Numerical models may be exchanged between
Saphir, Topaze and Rubis with the model grid
dynamically adapting to its new environment.
Although analytical models are still an integral part of
the workflow and remain under active development,
numerical models are at the core of the suite and
of increasing importance. Without the numerical
capability rigorous treatment of certain cases,
especially unconventional resources, would not be
possible.
Well models calculated by Amethyste can be sent to
and used by Saphir, Topaze and Rubis.
The KAPPA numerical model
The basic premise of the Voronoi numerical model
is that the grid is a necessary evil and that the
engineer’s focus is the physical problem. We simplify
and automate as far as possible. The sequence
shows the workflow in this example of building a
simple 2D model that might be utilized in Saphir and
Topaze.
1.
Define the reservoir boundary, the wells and
faults using interactive drawing tools overlaying a
scaled bitmap representing the reservoir.
2.
Define composite zones, thickness, porosity and
permeability fields
3.
The grid fills the area automatically.
4.
During and post-simulation the static and
dynamic properties can be visualized and
animated in 2D, pseudo-3D and 3D.
5.
At each well, the 2D unstructured grid is
replaced by a 3D unstructured grid as needed,
for example, in the case of a limited entry or
horizontal well.
6.
Vertical and horizontal anisotropy can be
introduced.
When extending into 3D in the Rubis model, strata
and gravity are added. Alternatively horizons,
volumes and static properties can be directly
imported from Geomodelers such as Petrel™
using GRDECL or CMG formats.
By extension, the numerical model is the tool for
the non-linear case in PTA and PA including real gas
diffusion, multiphase flow, water and gas injectors,
water drives, non-Darcy flow (Forscheimer),
unconsolidated formations, desorption and
extreme compressibility environments found in
unconventional resources.
The KAPPA numerical modules use the same
technical kernel and the same basic reservoir grids
with flexible upscaling adapted to very different
requirements around the well.
Considering the case of a horizontal well, PTA
needs very significant refinement, with around two
thousand cells to perfectly simulate the different 3D
flow regimes on a loglog scale. PA only requires a
detailed 2D or limited 3D representation with around
300
cells around the well. Whilst HM time steps,
being days or weeks, require very coarse grid with
only six cells being sufficient.
Comparing these three different refinements on a
loglog scale shows that all responses merge on a
reference analytical model after a time adapted to
the required minimum time steps. The ‘trick’ is that
rather than using an analytical well index, before any
run coarse grids are calibrated with a refined PTA
grid with a small single phase simulation around
each well. The value of the coarse grid well index
is adjusted to match the long-term productivity of
the refined grid. Numerical problems can therefore
be transferred between modules, upscaled or
downscaled, whilst remaining consistent.
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