Page 282 - Fundamentals of Reservoir Engineering

OILWELL TESTING 219

Time Rate p wf (p wf N − p wf n ) p D (t D) n ∆ q j )
n p( t δ D n − t δ D j 1
D
hrs stb/d psi q − q N jN 1 q − q N −
n
=+
n
4 600 1815 1.350 5.968 5.968
8 800 1533 1.380 6.315 6.142
12 1000 1244 1.402 6.518 6.267
16 1200 950 1.419 6.662 6.366

TABLE 7.16

(p wf N − p wf n )
1.41 (q − q )
N
n
(psi/stb /d)

1.39

1.37

1.35
∆ q j
p( t D − t δ )
δ
D
q − q N n j D − 1
n
1.33
5.9 6.0 6.1 6.2 6.3 6.4

Fig. 7.30 Multi-rate test analysis in a partially depleted reservoir

The slope and intercept of the straight line have values of 0.173 and 0.317,
respectively, from which it can be calculated that k = 19.6 mD and S = 1.8. These
values compare very favourably with the actual values of k = 20 mD and S = 2.0.

7.9 THE EFFECTS OF PARTIAL WELL COMPLETION

In deriving the basic diffusivity equation for liquid flow, equ. (5.20), it was assumed that
the well was completed across the entire producing interval thus implying fully radial
flow. If for some reason the well only partially penetrates the formation, as shown in
fig. 7.31 (a), then the flow can no longer be regarded as radial. Instead, in a restricted
region at the base of the well, the flow could more closely be described as being
spherical.