings in the current reserve definitions, and then, wewill present some examples on how some of theseshortcomings can be addressed in the evaluation of reserves.

Discussion of Probabilistic Analysis of Reserves

The probabilistic analysis of reserves relies on the use ofprobabilistic techniques to estimate the uncertainty of therecoverable hydrocarbon volumes. In its purest sense, theseprobabilistic methods are used to collect and organize,evaluate, present and summarize data. These methods providethe tools to analyze large amounts of representative data sothat the significance of that data’s variability anddependability can be measured and understood.

Probabilistic analysis should be considered an important toolfor internal company analysis to understand and rank itshydrocarbon reserves and resources and associated risks. Thismethod provides the tools to identify the upside and thedownside hydrocarbon potential to better organize thecompany’s portfolio and to more efficiently allocate capitaland manpower resources. However, it should be understoodthat the objectives of a hydrocarbon property ranking studyand a SPE/WPC or SEC reserve reporting evaluation might bedifferent. For example, companies may have their ownguidelines to group and analyze hydrocarbon assets to allocatecompany resources or for property acquisitions. Thesecompany guidelines may vary from project to project or yearto year (depending on pricing assumptions) and may bedifferent from those guidelines provided in the SPE/WPC andSEC definitions. It becomes then the primary challenge of theevaluator to reconcile both evaluations.

E.C. Capen1 discussed this issue of having different objectivesand different audiences for the evaluation of reserves. Hecorrectly remarked that the evaluation needs of theexplorationists, geologists and geophysicists may not 1 E. C. Capen: “A Consistent Probabilistic Definition ofReserves,” SPE Reservoir Engineering Journal, February1996, pp 23-28.

necessarily be the same as the needs arising from lendinginstitutions or stockholders. While the reserve evaluationshould allow the explorationists “... to dream a little but stillhold them accountable,” the lenders should be able to “...sleep well at night knowing their money takes no inordinaterisks.” This is an obvious conclusion since the lenders’exposure to the downside risk is much greater than theirexposure to the upside. Lending institutions do not particularlybenefit from having large project upsides with lowprobabilities since they generally lend money at fixed rates. It,thus, follows that lending institutions are much moreinterested in the quantification of the downside risks and notso for the upside. About the stockholder, Capen wrote that he“... cannot afford biased estimates lest the buy and sell signalsget all confused and cost him money.”

Probabilistic analysis is not a substitute for the reserveguidelines adopted by the SPE/WPC and the SEC. A commonbut, in our opinion, unacceptable trend in reserve evaluationshas been to rely on probabilistic evaluations to boost reservevalues if they cannot be supported by deterministic methods.This generally results from the aggregation of variousdistributions as will be discussed later in this paper.Probabilistic methods should not be considered as a sequenceof simple mechanical steps to reach the desired outcomes. Infact, probabilistic analysis requires as much, if not more, goodjudgement than deterministic methods for assigning reserves.

Probabilistic methods are most suitable for early hydrocarbonresource/reserve evaluation. They provide flexible modelingtechniques to evaluate variable interactions and outcomeoptions. Therefore, these methods require a customizedapproach to correctly model the variable interactions.

Unfortunately, the great flexibility of probabilistic analysismakes this method easy to abuse. Restricting the probabilisticanalysis to the guidelines provided by the reserve definitionscan help to standardize the results for reserve reportingpurposes. In the next section we first explore some of theshortcomings of the current definitions and then we willpresent some examples for the practical application of reservedefinitions and probabilistic analysis.

Conforming with the Reserve Definitions

The primary factor for inconsistent reserve reportingevaluations is the description of reserves as percentiles of adistribution. In the current SPE/WPC definitions, provedreserves are defined as P-90, the proved plus probable as P-50,and the proved plus probable plus possible (3P) as P-10.

These percentiles for the different reserve categories havebeen interpreted by some as finally quantifying the meaning ofthe phrases, “high degree of confidence,” “more likely thannot” and “less likely to be recoverable than probable”reserves. The industry was quick to adopt these percentiledefinitions at face value. Unfortunately, the SPE/WPC

SPE 63202 ADAPTING PROBABILISTIC METHODS TO CONFORM TO REGULATORY GUIDELINES 3

definitions do not provide direct guidance on how thedistributions are to be generated. Consequently, what may be aP-90 to one evaluator may be something else to anotherevaluator.

The definitions state without qualification that the percentiletests are sufficient for the establishment of reserves if theprobabilistic method is used, irrespective of other aspects ofthe definitions. Thus, the definitions permit the calculation ofat least two values of reserves, those estimated by thedeterministic method (honoring all terms of the definitions)and those estimated by the probabilistic method. Figure 1illustrates this point.

