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Distributed by permission of

Hart's E & Pand James Murtha

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2 Risk Analysi

Jim Murtha, a registered petroleumengineer, presents seminars and training

courses and advises clients in building

probabilistic models in risk analysis and

decision making. He was elected toDistinguished Membership in SPE in

1999, received the 1998 SPE Award in

Economics and Evaluation, and was

1996-97 SPE Distinguished Lecturer in

Risk and Decision Analysis. Since 1992,

more than 2,500 professionals have taken

his classes. He has published Decisions

Involving Uncertainty - An @RISK

Tutorial for the Petroleum Industry. In

25 years of academic experience, he

chaired a math department, taught petro-

leum engineering, served as academicdean, and co-authored two texts in

mathematics and statistics. Jim has a

Ph.D. in mathematics from the Uni-

versity of Wisconsin, an MS in petroleum

and natural gas engineering from Penn

State and a BS in mathematics from

Marietta College. x

Risk Analysis:

Table of Contents

When I was a struggling assistant professor ofmathematics, I yearned for more ideas, for we

were expected to write technical papers and

suggest wonderful projects to graduate students.

Now I have no students and no one is counting

my publications. But, the ideas have been

coming. Indeed, I find myself, like anyone who

teaches classes to professionals, constantly

stumbling on notions worth exploring.

The articles herein were generated during a

few years and written mostly in about 6

months. A couple of related papers found theirway into SPE meetings this year.

I thank the hundreds of people who listened

and challenged and suggested during classes.

I owe a lot to Susan Peterson, John Trahan

and Red White, friends with whom I argue and

bounce ideas around from time to time.

Most of all,these articles benefited by the careful

reading of one person,Wilton Adams,who has often

assisted Susan and me in risk analysis classes.

During the past year, he has been especially helpful

in reviewing every word of the papers I wrote for

SPE and for this publication.Among his talents are

a well tuned ear and high standards for clarity.

I wish to thank him for his generosity.

He also plays a mean keyboard, sings agood song and is a collaborator in a certain

periodic culinary activity.

You should be so lucky. x

Acknowledgementsv

A Guide To Risk Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 3

Central Limit Theorem Polls and Holes . . . . . . . . . . . 5

Estimating Pay Thickness

From Seismic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Bayes Theorem Pitfalls . . . . . . . . . . . . . . . . . . . . . . . . 12

Decision Trees vs. Monte Carlo Simulation . . . . . . . . 14

When Does Correlation Matter?. . . . . . . . . . . . . . . . . 20

Beware of Risked Reserves . . . . . . . . . . . . . . . . . . . . 24

Decisioneering Company Profile . . . . . . . . . . . . . . . . 26

Landmark Company Profile . . . . . . . . . . . . . . . . . . . 28

Palisade Company Profile . . . . . . . . . . . . . . . . . . . . . . 30

Table of Contentsv

Biographyv

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24 Risk Analysi

Risk Analysis:

Risked Reserves

RRisked reserves is a phrase we hear a lot these days.It can have at least three meanings:

1. risked reserves might be the product of the

probability of success,P(S),and the mean value

of reserves in case of a discovery. In this case,

risked reserves is a single value;

2. risked reserves might be the probability

distribution obtained by scaling down all thevalues by a factor of P(S); or

3. risked reserves might be a distribution with

spike at 0 having probability P(S) and a reduced

probability distribution of the success case.

Take as an example Exploration Prospect A. I

has a 30% chance of success. If successful, then it

reserves can be characterized as in Figure 1,

lognormal distribution with a mean of 200,000

STB (stock tank barrels) and a standard deviationof 40,000 STB. Then:

definition 1 yields the single numbe

0.3*200,000 = 60,000 STB;

definition 2 yields a lognormal definition with

a mean of 60,000 and a standard deviation o

12,000 (See Figure 2); and

definition 3 is the hybrid distribution shown in

Figure 3.By contrast,suppose another prospect

B, has a 15% chance of success and a reserve

distribution with a mean of 400,000 STB and a

standard deviation of 200,000 STB.Then unde

definition 1,B would yield the same risk reserveas A, 0.15*400,000 = 60,000 STB. However, conside

Figure 2, which shows how B would be scaled

compared with A,with the same mean but large

standard deviation.And Figure 4 shows how th

original distributions compare.

