Page 5 - Transmissibility Corrections and Grid Control for Shale Gas Numerical Simulation

VA - DF: Transmissibility Corrections and Grid Control for Shale Gas Numerical Simulation p 4/23
Figure 3 – Comparison of pressure and pressure derivative curves
between analytical (markers) and numerical (continuous lines) results. k=30 mD.
Figure 4 – Comparison of analytical (markers) and numerical (‘model’) forecasts. k=30 mD.
Let us now reduce the permeability of the medium, so that k=1e-4 mD.
It is worth recalling here that reducing k by several order of magnitudes is quite similar to
zooming on short times with a conventional case. Small k will hence amplify the importance of
transient effects, in a zone where most numerical errors typically appear. Indeed, on figures 5
and 6, we now see that several discrepancies arise, both at early time (loglog plot figure 5)
and at late time (production forecast, figure 6).
1E-4 1E-3 0.01 0.1 1 10 100 1000 10000 1E+5
Time [hr]
0.01
0.1
1
10
100
1000
Pressure [psi]
Integral of normalized pressure
Integral of normalized pressure Derivative
0
1E+7
2E+7
Liquid rate [STB/D]
0
1E+8
2E+8
3E+8
Liquid volume [STB]
q (Analytical K=30mD)
Q
q model
Q model
0 10000 20000 30000 40000 50000 60000 70000 80000 90000
Time [hr]
1500
3500
Pressure [psia]
Pi
p