Figure 1: Example of Early Reserve Assessment

For discussion purposes let us assume that there is 3-D seismicdata over the entire structure shown in Figure 1 and that onewell has been recently drilled and tested oil at economicalrates. The location of the well is represented by the dot inFigure 1. The lowest known oil (LKO) is represented by thefirst contour around the well. The total area on both sides ofthe fault represents the area that may be productive asindicated by seismic analysis. The different contours representvarious degrees of confidence that the reservoir may beproductive from the seismic and geologic analysis.

A distribution of recoverable oil can then be generated toestimate the reserves attributable to this structure. Figure 2shows such a distribution.

Figure 2: Example of Recoverable Hydrocarbons Distribution

From Figure 2, one can see that there are different values ofrecoverable oil that fit the definition of P-90 for provedreserves. While it is important to generate and understand thepotential for the entire structure, it is obvious from this simpleexample that for reserve reporting purposes the definition ofproved reserves based on a P-90 definition may not be enough.

For reserve reporting, one also should incorporate all theguidelines that traditionally may be associated withdeterministic methods. For example, can the structure on theopposite side of the tested fault block be considered as aknown reservoir? If not, should it be left out of the analysis ofproved reserves? Similarly, the volumes of rock below theLKO may not be included.

Application of these guidelines would then result in thedetermination of proved reserves from the first distribution inFigure 2. This distribution is what we would call the provedreserve distribution. Subsequently, the question is whetherafter restricting the distribution to account for various reserveguidelines, one should still use a P-90 to estimate the provedreserves. To answer this, let us first examine the approach thatwould have been taken in a deterministic analysis.

In a deterministic analysis, the evaluator would have restrictedthe reservoir area to conform with the LKO guideline. Thenweighted average values of porosity, water saturation, net-to-gross ratios and recovery factors would have been applied toestimate the proved reserves. The deterministic analysis istherefore arriving at the expected value of reserves of theproved reserve distribution. Therefore, in probabilisticanalysis, the proved reserves may be represented better by theP-50 of the proved reserve distribution than the P-90 of thatdistribution. However, notice in Figure 2, that the P-50 of theproved reserve distribution may still only represent a smallfraction, P-98 or less, of the entire recoverable oil distribution.

Two important conclusions can be made from this example.First, special considerations need to be made whenconstructing the distribution of recoverable hydrocarbons toensure that the definition guidelines are being honored.Second, the actual percentile assigned to each of the reservecategories may be different depending on which distributionthey apply to. Moreover, the distributions of recoverablehydrocarbons need not be the same for each reserve category.

There are currently at least two acceptable alternatives in theevaluation of proved reserves using probabilistic analysis toconform with the regulatory guidelines.

The first alternative would be to proceed as shown in the priorexample. That is to first derive a proved reserve distributionby conforming to certain variables that cannot be subjected tospeculation based on regulations. Then, selecting the P-50value from this distribution to estimate proved reserves. Afterestimating the proved reserves in this way, the percentilecorresponding to proved reserves from the overall reserve and

Cumulative Probability

Recoverable Oil

P-90

P-50

P-10

4 H. G. ACUÑA, D. R. HARRELL SPE 63202

resource base can be backcalculated from a seconddistribution that has not been constrained by the provedguidelines. If the opportunity for upside is large or if the fieldis in the very early stages of development, reportable provedreserves may only represent a small fraction of the overalldistribution (i.e., a percentile higher than P-90).

On the other hand, if the current stage of field development issuch that the “proved” distribution is the same as the overalldistribution, then proved reserves may be better represented bythe P-50 of that distribution.

In fact, it follows from this discussion that the percentilesapplicable to each of the reserve categories are dynamicthroughout the life of the reservoir and are not a fixed value.Obviously, during the early field development stagesreportable proved reserves may represent only a smallpercentile of the overall reserve and resource opportunity.With increased development and decreased uncertainty,proved reserves may approach a P-50 or expected value.

The second approach is similar to what has been discussed,except that proved reserves are estimated deterministically.23

That value would then be compared to the unrestricteddistribution of recoverable hydrocarbons to determine itscorresponding percentile. By determining the proved reservesdeterministically, conforming with the regulation guidelinesand using expected values of rock properties and engineeringfactors, the evaluator is basically determining the expectedvalue of the proved distribution as previously defined.

Evaluation Variables

In general when estimating reserves, the evaluator deals withthree types of variables: 1) Geologic, 2) Engineering and 3)Economic. Each of these variables may have degrees ofuncertainty that may be represented as distributions.

