A Lot to the Project

'Mean' Can Mean

There seems to be a lot of confusion about the relationship between chance of success for a drilling prospect and various possible outcomes of recoverable reserves. Such confusion could lead to bad E&P business decisions.

Here's an example: Assume an onshore trend wildcat (Prospect Alpha) in a known play. The estimated prospect reserves distribution (PRD) is shown in figure 1: P90 = .15MMBOE, P50 = 1.0MMBOE, P10 = 7.0MMBOE.

Employing Swanson's Rule, the mean (= average) of the PRD, truncated at P1 and P99, is about 2.5MMBOE, which happens to fall at about P27.

Assume further that Prospect Alpha's chance of success (Pc = Pcompletion) is estimated at 30 percent.

In simplistic applications of E&P risk analysis, the prospect-team would say that the chance of success represents their confidence in "landing somewhere on the PRD," the mean of which is about 2.5MMBOE.

But that's not the same as saying that Prospect Alpha has a 30 percent chance of finding 2.5MMBOE!

Figure 2 expresses reality, and presents quite a different picture. It confirms that the team is 30 percent sure (Pc = 0.3), that Prospect Alpha will find 30,000 BOE (= P99) or more, and that the Swanson's Mean of all reserve outcomes between P99 and P1 is indeed about 2.5MMBOE.

However, what's the chance of finding the P90 reserves outcome (= .15MMBOE) or more? That's 0.3 x 0.9 = 27 percent.

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There seems to be a lot of confusion about the relationship between chance of success for a drilling prospect and various possible outcomes of recoverable reserves. Such confusion could lead to bad E&P business decisions.

Here's an example: Assume an onshore trend wildcat (Prospect Alpha) in a known play. The estimated prospect reserves distribution (PRD) is shown in figure 1: P90 = .15MMBOE, P50 = 1.0MMBOE, P10 = 7.0MMBOE.

Employing Swanson's Rule, the mean (= average) of the PRD, truncated at P1 and P99, is about 2.5MMBOE, which happens to fall at about P27.

Assume further that Prospect Alpha's chance of success (Pc = Pcompletion) is estimated at 30 percent.

In simplistic applications of E&P risk analysis, the prospect-team would say that the chance of success represents their confidence in "landing somewhere on the PRD," the mean of which is about 2.5MMBOE.

But that's not the same as saying that Prospect Alpha has a 30 percent chance of finding 2.5MMBOE!

Figure 2 expresses reality, and presents quite a different picture. It confirms that the team is 30 percent sure (Pc = 0.3), that Prospect Alpha will find 30,000 BOE (= P99) or more, and that the Swanson's Mean of all reserve outcomes between P99 and P1 is indeed about 2.5MMBOE.

However, what's the chance of finding the P90 reserves outcome (= .15MMBOE) or more? That's 0.3 x 0.9 = 27 percent.

How about the P50 outcome (1.0MMBOE) or more? That's 0.3 x 0.5 = 15 percent.

What about the P10 outcome (7.0MMBOE) or more? That's 0.3 x 0.1 = 3 percent!

Now, back to the original question: What's the chance of Prospect Alpha finding the mean reserves outcome of 2.5MMBOE or more?

Answer: 0.3 x 0.27 = 8 percent.

A key point here — whenever you're working in the cumulative probability domain, always remember to add "or more" to any reserves outcome.


Now let's introduce another dose of reality.

Again, following simplistic risk analysis procedures, we would construct a cash-flow model of the project — based on the mean reserves outcome, laying out projected investments, production revenues and operating costs over the life of the contemplated field and taking into account the time-value of money.

Obviously, such a cash-flow model has to "fit" the geologic parameters leading to the mean reserves outcome — that is, the values employed for numbers of development wells must be compatible with the mean productive area.

Similarly, projected production rates must be compatible with average net pay and HC-recovery factors for the mean reserves case.

The result is project present value (PV) that fits the geology and risk analysis.

Now, suppose that the PV of the mean reserves case (2.5MMBOE) turns out to be $10MM, discounted at 8 percent — or $4 PV per recoverable BOE.

If you're still tracking, you already realize that Prospect Alpha does not have a 30 percent chance of being worth $10MM, or more! If the $4 PV per BOE is constant for all reserves outcomes, we could say there's:

  • A 27 percent chance of a result worth $0.6MM (.15MMBOE x $4 PV/BOE) or more.
  • A 15 percent chance of reserves worth $4 MM (1MMBOE x $4 PV/BOE), or more.
  • A 3 percent chance of reserves worth $28MM (7.0MMBOE x $4 PV/BOE) or more.

But in the real world, we know that PV/BOE is seldom constant. Onshore, relative profitability is commonly larger for large fields than small ones (usually because of economies of scale), so PV/BOE is successively greater for the P90, P50, mean and P10 outcomes.

Let's suppose that PV/BOE for the P90 reserves case (.15MMBOE) is (-)$2, giving a PV of $(-)$.30MM, which indicates an outcome that is commercial but not full-cycle economic.

For the P50 case, PV/BOE is $3, giving a PV of $3.0MM. And for the P10 case, PV/BOE is $5.50, giving a PV of $38.5MM. The mean of the calculated PV's is $12.7MM, substantially more than the PV of the mean ($10MM).

Simplistic risk analysis procedures have undervalued Prospect Alpha!


A few concluding comments:

  • For many international production-sharing contracts, PV/BOE decreases as size of discoveries increases because the country-share gets larger as field size gets larger. Offshore projects may show non-linear "step-functions" in the PV/BOE curve, owing to irregular variations in costs of marine facilities.
  • The implication here is that proper economic evaluation of prospects requires not one economic run, but at least three.

Some overworked reservoir engineers may understandably complain that this approach triples their work, generating economic analyses. However, getting the appropriate project mean PV will lead to more realistic evaluations, better decisions and improved profitability — and that's well worth the extra time and work!

In any case, however, it's usually better to calculate the mean of all the PVs rather than the PV of only the mean reserves case.

Most important, though, is to understand the difference!


Recommended Reading: The Nature of Economies, by Jane Jacobs, Modern Library (Random House), 2000.

A very interesting, very unusual little book (190 pp.) by a distinguished American author that explores the remarkable similarities between ecological and economic communities — and establishes clearly that, rather than ecology and business being natural enemies, they are in fact both part of the same larger natural system, with many mutually beneficial benefits.

I've read this book twice now, and believe it should be required reading for environmental activists as well as free-market proponents.

Read it, you'll like it!

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