Properly evaluated, drilling opportunities
with multiple prospective zones can be significantly more attractive
than single-objective proposals. The combination of the various
zones can add pre-drill expected value (EV) to the portfolio by
demonstrating the improved chance of a flowing discovery, increasing
the estimated resource potential, or both.

However, with this increased value there also comes
increased complexity.

This article describes some of that complexity associated
with multiple-zone systems, and explains the difference between
reciprocal dependency and conditional dependency. The extent of
dependency should be forecast relative to geologic phenomena that
have influenced the total subsurface system.

Geoscientists and engineers need to have a good understanding
of the various types of dependencies that should be considered —
and the impact they will have on the calculation of potential reserves
and chance.

To assess the chance and resource assessment of multiple
zones, start by evaluating, for each zone, the range of resource
potential (which we will refer to in terms of the mean, Mz, of the
distribution) and geologic chance of success, Pg.

These two sets of data are then combined using appropriate
statistical procedures — a statistical process that requires the
additional estimate of the extent of dependency between the zones.

Consider two zones, A and B:

**Zone A**

3 Pg = 30 percent.

3 Mz = 60 MMBO.

3 CWR = Chance-weighted resource

= Pg x Mz = 18 MMBO.

**Zone B**

3 Pg = 20 percent.

3 Mz = 80 MMBO.

3 CWR = Chance-weighted resource

= Pg x Mz = 16 MMBO.

**Independence**

The chance of at least one zone being successful,
assuming no dependence between the zones, is simply 1 minus the
chance of all zones failing:

Pg(well) = 1- (1-Pg(A)) x (1-Pg(B))

= 1- (1 - 0.30) x (1- 0.20) = 1 — (0.7) x (0.8) = 1- 0.56 = 0.44.

To calculate the mean resource for the well, divide
the sum of chance weighted resources for the zones by the Pg(well).

Mz(well) = (CWR(A) + CWR(B)) ÷ Pg(well) = (18 + 16) ÷ 0.44 =
77.3 MMBO.

We now know the independent chance of having one
or more successful zones, 44 percent; and the mean resource (if
successful), 77.3 million barrels. The P10 and P90 range of resources
can be calculated using appropriate statistical tools. Available
multiple-zone software takes advantage of Monte Carlo sampling techniques
to selectively add success-case outcomes from each zone.

## Dependence

Now we calculate the analogous values assuming a
fully dependent state. Fully dependent zones can be either reciprocally
dependent or conditionally dependent. Reciprocal dependency means
that if one zone works the other must work, and if one zone fails
the other must fail.

Due to the forced similarity constraint, both zones
must have the same chance of success. Alternatively, in the common
case of conditional dependency, the success of the lower-chance
zone (B) relies on the success of the higher-chance zone (A), but
there is a possibility that zone B could fail even if zone A is
successful. Success of zone B is therefore fully conditional (only
possible) on the success or failure of zone A.

As an analog, consider Joe and Mary in a class demonstrating
a game of "standup or sit down." If the two are independent, Joe
and Mary can stand up or sit down without regard for the other.
If Mary is conditionally dependent upon Joe, then she MAY stand
when Joe stands and CAN NOT stand unless Joe stands.

If the above probabilities of Joe standing equal
30 percent and Mary standing equal 20 percent, then Joe would stand
up when asked 30 percent of the time, Mary would never stand unless
Joe stands, and when Joe stands Mary would stand 67 percent (20
percent ÷ 30 percent) of the time.

Since Mary can never stand without Joe standing,
the probability of at least one person standing is the same as the
probability of Joe standing, or 30 percent.

We can apply this same logic to zones A and B. If
the two zones are fully dependent, they cannot be reciprocally dependent
because they have different chances. B must be conditional on A
since A is the higher-chance zone. In other words, they are conditionally
dependent.

The overall chance of at least one zone is the same
as the chance of the lowest-chance zone, Zone A or 30 percent.

Now, back to our geologic system with this specific
conditional probability applied,

Pg(well) = Pg (highest chance zone)

= Pg(A) = 30 percent.

The mean resources are calculated the same way they
would be if the zones were independent; the sum of the chance-weighted
zone resources divided by the Pg(well).

Mz(well) = (CWR(A) + CWR(B)) ÷ Pg(well) = (18 + 16) ÷ 0.30 =
113.3 MMBO.

## Comparing the Results

Notice that independence generates the higher chance
and dependence generates the higher mean resource. In this example,
chance ranges from 30 percent in the fully dependent case to 44
percent in the fully independent case — a wide expanse of 14 percentage
points.

If the geologic data suggests that the zones are
partially dependent you can simply estimate the "strength of dependency,"
also referred to as the degree of correlation through the range
of the chance of success spectrum (which in this case is bounded
between 30 percent and 44 percent):

Level of dependence: Pg Mean

resource

Full dependence: 30.0% 113.3

Strong:

(1/3 through range) 34.7% 98.0

Moderate:

(halfway through range) 37.0% 91.9

Weak:

(2/3 through range) 39.3% 86.5

Full independence: 44.0% 77.3

Once the strength of dependency is assigned (here
we will assume there is a "strong" correlation) the mean resource
is calculated the same way as we did previously:

Mz(well) = (CWR(A) + CWR(B)) ÷ Pg(well) = (18 + 16) ÷ 0.347
= 98.0 MMBO.

Note: The chance of completing (Pc) this discovery
is derived by multiplying (1) the combined Pg of the test by (2)
the percentage of the combined revenues distribution that is larger
than the "threshold" reserves value required to pay for completion,
flowlines and production facilities.

Recommended Reading: Naked Economics: Undressing the
Dismal Science, 2003, by Charles Wheelan (Norton).

Now, listen up folks! This is a "must read" for every
geoscientist or engineer who thinks economics is probably important,
but impossibly opaque and boring. Very well written, clear, concise
and — best of all — entertaining!

**Read it, you'll like it!**

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