This paper does not deal with the aspects of generating therandom variable distributions or the correlations betweenthem. Nor does this paper address the issues of properlyincorporating the reservoir physics to represent the actualproducing mechanisms in the probabilistic model. Obviously,the evaluator should be familiar with how the data werecollected and what they represent. Also, the reader should beaware that throughout the discussion of reservoir variables,scale consistency between the variable distributions and themodel to which they apply should be maintained. This means, 2 Patricelli, J.A., McMichael, C.L.: “An IntegratedDeterministic/Probabilistic Approach to ReserveEstimations,” JPT (Jan. 1995) pp. 49-53.3 Nangea, A.G., Hunt E. J.:” An IntegratedDeterministic/Probabilistic Approach to Reserve Estimation:An Update,” SPE 38803, presented at the 1997 SPE AnnualTechnical Conference and Exhibition held in San Antonio,Texas, 5-8 October 1997.

for example, that if the exercise at hand is to evaluate fieldlevel reserve potential, then the distributions of reservoirproperties should be the distribution of average fieldproperties.

This paper deals, however, with the restrictions that may beimposed in a probabilistic evaluation by the definitions. Aspreviously stated, certain variables may not be represented in adistribution fashion for reserve reporting purposes. Theobjective of the definitions is not to limit the understanding ofthe hydrocarbon assets, but rather to ensure that the reportedreserves, in particular proved reserves, are evaluatedconsistently.

For example, some of the geologic variables to consider maybe:

• Water-Hydrocarbon Contact• Gas-Oil Contact• Bulk Rock Volume• Net-to-gross ratios• Porosity• Water Saturation• Cutoff values• Reservoir Facies Distribution

The first geologic variable listed in bold letters above isdirectly affected by the definition of reserves. While there maybe some uncertainty as to the exact location of the fluidcontacts, the reserve definitions are very clear in that forproved reserves fluid contacts should not be speculated upon.Therefore, under the current definitions, the generation of theproved hydrocarbon-in-place distribution should incorporatethe LKO value and not a distribution of the contacts.However, it may be reasonable to expect that morehydrocarbons may exist below the LKO depth.

Engineering examples of variables that may be directlyaffected by the reserve definitions are: 1) well spacing, 2)recovery factors, and 3) implementation of secondary andtertiary projects. While downspacing or the implementation ofsecondary projects may result in increased recoveries, thedefinitions prevent us from speculating on these results unlessthere have been successful tests or pilots. Therefore, it wouldbe an inconsistent application of these guidelines if theincorporation of these operating practices in the probabilisticanalysis increases the estimate of proved reserves. Reservedistributions that incorporate the results from waterfloodingprojects yet to be tested through pilots may result inoverstating proved reserves, as currently defined, particularlyduring the aggregation of multiple field reserves. The subjectof reserve aggregations is discussed in the next section.

The reserve definitions are even less flexible when it comes toeconomic parameters. To categorize reserves as proved, thosereserves have to be economical under current economicconditions. While it may be appropriate to incorporate

SPE 63202 ADAPTING PROBABILISTIC METHODS TO CONFORM TO REGULATORY GUIDELINES 5

uncertainty and volatility in hydrocarbon prices, operatingcosts and development costs in probabilistic analysis, thesevariables are generally fixed in the reserve definitions.

A typical example of a proved reserves economical evaluationthat may not be appropriate under the current reservedefinitions is the consideration of a learning curve. We are allfamiliar with the concept that, in general, as we do tasksrepeatedly we get better at it. For example, a drilling learningcurve, which shows a reduction in drilling costs over time. Aprobabilistic analysis can be made from past companyperformance to define a function of drilling cost savings, inpercentages, with increased development.

While this type of analysis is important for internal companyreporting and analysis, it is not appropriate for reservereporting unless the cost savings trend has been clearlyestablished in the subject field. Otherwise, the appropriatedevelopment costs to use for proved reserve reporting are theactual costs regardless of expectations of future savings.

While dealing with projects outside of North America, theevaluator generally has to make assumptions regarding thetiming for infrastructure, such as pipelines and marketconditions, particularly for gas. While these considerations areimportant for company planning purposes and can beincorporated in risk economic models, they may prevent theclassification of proved reserves. In general, there must beestablished infrastructure and product markets to classifyreserves as proved for SEC purposes.

To illustrate this problem, consider for example five oil fieldson primary depletion with recovery factors ranging between12 and 18 percent for each field. As shown in Figure 3, theserecovery factors can be expressed as triangular distributionswith a P-90 of 12 percent and a P-10 equal to 18 percent witha mean value of 15 percent.

Figure 3: Primary Recovery Factors

Recovery Factor

These fields are considered good candidates for secondaryrecovery but no pilot has been implemented yet. Theadditional recovery factors due to secondary projects areestimated between 0 to 12 percent. These secondary recoveryfactors can also be represented by triangular distributions witha minimum of 0 and a P-10 of 12 percent as shown in Figure4.