Assigning these two prospects the same numbe

for the purpose of any sort of ranking could be

misleading. Prospect B is much riskier, both in th

sense that it has only half the probability of succes

than does A,and also because even if it is a success,th

range of possible outcomes is much broader. In fact

the P10,where P=Percentile,of Prospect B equals thP50 of Prospect A.Thus,if you drilled several Prospec

A types,for fully half of your successes (on average),the

reserves would be less than the 10th percentile of one

prospect B.

The only thing equal about Prospects A and B i

that, in the long run, several prospects similar to

Prospect A would yield the same average reserves a

several other prospects like B. Even this is deceptive

because the range of possible outcomes for severa

prospects like A is much different from the range o

Beware of

Risked Reserves

Figure 1.Lognormal distribution for Prospect A reserves

Figure 2.Comparing the original distributions for A and B

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Risk Analysis 25

Risk Analysis

Risked Reserves

possible outcomes of B-types. For instance, if we

consider a program of five wells similar to A, there is a

51% chance of at least one success,and a 9% chance of

success on two or more.However,with five prospects

like B, the corresponding chances are 26% and 2%assuming they are geologically independent.

Running economicsWhat kind of economics these two prospects would

generate is another story. Prospects like A would

provide smaller discoveries more consistent in size.

They would require different development plans and

have different economies of scale than would

prospects like B.

So, does that mean we should run economics?

Well, yes, of course, but the question is with what

values of reserves do we run economics? Certainly notwith risked reserves according to definition 1,which is

not reality at all.We would never have a discovery with

60,000 STB.Our discoveries for A would range from

about 120,000 STB to 310,000 STB and for B from

about 180,000 STB to 780,000 STB (we are using the

P5 and P95 values of the distributions). So, surely, we

must run economics for very different cases.We could

take a few typical discovery sizes for A (or B), figure a

production schedule,assign some capital for wells and

facilities, sprinkle in some operating expenses and

calculate net present value (NPV) at 10% and IRR

(internal rate of return).My preference is not to run afew typical economics cases and then average them.

Even if you have the percentiles correct for reserves,

why should you think those carry over to the same

percentiles for NPV or IRR? Rather, I prefer to run

probabilistic economics. That is, build a cashflow

model containing the reserves component as well as

appropriate development plans.On each iteration,the

field size and perhaps the sampled area might

determine a suitable development plan, which would

generate capital (facilities and drilling schedule),

operating expense and production schedule the

ingredients, along with prices, for cashflow. Theoutputs would include distributions for NPV and

IRR. Comparing the outputs for A and B would

allow us to answer questions like:

what is the chance of making money with A or

B? What is the probability that NPV>0? and

what is the chance of exceeding our hurdle rate

for IRR?

The answers to these questions together with the

comparison of the reserves distributions would give

us much more information for decision-making or

ranking prospects. Moreover, the process would

indicate the drivers of NPV and of reserves, leading

to questions of management of risks.

SummaryThe phrase risked reserves is ambiguous.Clarifying its

meaning will help avoid miscommunication.

Especially when comparing two prospects, one mustrecognize the range of possibilities inherent in any

multiple-prospect program. Development plans must

be designed for real cases not for field sizes scaled

down by chance of success. Full-scale probabilistic

economics requires the various components of the

model be connected properly to avoid creating

inappropriate realizations.The benefits of probabilistic

cashflow models, however, are significant, allowing us

to make informed decisions about the likelihood of

attaining specific goals. x

Figure 3.Hybrid distribution for A showing spike at 0 for failure case

Figure 4. Original distributions for A and B