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
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
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
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
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
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
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
Read it, you'll like it!