Page 6 - Transmissibility Corrections and Grid Control for Shale Gas Numerical Simulation

VA - DF: Transmissibility Corrections and Grid Control for Shale Gas Numerical Simulation p 5/23
First, as visible from Figure 5, the early-time behavior is completely lost. Part of this
discrepancy is explained by the compressibility of the fluid inside the fracture, which is
accounted for by the numerical model only. However, as was already noticed in [1], the
derivative curve obtained with the standard grid shows a purely numerical, ‘double-porosity
looking’ effect. This has to be related to the size of the first rings of cells around the fractures.
Although the standard size was quite sufficient to capture the early-time behavior for a
conventional range of permeability values, we see that it cannot be set irrespectively of the
permeability field in nano to micro Darcy permeability formations. Indeed, reducing the grid
size to millimeter scale in the vicinity of the fracture solves the problem (ultra-fine grid in
Figure 5). A practical objective of this study is to find the best resolution depending on the
context, without having to systematically use the finest grid. This will be developed in section
5, dedicated to grid refinement control.
Figure 5 – Comparison of pressure and pressure derivative curves
between analytical (markers) and numerical (continuous lines) results. k=1E-4 mD.
1E-3 0.01 0.1 1 10 100 1000 10000
Time [hr]
0.1
1
10
100
1000
Pressure [psi]
standard grid
ultra-fine grid