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OH – ET – VA - LL: Analysis of Dynamic Data in Shale Gas Reservoirs – Part 1 – Version 2 (December 2010)
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7 – Validating the numerical model
The first part of the work below is to validate the numerical model, by comparing the run of
linear problems with the equivalent analytical tool. To do this we will cover the different
configurations that may be analytically modelled.
Let us first step aside from the multi-fractured complex gridding and consider a simple, single
infinite conductivity fracture, with no wellbore storage and infinite behaviour. We just use the
slightly compressible fluid assumption, i.e. we also put aside the different nonlinearities we will
be dealing a little later with shale gas.
First we take the reference parameters listed in §3, except for the permeability. We will start
with a more standard 1 md formation. On the Saphir loglog plot below we see that the
numerical and analytical models match very well:
Now if we run the same case with the permeability assigned to shale gas, we see that a first
run using the standard gridding of Saphir, which was working perfectly for the 1 md formation
shown above, no longer matches the early time response. There is now this infamous early
time “double-porosity looking” numerical effect, which has for consequence that numerical and
analytical models will only merge after one to ten hours.
In reality this is not that bad, because in shale gas cases one will not seriously expect to see
anything on the first ten hours of production or shut-in. However this illustrates the fact that
we were a bit optimistic in our initial option to set the grid irrespective of the permeability.
So, for the sake of validation we had to create an additional upscaling (a
downscaling
, in fact)
in our numerical model, especially to model early time responses in micro-permeability
formations. The result is also shown in the loglog plot below.
In the rest of this document, we will use, when needed, this additional refinement. Before
running any complex nonlinear simulation, we run the equivalent linear case and validate it
with the corresponding analytical model for the same geometry and permeability value.