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VA – GP - OA: Numerical Multiphase PTA
p 9/29
We consider the following history (Table 1), which allows analyzing 3 different positions of the
water bank during fall-offs:
Duration (hr)
Rate (stb/d)
Injection 1
1
-10,000
Buildup 1
9
0
Injection 2
10
-10,000
Buildup 2
90
0
Injection 3
100
-10,000
Buildup 3
900
0
Table 1: Injection history for Test Case 2
Results
Figure 11 presents the 3 simulated injection phases. On this figure, the data sets with markers
correspond to the results obtained with the correction based on pseudo-kr curves, while the
solid lines are the uncorrected simulations. We see that although strong oscillations were
visible with the standard model, they are almost completely damped using the correction.
Figure 11: 3 injection curves for Test Case 2. Comparison between standard results (solid
lines) and the correction based on pseudo-kr curves (markers)
Let us call
λo
the mobility in the original reservoir, and
λw
the mobility in the water invaded
zone, where we assume that
Sw
=
1 – Sorw
. From the viscosity values and the relative
permeability data, we get:
λo
= 0.8 / 0.3
λw
= 0.2 / 0.25
λw / λo
= 0.3
The 3 injection derivatives in figure 11 show common behavior. While the pressure
investigation progresses in the reservoir, each derivative can exhibit up to 3 parts,
corresponding to three successive values of the mobility:
λw, λo, λw.
Obviously,
the first part
does not appear during the first injection, because no water bank is present at the beginning.
Also, the last part does not appear if the injection duration is not sufficient.
Figure 12 represents the obtained results for the 3 fall-off phases. The derivatives have 2
parts, corresponding first to
λw
,
then to
λo.
The last part does not appear if the falloff duration
is not sufficient.
1E-5
1E-4
1E-3
0.01
0.1
1
10
100
Time [hr]
10
100
PMatch (injected fluid)
PMatch (multiphase)
injection #1 (ref)
injection #2
injection #3