structural geology, propagation mechanics and - Stanford School of ...

isotropic) can lead to numerical discretization errors when TPFA is applied. Such errors
can be eliminated through use of multipoint flux approximations (see Karimi-Fard et al.,
2004, for discussion of this issue). Errors resulting from TPFA are, however, reduced
when the grid is formed via a Delaunay triangulation. Given a set of points (vertices), a
Delaunay triangulation (Shewchuk, 1996) satisfies a Max-Min property, which means
that, for all possible triangulations of the set of points, the Delaunay procedure maximizes
the minimum angle of the triangulation. This tends to avoid very small or very large
angles, which lead to large discretization errors when TPFA is applied, and gives
triangles that are more nearly equilateral. For a grid comprised of equilateral triangles
(and isotropic permeability), a two-point flux approximation is strictly valid.
The overall solution procedure is compatible with general-purpose flow simulators
that apply connection lists for the definition of cell to cell connectivity. The
transmissibilities defined above along with the associated cell volumes are input to the
Stanford General Purpose Research Simulator (GPRS) for flow simulation. See Cao
(2002) for a detailed description of this simulator.
The CB map (Figure 7.3) was gridded using a standard Delaunay triangulation
(Shewchuk, 1996) technique. The resulting 2-D grid (Figure 7.5) contains 146,682
triangular and segment control volumes representing 1,948 discrete band traces and the
surrounding sandstone matrix. To avoid spurious boundary effects, an oval, no-flow
exterior boundary was established well outside the mapped pattern, while all flow effects
are evaluated inside the pattern. We note that these simulations are relatively demanding
computationally, and that it is not currently practical to perform such runs on full-field
models. However, by considering sectors, as is done here, it is possible to quantify the
impact of CBs on large-scale flow and transport.
In all of the simulations presented below, we specify a uniform band thickness (lb) of
3 cm, band porosity of 10%, homogeneous and isotropic internal band permeability of 1.5
mD, sandstone matrix porosity of 25%, and homogeneous, isotropic matrix permeability
of 1.5 Darcys. The stipulation of 3-cm band thickness approximately accounts for the
under-representation of band density in the final map as discussed above. The
band/matrix permeability ratio of 10 -3 falls in the middle of the range reported in the
literature (Sternlof et al., 2004).
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