Page 334 - Fundamentals of Reservoir Engineering

REAL GAS FLOW: GAS WELL TESTING 269

2
Q t n Q j ∆ mp 2 n psia /cp/(Mscf/d)
() FQ−
j1 Q
Mscf/d hrs n t ∆ j Q n .03 .035 .04
=
hrs F = .047
10 × 10 3 12 12 3263 3433 3383 3333

20 " 24 18 3260 3600 3500 3400

30 " 36 24 3268 3778 3628 3478

40 " 48 30 3271 3951 3751 3551
TABLE 8.4

These data points plot almost as a horizontal straight line which implies an infinite area.
This is to be expected since the value of F determined in the first part of this exercise is
under the assumption that the reservoir pressure remains constant throughout the test,
which implicitly assumes that the reservoir is infinite.

The correct plot should have some positive slope corresponding to the fact that a finite
volume is being drained. This means that the value of F should be decreased on a trial
and error basis until a straight line is obtained. The plot has been re-drawn for values of
F of 0.040, 0.035 and 0.030, refer table 8.4 and fig. 8.10. For the latter two values there
is a slight degree of upward curvature, whereas for the value of F = .04 the plot is linear
2
with slope 12.2 psia /cp/Mscf/d/hr, which implies that the pore volume drained is
6
35.5 × 10 cu ft. Using the values of h = 40 ft and φ = .2 as average for the drainage
volume, the area is approximately 100 acres. Further, the intercept gives the value of
2
the Darcy flow coefficient B as 3186 psia /cp/(Mscf/d).
It must be admitted that the stabilized analysis technique using the plot of equ. (8.47) is
a precarious business, to say the least. In this exercise any of the plots in fig. 8.10, for
different values of F, could be taken to be linear leading to estimates of the area of
60 acres, for F = .035, or 43 acres for F = .030. In a great many cases the high degree
of sensitivity to the value of F precludes any reliable estimate of the pore volume or
area drained being made.

To summarize the foregoing remarks on stabilized gas well testing; semi-steady flow
conditions will occur for some fixed value of

kt
t DA = 0.000264 (8.36)
( ) cA
φµ
i
Therefore, such tests will be appropriate in reservoirs which have a high permeability
and small drainage area so that the semi-steady state condition will be reached in a
relatively short period of time. The reader should be cautioned, however, that these are
not the sole criteria. In exercise 8.1, for instance, the actual permeability is 100 mD and
the well is draining from the centre of a square of area 100 acres. Under these
circumstances the value of t DA which must be exceeded before semi-steady state
conditions prevail is 0.1 (refer either MBH charts, fig. 7.11, or the Dietz chart fig.6.4).