Page 178 - Well Logging and Formation Evaluation

168 Well Logging and Formation Evaluation

certain period of time, then shutting them in and observing the buildup of
pressure with time. If the well is flowed for a period T, then shut in, the
pressure behavior will simply follow that of the pressure observed in a
well flowed from t = T subtracted from that of a well flowed from t = 0.
Note that the pressure observed thereby becomes independent of S, which
cancels out.
When analyzing buildups, it is common, in addition to defining
the dimensionless time, to introduce the dimensionless pressure P d
given by:

p
k h (
Q
P d = 2* * * * P i - P) ( *m ). (11.5.9)
Then it can be shown that:
2* * * * P i - P w ( Q *m) = P T d + D t d - P d (Dt d . ) (11.5.10)
(
(
p
)
)
kh
d
In this equation, P d(T d +Dt d) represents the pressure at a dimensionless
time T d +Dt d, converted into a dimensionless pressure using equation
11.5.9. For an infinite reservoir:
)
P d = (12 *ln (4* t d g ). (11.5.11)
Hence

)
kh (
)
)
2* * * * P i - P w ( Q *m) = ( 1 2 *ln T d + D t d Dt d . ] (11.5.12)
( [
p
This is the basis of the so-called Horner plot.
If pressure measurements are made at two different times (P 1 and P 2 ),
it can be shown that:
m
**(
*
kh = (12 * ) Q**( L - L ) [2 p P - P )] (11.5.13)
2
1
2
1
where:
L 1 = ln (T +Dt 1) / Dt 1)
L 2 = ln (T +Dt 2) / Dt 2).
The extrapolation of the pressure on a Horner plot yields the initial reser-
voir pressure (Figure 11.5.1).