Figure 4: Secondary Recovery Factors

Recovery Factor

The primary plus secondary recovery factors can, thus, beobtained for each probabilistic iteration as the summation ofthe two distributions. Figure 5 shows the aggregated recoveryfactors for all the fields.

Figure 5: Primary Plus Secondary Recovery Factors

Recovery Factor

Multiplying the original oil in place volumes by the primaryplus secondary recovery factors could then calculate reserveestimates. The aggregated percentile recovery factors for allfive fields are shown in Table 1.

Table 1: Portfolio Primary plus Secondary Recovery Factors

Recovery Factor (%)P-90 20.5P-80 21.3P-70 21.8P-60 22.3P-50 22.7P-40 23.2P-30 23.7P-20 24.2P-10 24.9

Notice that the P-90 from the aggregated recovery factordistribution is higher than the P-10 of the primary alone.Obviously, disclosing proved aggregated reserves with anequivalent recovery factor of 20.5 percent would not beappropriate in this case.

Although the aggregated recovery factor distribution shown inFigure 5 and Table 1 may be the correct outcome if all fivefields are waterflooded, these expectations can not be used tobook proved reserves at the current field development stagesand under the current reserve definitions. So what is the

0.10 0.12 0.15 0.18 0.20

.000

.006

.013

.019

.026

0.18 0.21 0.23 0.26 0.28

Probability

0.00 0.04 0.08 0.12 0.15

6 H. G. ACUÑA, D. R. HARRELL SPE 63202

solution to this problem? Obviously, proved reserves shouldbe based only on reserve distributions that have been derivedexclusively from primary recovery factors until theappropriate waterflooding pilots have been implemented andresponse has been verified.

One may argue that calculating proved reserves based onprimary recovery factors in this example underestimates theoverall potential of the fields. Someone else may point out thatthis conservatism is the reason for the reserve growth observedwith added development. While these arguments may becorrect, one should keep in mind that the reserve categorieshave meaning only within the context of their definitions.Therefore in this example, proved reserves have meaning onlyfor those volumes calculated without consideration ofsecondary recovery. Under the current definitions, secondaryreserves without a successful pilot should be excluded fromthe proved category regardless of the waterfloodingperspectivities of the field.

Of course, the reservoir engineer should make thosecalculations to allocate company resources and funds. Thisbrings us back to our original statement that during the earlystages of field development proved reserves may berepresented by percentile values of the overall reservedistribution higher than the P-90.

If we return to the original postulation of this paper to firstdetermine individual distributions that comply with the reservedefinitions and then select the P-50 from those distributions toestimate the proved reserves, then the summation of those P-50 values should be very similar to the P-50 of their aggregate.Additionally, reserve distributions derived using thedefinitions for proved should be risk-equivalent and, thus,compatible for aggregation without the problems discussed inthe next section.

After determining the proved reserves, one can determine theappropriate percentile of proved reserves within the overallcompany asset reserve distribution, and maybe even discloseor discuss this percentile and its relationship to companyupside. Probable and possible reserves may be estimated fromP-50 and P-10 of the overall aggregated distribution ofreserves (excludes exploratory assets).

In conclusion, the application of probabilistic analysis and thevariable distributions used thereof should not conflict with theguidelines established by the definitions. These definitionswere established to standardize, as much as possible, reservereporting. This is not to say that the current reserve definitionsshould not evolve. On the contrary, these definitions shouldand will continue to evolve to address these issues and otherissues. Capen1 wrote “As long as estimators provide the entiredistribution, others can define reserves however they chooseas long as they pick some point in the distribution.” Whilethis may be applicable for internal company reserve andbudgeting purposes, this statement is obviously unacceptable

for the purpose of reserve reporting. No lending institution,market analyst or shareholder would be able to conductmeaningful comparative reserves and income evaluationsbetween E&P companies without the standards.

Dry Hole Risk Factor and Aggregation ofDistributions

One aspect that is often overlooked during the aggregation ofdistributions is the fact that distributions may have differentrisk levels. Consistent with the accepted practice that thesummation of proved, probable and possible deterministicreserves is not appropriate without risk adjusting each reservecategory first, reserve distributions should not be aggregatedunless they have been adjusted for their “dry hole” factor.Consider for example the three fault blocks in Figure 6.

