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VA – GP - OA: Numerical Multiphase PTA
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3. Black-oil production
We now analyze multiphase effects in the case of black-oil production. In this situation, mass
transfer exists between the oil and the gas phases, as the light component can vaporize during
depletion.
3.1. Test Case 3
Test description
The reservoir is circular, with a central production well. No water phase is considered. The
initial pressure is Pi=5,000 psi. The porosity is
Φ
= 0.20 and the rock compressibility is cr=3e-
6 psi
-1
.
The oil phase is defined using the “saturated oil” option, with T=212 °F and GOR = 1520
scf/stb. This gives Pb=4500 psi. All other data are kept at their default values. The resulting
data at bubble point are Bo=1.863,
o=0.226 cp.
The relative permeability curves are of power-law type with exponent 2, using Sorg =0.25,
Sgr=0.05, Krogmax=0.8 and Krgomax=0.5.
The production history is:
Production: duration 10,000 hr, rates Qo=10,000 stb/D and Qg=15,200 Mscf/D, giving a
total constraint rate Qt=10,000 stb/D.
Build-up: duration 10,000 hr.
In order to investigate different levels of depletion, we ran more than 30 simulations on this
case, varying both the reservoir radius R (from 5,000 ft to 50,000 ft) and the reservoir
permeability k (from 50 mD to 200 mD).
Results
Figure 16 shows the results for limited depletion, using R=50,000 ft and k=200 mD. In this
case, the bubble point pressure is reached around the well after 30 hr production, leading to
the apparition of gas in the system. As the pressure continues to drop down, the gas zone
expands further away from the well, leading to oscillations. Each oscillation can be related to
the apparition of gas in a new ring of cells around the well (Figure 17).
As in the case of water injection, oscillations can be explained by the progression of a
saturation shock in the medium, although the physical process is different here, because the
gas appears locally by depletion below the bubble point. Again, reducing the gridding
progression ratio increases the frequency of oscillations but reduces their magnitude (Figure
16).
Figure 16: Effect of the discretization during production period (R=50,000 ft, k=200 mD)
0.01
0.1
1
10
100
1000
10000
Time [hr]
100
1000
K=200mD
K=200mD refined