Page 269 - Well Logging and Formation Evaluation

Additional Mathematics Theory 259

program such as thermal decay logging. This program will not, of course,
change P(i), but it will change NPV(i). More money will be spent (reduc-
ing NPV(i)) but in return, if the data are reliable and useful (which they
may be for only some of all possible field states), there will result an
increase in revenue or decrease in other costs, having the net effect of
increasing NPV(i).
Since the NPV(i) has changed, the EMV will change, to EMV¢. The
EMV of the proposed change, which we will call DEMV is given by:

DEMV = EMV¢ - EMV (A4.7)

It is important to note that DEMV, irrespective of any issues concern-
ing reliability, depends on all the possible states of the field, not just the
base case.
In order to introduce the concept of reliability, it will be much simpler
to consider for now that the field has only two possible states, which will
be denoted as S 1 and S 2. The EMV of the field is then approximated by:

EMV = P( )* NPV( ) + P(S 2 * NPV(S 2 ). (A4.8)
)
S 1
S 1
Now consider a proposal for a change to the FDP. This will involve the
acquisition of data at a cost of Z and be such that a parameter C will be
determined as being true or false. C is such that:

1. If C is true, the field is known to be definitely in state 1. If C is false,
the field is known to be definitely in state 2. Knowing which state the
field is in would allow the FDP to be optimized.
2. If C is true, the FDP may be optimized to yield a new NPV given by
NPV(S 1 and C). the field being in state S 1 .
3. Likewise if C is false, the FDP may be optimized to yield a new NPV
given by NPV(S 2 and C¢), the field being in state 2.

The change in the EMV is given by:

DEMV =- + P( )* NPV(S 1 and )
Z
C
S 1
+ P(S 2 * NPV(S 2 and ¢) - EMV. (A4.9)
)
C
For the change to be worthwhile, we clearly require that at least one of
the NPV(S 1 and C) or NPV(S 2 and C¢) be greater than NPV(S 1) or
NPV(S 2).