Figure 6: Aggregation of Distributions

Only fault block “Adevelopment and the(LKG). Seismic daadditional gas downdesirable then to avolumes from all th“B” and “I” have a hi

Distributions for bporosity, gas saturagenerate recoverableproperty distribution in this area and for th

A

I

L

” has been drilled at this stage of field well proved gas to a lowest known depthta analysis indicates the possibility of to the deepest shaded area. It may beggregate the estimated recoverable gasree fault blocks. Obviously, fault blocksgher risk than fault block “A”.

ulk rock volumes, net-to-gross ratios,tion, and recovery factors are used to gas volumes for each fault block. Eachis based on fault block averages expectede specific reservoir age.

B

LKG

SPE 63202 ADAPTING PROBABILISTIC METHODS TO CONFORM TO REGULATORY GUIDELINES 7

The individual reservoir variable distributions are applied tothe volumetric gas equation to estimate the original gas inplace. The original gas-in-place is then multiplied by arecovery factor, sampled from the recovery factor distribution,to obtain the recoverable gas for each fault block. Thesevalues are shown in Table 2.

These recoverable gas volumes reflect only the uncertainty inthe reservoir properties and performance and, therefore, arerepresentative of the success cases only. Although theinformation obtained this way may provide an importantperspective to the overall upside of the prospect, there is noreason why the probability of “dry hole” shouldn’t beincorporated into the probabilistic analysis and the aggregateddistribution of recoverable gas volumes.

Table 2: Recoverable Gas Volumes (MMscf)

Fault Block A Fault Block B Fault Block IP-90 9,658 13,124 4,904P-80 11,517 15,655 5,852P-70 12,818 17,539 6,508P-60 13,943 19,083 7,084P-50 14,971 20,493 7,629P-40 16,002 21,909 8,188P-30 17,102 23,588 8,744P-20 18,352 25,265 9,480P-10 20,146 27,500 10,475

The aggregation of these three distributions results in thedistribution of unrisked recoverable gas shown in Figure 7,which assumes that all three fault blocks are successful.

Figure 7: Unrisked Aggregation of Fault Blocks A, B and I

Recoverable Gas (MMscf)

To calculate the risked and, therefore, more representativerecoverable gas distribution at this stage of development, oneshould apply the individual chances of success (COS) for eachfault block during the simulation. Figure 8 compares theunrisked distribution with the risked distribution obtained byassuming a COS of 100 percent in fault block A, 75 percent infault block B and 50 percent in Fault block I.

Figure 8: Comparison of Aggregated Distributions

Recoverable Gas (MMscf)

Table 3 compares the unrisked and risked aggregated gasrecoverable volumes from these three fault blocks.

Table 3: Comparison of Recoverable Gas Volumes (MMscf)

Unrisked RiskedP-90 33,731 16,864P-80 36,909 22,963P-70 39,301 28,141P-60 41,184 32,498P-50 42,923 35,658P-40 44,954 38,553P-30 46,932 41,279P-20 49,299 44,357P-10 52,286 48,534

While the prior discussion of risk and aggregation ofdistributions may be obvious to some, it is still commonpractice to see reserve distributions aggregated withoutconsideration for risk. The fact that data are presented indistribution form can make it counterintuitive that additionalrisking may be necessary prior to aggregation.

The amount of recoverable gas that can be booked as proved,probable and possible for this example will be discussed laterin this paper.

Aggregation of Reserve Portfolio

The aggregation of company reserves has traditionally beenfairly straightforward. The summation of all individual provedreserves within its portfolio provide the total company provedreserves. Similar arithmetic is performed for probable andpossible reserves. This process has been slightly complicatedby the introduction of probabilistic evaluation of reserves andthe current reserve definitions.

It has been well established that the summation of individualpercentiles from various distributions is not equal to the samepercentile of the aggregate. Thus it follows that adding up theP-90, as defined for proved reserves, from the various reserve

.000

.250

.500

.750

1.000

0 17,500 35,000 52,500 70,000

Unrisked

Risked

Cumulative Probability

.000

.250

.500

.750

1.000

20,000 31,250 42,500 53,750 65,000

Cumulative Probability

Mean = 43,091

8 H. G. ACUÑA, D. R. HARRELL SPE 63202

portfolio components will not be equivalent to the P-90 of theaggregated total. In fact, the summation of the P-90 will be, ingeneral depending on the number of uncorrelatableopportunities in the portfolio, much lower than the P-90 of theaggregate. On the other hand, the summation of the P-10 willtend to exaggerate the upside and be much higher than the P-10 from the aggregated distribution. The reason for this is verysimple -- the larger the amount of opportunities available to acompany, the more it can diversify risk. In other words,independent opportunities will tend to compensate each other;some may be low and some may be high, thus reducing theuncertainty of the total portfolio outcome. The addition ofindividual P-50 values should approach the P-50 of theaggregated distribution, as long as the median and the meanare not too dissimilar.

