Page 268 - Well Logging and Formation Evaluation

258 Well Logging and Formation Evaluation

from a to c. Hence, say a lies in a northerly direction and c in an easterly
direction; the cross-product would point downward into the Earth. Of par-
ticular reference to surveying is the fact that taking the vector product of
a unit gravity vector with a vector in the hole direction yields a horizon-
tal vector 90 degrees to the right of highside in the sensor plane. Taking
the vector product of this vector with a vector in the hole direction yields
a vector in the direction of highside.

A4.5 PROBABILITY THEORY

It may be helpful for readers who are involved with VOI calculations
to have more background information on probability theory to understand
better the concepts of EMV and reliability. Some of these will be
explained in this section. Suppose that you have discovered an oil field.
This field has many uncertainties surrounding it. However, you have deter-
mined a field development plan that you intend to carry out, and wish to
know the EMV of such a plan.
In reality, depending on the actual true nature of the field, your plan
may be either a very good one, a very bad one, or somewhere in between.
While the true nature of the field may obviously have an infinite number
of different states, consider for now that there are N possible states that
more or less encompass all the range of possibilities.
For a particular state i (out of the N possibilities), your field develop-
ment plan will yield a value of NPV(i), this being the present value of the
net revenue minus expenditure over the life of the field. The state i has a
probability P(i) of being close to the true state of the field. Clearly it must
be true that

 N P i ( ) = 10 (A4.5)
.
i=1
The EMV will be given by:

EMV = Â N ( ) i * NPV( ) i (A4.6)
= i 1

Some of the NPV(i) may be negative (e.g., if the field is much smaller
than originally thought), and some may be very positive (if the field is
larger than expected). The final EMV should certainly be positive, or else
the whole development would not be worth embarking on.
Now consider that someone proposes an amendment to the field devel-
opment plan. An example might be the addition of a data acquisition