Page 258 - Fundamentals of Reservoir Engineering

OILWELL TESTING 195

kh *
p D(MBH) (t )0.01416 qB o (p - p) = 2.303 log (C t ) (7.58)
DA
A
DA
µ
n
or
µ
* qB o
n
p − p = 162.6 log (C t ) = m log (C t ) (7.59)
A DA
A DA
kh
Equation (7.59) is appropriate for the effective flowing time while for the real time
*
p − p = m log(C t ) (7.60)
n t n t A DA n
Subtracting equ. (7.59) from (7.60) gives

*
( p − p * ) ( p − p = m log t t n (7.61)
)
−
n t
n t
which, when compared with equ. (7.57), shows that p − and therefore the
p
n t
determination of the average pressure using the MBH method is the same whether the
real or effective flowing time is employed in the analysis.

Using an identical argument it can easily be demonstrated that the average pressure
determined from a survey is independent of the flowing time used in the analysis. This
is correct providing that the flowing time is equal to or greater than t sss, the time
required for semi-steady state conditions to be established, within the drainage volume,
and the final production rate is also used in the analysis. As an illustration of this
statement, plot C in fig. 7.20 has been drawn for the limiting value of t sss. In this case
plot C is laterally displaced with respect to plot B, for the effective flowing time, so that
the equivalent equations to equ. (7.57) and (7.61) are now

t
p* p* sss = m log t sss
−

and

( p − p * sss ) ( p p− − sss ) = m log t t sss
*

which shows that the MBH analysis technique will yield the same values of p whether t
or t sss is used to plot the buildup. This same conclusion has been presented in the
12
13
literature by Pinson and Kazemi .
It should also be noted that the value of the skin factor determined from the analysis is
also independent of the flowing time. This is because the value of p ws(LIN)1-hr required for
the calculation of S, (equ. (7.52), does not depend on the flowing time and is the same
for plots A, B and C in fig. 7.20.

It is for the above reasons that the convenient combination of final flow rate and
effective flowing time is generally used in buildup analysis. The only assumption that
can be regarded as restrictive is that the final flow period should be of sufficient