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

vertically such that both the magnitude and directionality of the flow and transport effects
realized in 2-D would substantially persist into 3-D.
While it might be interesting and useful to assess whether current dispersion theory
could capture the gross plume behavior exhibited in Figures 7.12-7.14, it is unlikely that
this approach would provide quantitatively accurate results. Even for idealized (Gaussian,
log-normal, etc.) permeability descriptions, it has been demonstrated that, as log
permeability variance increases, so does the gap between simulation results and
theoretical predictions (Naff et al., 1998; Dentz et al., 2002). It may nonetheless be
possible to describe the observed plume behavior qualitatively, or even semi-
quantitatively using effective dispersivity methods.
Accounting for capillary pressure effects in our two-phase simulations would, of
course, also be desirable. Although the modeling methods used in this study can in theory
handle these effects, as stated earlier, attempting to include them in the five-spot
production simulations led to significant degradation in computational efficiency. We
believe that this occurs as a result of the simulator attempting to resolve the very short
capillary time scales associated with the bands. Further investigation, testing and possible
modification of the numerical methods will be required to address this issue adequately. It
is important to note, however, that in many practical cases viscous (convective) effects
dominate capillary effects, so the neglect of capillary pressure is physically reasonable in
such systems.
Although not addressed in this paper, coarse-scale descriptions (i.e. upscaled models)
for detailed CB systems such as considered here would comprise the actual input
parameters to real-world aquifer- and reservoir-scale simulations. We note, however, that
coarse-scale flow attributes such as permeability and transmissibility might not be
independent of the flow process under consideration, but rather could depend on specified
parameters such as boundary conditions, well locations and flow rates. This sort of
process-dependent behavior has previously been observed in highly heterogeneous
systems with permeability features that are of a length scale comparable to the system
size or well spacing, as is the case here (Chen et al., 2003). For such systems, accurate
upscaling may require the incorporation of global flow information, which can
significantly complicate the computations.
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