Page 270 - Well Logging and Formation Evaluation

260 Well Logging and Formation Evaluation

The VOI is clearly given by VOI = (DEMV - Z). Now consider the
effect of reliability. This means in effect that sometimes the parameter C
will be found to be true even though the field is in state 2, and vice versa.
The reliability is expressed via:

R = ( P C S )
1

i.e., the probability that C is found to be true when the field is indeed
in state 1. For simplicity we will also assume that this is the same as
P(C¢/S 2), i.e., the probability that C is found to be false when the field is
indeed in state 2. The introduction of R clearly leads us to have to con-
sider the additional NPV scenarios:

1. NPV(S 1 and C¢): the NPV realized when the field is thought to be in
state 2 but is actually in state 1.
2. NPV(S 2 and C): the NPV realized when the field is thought to be in
state 1 but is actually in state 2.
We will now calculate DEMV, introducing these additional scenarios:

)
)
Z
DEMV =- + P() [ * P(C S 1 * NPV(S 1 and )+ P(C S 1 *
¢
C
S 1
)
C
¢
and ¢)]+ P() [ * P(C S 2 *
NPV(S 1 S 2
)
C
and ¢)+ P(C S 2 * and )]- EMV (A4.10)
C
NPV(S 2 NPV(S 2
Using our definition of R:
S 1 *
DEMV =- + P() [R* NPV(S 1 and )+ (1 - R *
C
)
Z
C
C
S 2 *
and ¢)]+ P() [R* and ¢)+
NPV(S 1 NPV(S 2
)
C
(1 - R * NPV(S 2 and )]- EMV (A4.11)
Another way to look at this is that we have four possible combinations
of C, C¢, S 1 , and S 2 , each having a probability and NPV associated with
it. The EMV is therefore:
DEMV = P(S 1 and )* NPV(S 1 and )
C
C
+ P(S 2 and )* NPV(S 2 and )
C
C
+ P(S 1 and ¢)* NPC(S 1 and ¢)
C
C
+ P(S 2 and ¢)* NPV(S 2 and ¢)
C
C
- Z - EMV (A4.12)