Page 7 - Transmissibility Corrections and Grid Control for Shale Gas Numerical Simulation

VA - DF: Transmissibility Corrections and Grid Control for Shale Gas Numerical Simulation p 6/23
Figure 6 – Comparison of analytical (markers) and numerical (‘model’) forecasts. k=1E-4 mD.
Second, the long-term forecasts can be significantly deviating (Figure 6). After 10 years, the
cumulative predicted by the numerical model can be up to 5% greater than the analytical
prediction in some cases. This is related to the strong non-linear behavior of the pressure field
in the vicinity of the fractures. As a consequence of this effect, the standard linear assumption
behind transmissibility derivations cannot hold anymore, although the grid is very fine and K-
orthogonal. This phenomenon was negligible with a conventional permeability. With shale gas,
however, the pressure drop remains localized in the vicinity of the fractures even after years of
production, and non-linear effects cannot be neglected anymore.
Finally, let us consider the non-linear nature of gas PVT properties. As previously noticed in
[1], the high compressibility of the gas in the vicinity of the fractures increases the overall
productivity. This effect can be accounted for by the numerical model only. Indeed, by
assuming a constant µg.cg product (gas viscosity  compressibility), analytical calculations
systematically underestimate the productivity in this context (Figure 7), leading to significantly
lower cumulatives. However, in order to fully rely on the numerical answer, we must ensure
that the numerical model correctly captures the variations of cg and µg close to the fractures,
i.e. that the grid is fine enough.
200
300
400
500
600
Liquid rate [STB/D]
4E+5
6E+5
8E+5
1E+6
1.2E+6
Liquid volume [STB]
Reference
Standard Solution
42000 46000 50000 54000 58000 62000 66000 70000 74000 78000 82000 86000 90000
Time [hr]
200
300
Pressure [psia]