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VA – GP - OA: Numerical Multiphase PTA
p 10/29
In all cases, the first period corresponds to the nearby region, with water mobility, and the
second period to the original fluid, with oil mobility. We see that the injection curve differs
from the falloff curve by exhibiting a third period at the water mobility level. This corresponds
to a period of predominant water displacement, and the curve shows the increase of overall
pressure drop due to the extension of the water zone. Without the correction based on pseudo-
kr curves, the original oscillations occur during this period, while the water front progresses
from one ring of cells to another.
Figure 12: Fall-off curves for Test Case 2.
Comparison with analytical model
In order to justify the classical analytical interpretation, equivalent analytical simulations have
been performed using a single-phase, radial composite model. The composite radius ri is
computed by assuming a sharp front of injected water from
Swr
to (
1–Sorw
). This leads to
three models, with radius ri=8.2, ri=27.3 and ri=86.7 ft.
From the mobility ratio, the values
μ,
M and D are computed:
The viscosity of the equivalent fluid close from well is
μ
=
μw / krw =
1.25 cp
M = D = (
λw / λo
) =0.3
The superposition of the different curves (figures 13, 14 and 15) shows a very good agreement
between the numerical and the analytical models. Note that on figure 15, the late-time
discrepancy on the effective boundary position is linked to existing connate water saturation in
the numerical model, and could be easily corrected.
1E-5 1E-4 1E-3 0.01
0.1
1
10
100
1000
Time [hr]
10
100
PMatch (injected fluid)
PMatch (multiphase)
fall-off #1
fall-off #2
fall-off #3 (ref)