The obvious dilemma becomes how to report individual andtotal company portfolio reserves. To make matters worse, eachdistribution in the reserve portfolio needs to be properly riskedand may or may not comply with all the definitions. Thecurrent definitions provide no wording for the proper methodfor aggregating reserves; neither do the definitions provideguidance for the appropriate level of aggregation to apply thepercentiles associated with each reserve category.

Consider, for illustration purposes, a company with onlyprobable reserves from ten fields defined at the field level atthe P-50s. Recoverable hydrocarbon volumes above P-55 arezero. That is, the prospects may have a COS of 55 percent.The following table shows the recoverable oil volumes for onefield and the aggregates of two, three, five and all ten fields.

Table 4: Field Reserve Aggregation Example (MMBbl)

1 Field 2 Fields 3 Fields 5 Fields 10 FieldsP-90 0.0 0.0 9.6 16.6 50.5P-80 0.0 0.0 13.5 27.1 61.3P-70 0.0 12.4 15.9 31.3 69.5P-60 0.0 14.3 19.2 36.2 76.4P-50 10.9 15.9 26.1 42.0 82.7P-40 13.2 17.8 29.4 45.8 88.8P-30 14.7 21.4 32.3 50.4 94.9P-20 16.2 28.2 35.9 56.7 102.8P-10 18.0 31.9 43.6 64.2 114.3

This simple example highlights the problem that oneencounters when aggregating multiple fields. Although at theindividual field level none of the fields have proved reserves,the aggregated total shows significant reserves at the P-90level for three or more fields.

Should this company then be in a position of disclosing theaggregated reserves as proved? If so, how should thisinformation be disclosed to the investors and shareholders?What if the company decides to divest individual fields or allof them? Prospective buyers may not pay anything for provedreserves for the individual fields. How can the company then

explain or disclose this risk to their investors? All these arereal and difficult questions without simple solutions. As wehave mentioned earlier, the definitions provide no guidancefor the process of aggregating portfolios.

For reserve aggregation, we emphasize one more time that theevaluator should consider the audience for the report. Clearly,this type of analysis is of great value for the company’sinternal resource allocation and portfolio risk analysis. It helpsthe company understand the diversification of their portfolio.It provides an insight to the impact that divesting fields andproperties may have on their overall risk profile. It helps thecompany measure the level of commitment necessary to reacha certain level of success.

However, for reserve reporting purposes and under the currentdefinitions it may be difficult if not impossible to justifyproved reserves in this example. Under SEC guidelines, weshould not disclose any proved reserves. The P-90 volumes ofthe aggregated totals can not be allocated with reasonablecertainty to any specific field or prospect.

In fact, to realize the P-90 volumes (or any other percentilevolume of the aggregated totals), the company would have tobe committed to the development of all ten fields regardless ofearly disappointments or successes. The SEC/WPC providesno guidance to handle this type of problem probabilistically.However, the only justification to book proved reserves underthe SPE/WPC guidelines would be the fact that the aggregatedP-90 value has a positive value. This, however, would conflictwith the grain of the remaining guidelines.

Disclosing the aggregated volumes in this case as proved mayleave investors unprotected against portfolio changes,divestitures, delayed or incomplete portfolio development. Onthe other hand, not presenting this information at all does notadequately reflect the upside of a company’s portfolio.

Until the reserve definitions are modified to accommodate thistype of problem and the investing public has been familiarizedon this subject, we would recommend against disclosingaggregated proved reserves that can not be readily identified atthe individual field level. However, we would recommenddiscussing these volumes and the overall risk profile of thecompany that results from its existing portfolio in companyfilings and reports. This allows investors to make their owndecisions based on their comfort level about the overallcompany’s upside without the assumption of reasonablecertainty associated with the proved reserve category.

Example Problem

In this example, we will walk through the analysis of reservesas a gas exploratory prospect is first drilled. Figure 9 showsthe Gross Hydrocarbon Isochor for this example.

SPE 63202 ADAPTING PROBABILISTIC METHODS TO CONFORM TO REGULATORY GUIDELINES 9

Figure 9: Gross Hydrocarbon Isochor

The exploration prospect consists of 9 fault blocks labeled Athrough I. The first step involves the determination of thedistributions for the gross hydrocarbon bulk rock volume, net-to-gross ratios, porosities, water saturations, formation volumefactors and recovery factors. These distributions and theirappropriate correlations are used in the volumetric equation toderive original and recoverable gas distributions for each faultblock. This is shown schematically in Figure 10. This figurealso shows the type of distribution used for each variable.

Figure 10: Gas Volumetric Equation

The results from this exercise then provide the distribution ofgas resources by aggregating the recoverable volumes from allthe fault blocks.

