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OH – ET – VA - LL: Analysis of Dynamic Data in Shale Gas Reservoirs – Part 1 – Version 2 (December 2010)
p 14/24
Physical explanation: this very low permeability system creates a high pressure gradient close
to the well. Because of the corresponding increase in compressibility, the real performance of
the well will be higher than if we use the corresponding analytical model. In order to
compensate this higher productivity and match the simulation, the analytical model will require
a higher permeability or a higher well productivity.
One may object that the problem comes from the fact that we initialized the PVT parameters at
the initial pressure (in other terms, that we used the
.c
g
product computed at p
i
in the
analysis), whereas we should have used a much lower pressure – closer to the flowing
pressure (500 psia) at least. This is perfectly correct, but the truth is that we do not know
which pressure should be used if we want the error to be minimized – and no one does. For
instance, the results actually get much worse if we use p
wf
in the equations...
Naturally, the single fracture geometry, with such a long linear flow, will allow a straight line
analysis that is completely consistent (within 1% or less) with the analytical model. So the
error found on the analytical model will be exactly the same as for a straight line analysis.
The same process was repeated for higher permeability values, and the results are compared
in the table below. As stated just above straight line results and analytical models are
consistently wrong in the assessment of k.X
f
2
.
Permeability
Numerical model
Analytical model and straight line analysis
k.X
f
2
(md.ft
2
)
k.X
f
2
(md.ft
2
)
Error
1 md
4.0 E+6
4.08 E+6
2 %
1E-2 md
40,000
48,000
20 %
1E-3 md
4,000
5,600
40 %
1E-4 md
400
660
65 %
To be totally honest, we tried to lower even more the permeability (down to 1.E-6 md) and
started to encounter serious convergence issues in the numerical model. We expect the error
above increase even more for these values of permeability, but at this stage we do not have a
suitable benchmark numerical model yet. This is part of the work in progress listed in §17.
Summary:
When dealing with a single fracture in a typical shale gas case, the use of an
analytical model or the drawing of a straight line on the early time linear flow will give an order
of magnitude of the k.X
f
2
product, but will still be substantially off.