Page 21 - Transmissibility Corrections and Grid Control for Shale Gas Numerical Simulation
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VA - DF: Transmissibility Corrections and Grid Control for Shale Gas Numerical Simulation
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Figure 23
– Transient numerical results for various ‘time resolution’ choices,
with the automatic grid setting procedure – Non-linear gas PVT
Conclusions
Specific transmissibility derivations have been developed to address the production of multi-
fractured horizontal wells in low-permeability formations. New transmissibilities are shown to
improve the coherency between analytical and numerical production cumulatives, compared to
the standard, linear case. It should be noticed, however, that these corrections assume high
fracture permeability compared to the matrix.
When the matrix permeability is very low, transients last much longer than in the case of
conventional permeability. As a consequence, for transient analysis, the size of the grid must
be carefully chosen in order to account for the expected effective resolution of the simulation.
An automatic grid refinement procedure has been implemented, which depends on the
investigation radius at the desired resolution time scale. This process is shown to be quite
robust, as long as non-linear PVT effects within the first cell are not too strong.
The proposed solutions are shown to significantly reduce numerical errors linked to the low-
permeability, transient context. These initial errors can be shown to be in the same range as
the uncertainty due to physical parameters in some real cases [2]. Before history matching
real data, such validation hence seems essential to avoid using purely effective physical
parameter values in order to simply compensate for strong numerical effects.
Acknowledgement
This material has originally been prepared and accepted for publication in Oil and Gas Science
and Technology
. The authors wish to acknowledge Kappa Engineering for
permission to publish this work. Simon Trin and Diego Molinari (Kappa Engineering) are also
gratefully acknowledged for early tests of the grid control approach, and for their faithful
struggle against early versions of the code for transmissibility corrections.
0.1
1
10
100
1000
Time [hr]
10000
1E+5
1E+6
Gas potential [psi2/cp]
t=0.01 hr
t=0.1 hr
t=1 hr
t=10 hr
t=100 hr
ultrafine
t=0.001
t=0.0001