Table 5: Salt Dome Example Unrisked Recoverable Gas

MMscfP-90 118,288P-80 123,751P-70 127,762P-60 131,104P-50 134,323P-40 137,655P-30 141,116P-20 145,033P-10 150,801

From the stage of field development it is obvious that there areno bookable reserves for this prospect. Although we havederived a P-90 for a gas resources distribution, the P-90 of this

distribution carries a much higher risk than a P-90 from a gasreserves distribution. The salt dome prospect is not yetconsidered a known reservoir and Table 5 shows the result fora successful case without dryhole consideration. A similartable, after applying the risk factors to each fault blockthrough correlated binomial distribution of the COS, could begenerated to get the risked recoverable gas distribution.However, this still would not be enough to elevate any of thegas volumes to a reserve category.

The company then successfully drilled fault block A to test theexploration concept. The well A-1 found gas down to the baseof the sand thus establishing the LKG for that fault block.Seismic analysis indicates the possibility of more gas downdipof the LKG, but the seismic analysis is not conclusive. This isshown schematically in Figure 6. Knowing that we have 9prospective fault blocks with one already tested, the issuebecomes now how much proved, probable and possiblereserves can be booked.

Following our prior discussion, the first step would be toestablish a distribution of recoverable gas that complies withthe definitions for fault block A. We will call this distributionthe proved distribution. In this case, the proved distributionwas restricted by the LKG. There may still be someuncertainty associated with the petrophysical and structuralelements of fault block A that would make the generation ofthe proved distribution necessary. Otherwise, a deterministicevaluation of that fault block may be enough. The second stepis to generate the distribution for the entire fault block Arecoverable gas. This distribution would include the upsidethat is indicated by the seismic below the LKG.

Table 6 compares the recoverable volumes of gas from thetwo distributions. The second column shows the recoverablevolumes of gas estimated from the proved distribution for eachof the percentiles in column one. The third column shows thetotal distribution of recoverable gas.

Table 6: Comparison of Recoverable Gas for Fault Block A

Proved toLKG (MMscf)

Entire Fault Block AAfter Drilling

(MMscf)P-90 3,920 9,658P-80 4,628 11,517P-70 5,184 12,818P-60 5,619 13,943P-50 6,007 14,971P-40 6,411 16,002P-30 6,842 17,102P-20 7,286 18,352P-10 7,982 20,146

Several observations can be made from Table 6 whiledetermining the appropriate amount of reserves to be bookedfrom this fault block. First, notice that the P-10 from the

0.09 0.29 0.49 0.69 0.89

S W A

72,622 80,342 88,061 95,781 103,500

BR V A

0.650 0.740 0.830 0.920 1.010

NTG A

0.110 0.170 0.230 0.290 0.350

P orosity A

0.028 0.030 0.031 0.033 0.034

BG A

43,560 * * * * (1- )

BRV NTG POR Sw

Bg

OGIP =

10 H. G. ACUÑA, D. R. HARRELL SPE 63202

proved distribution is less than the P-90 of the entire faultblock as defined from seismic. This results from the welllocation, which is not the subject of the discussion. But if wewere to use the P-90 from the second distribution to determinethe proved reserves, we would obviously be stretching thevolumes beyond those proved by the bit. Since this fault blockwill most likely be a one well fault block, only performancewill be able to prove or disprove the geologic and seismicassumptions that define the upside.

Given the fact that there is no production data to verify theupside from this fault block, one then has to look at the provedreserve distribution. Consistent with our prior discussion,proved reserves would be defined as the P-50 recoverable gasvolumes from this distribution. In this case, the 6,007 MMscfare the expected recoverable gas volumes from the proveddistribution and are, thus, the proved reserves. The provedplus probable reserves would be defined as the P-50 of theentire fault block A distribution and the 3P reserves (provedplus probable plus possible) would then be estimated from theP-10 of the same distribution. Table 7 then shows the reservesper category for this fault block.

Table 7: Gas Reserves Fault Block A

Fault Block A (MMscf)Proved 6,007

Probable 8,964Possible 5,175

After determining the appropriate reserve levels for fault blockA, the question remains whether additional reserves can bebooked for the remainder of the structure. Statisticalinformation on fault block success ratio in tested structuresmay be of some use if available.

Let’s first examine the two fault blocks adjacent to fault blockA. These blocks are fault blocks B and I in Figure 6. In ouropinion, it would not be appropriate to book proved reservesfor these fault blocks at this stage since the structures have notyet been penetrated by a well. Probable and possible reservescan be booked based on seismic analysis and analogy to faultblock A. Table 8 shows the unrisked recoverable gas for faultblock A and each of the adjacent fault blocks.

Table 8: Recoverable Gas Volumes (MMscf)

Fault Block A Fault Block B Fault Block IP-90 9,658 13,124 4,904P-80 11,517 15,655 5,852P-70 12,818 17,539 6,508P-60 13,943 19,083 7,084P-50 14,971 20,493 7,629P-40 16,002 21,909 8,188P-30 17,102 23,588 8,744P-20 18,352 25,265 9,480P-10 20,146 27,500 10,475

As we discussed earlier, these distributions are not risk-consistent since fault block A has a penetration while the othertwo do not. During the aggregation of these three distributionsone should apply the COS to determine the total probable andpossible reserves from all three blocks.

This process was discussed earlier in the section dealing withrisk and aggregation of distributions. Assuming a COS of 100percent for fault block A, 75 percent for fault block B and 50percent for fault block I, the aggregated recoverable gasdistribution shown in Table 9 is obtained. From this table thethree fault block probable reserves are determined from the P-50. Possible reserves for the same blocks are estimated fromthe P-10 of the same risk adjusted distribution.

Table 9: Risked Recoverable Gas Fault Blocks A, B and I

MMscfP-90 16,864P-80 22,963P-70 28,141P-60 32,498P-50 35,658P-40 38,553P-30 41,279P-20 44,357P-10 48,534

Whether or not reserves can be assigned to any of theremaining 5 blocks will depend on the certainty of the seismicanalysis and the fault block COS observed in this gasprovince. Despite the mechanics of probabilistic evaluations,the experience and good judgement from the evaluator are stillnecessary and valuable. In this example, no reserves wereassigned beyond the two adjacent fault blocks resulting in totalreserves shown in Table 10.

Table 10: Total Gas Reserves

Fault Block A (MMscf)Proved 6,007

Probable 29,651Possible 12,876

As a final analysis, one can compare the current reserve basewith the overall unrisked and risked gas resource distributionto better understand the additional potential and prioritizecompany resources. The unrisked distribution shows thevalues of recoverable gas if all 9 fault blocks are successful.The risked distribution was generated with a relatively high(75 percent) correlation coefficient between adjacent faultblocks’ COS. Table 11 shows the total recoverable gasvolumes for the entire structure.

SPE 63202 ADAPTING PROBABILISTIC METHODS TO CONFORM TO REGULATORY GUIDELINES 11

Table 11: Total Recoverable Gas Volumes (MMscf)

Unrisked RiskedP-90 118,018 33,241P-80 123,711 44,390P-70 127,621 56,310P-60 131,193 67,592P-50 134,681 79,533P-40 137,929 90,543P-30 141,361 102,817P-20 145,432 113,558P-10 150,695 127,563

Notice that the unrisked 3P value of reserves of 48,534 MMscfcorresponds to approximately a P-75 of the total riskedrecoverable gas distribution. This information is veryindicative of the significant upside, beyond current bookablereserves, that can be achieved with further development.

Conclusions

In this paper, we have discussed how the reserve definitionsmay affect the implementation of probabilistic methods. Thefollowing conclusions can be made from the precedingdiscussions:

1. Probabilistic methods should not be used as a tool toboost reserve reporting. Probabilistic methods are mostuseful for the prioritization of the company’s portfolioand the allocation of capital and manpower resources.

2. The evaluation of hydrocarbon resources and reservesmay have different objectives and parameters for differentaudiences. The SEC set those parameters for provedreserve-reporting purposes through their regulations andguidelines.

3. One should keep in mind that the reserve categories havemeaning only within the context of their definitions.Therefore, even when the evaluator expects upsiderecoverable hydrocarbon volumes, those volumes can notbe reported if they fall outside the definitions. Thisensures consistent reserve reporting among companies.

4. SEC regulations and SPE/WPC reserve definitions mayprevent certain variables from being expressed indistribution form during the probabilistic analysis.

5. Satisfying the P-90, P-50 and P-10 from a hydrocarbonresource distribution is not enough to book reserves.

6. The SPE/WPC reserve definitions do not provideguidelines to the appropriate level to which the P-90, P-50and P-10 are applicable. Also, these definitions do notprovide guidelines for the aggregation of prospects.Therefore, extreme caution should be exercised whenreporting aggregated volumes as reserves.

7. The percentiles applicable to proved, probable andpossible reserves are dynamic throughout the life of thereservoir.

8. Recoverable hydrocarbon volume distributions may notbe risk consistent. These distributions need to be adjustedfor risk (COS) prior to aggregation.

9. One approach to define proved reserves is to select the P-50 value from a proved distribution. Where a proveddistribution is defined as the distribution of recoverablehydrocarbons derived by strictly following the definitionsand regulatory requirements.