Our objective is improved understanding of how to model the effects of heterogeneity and viscous fingering in adverse-mobility-ratio miscible displacements. We hypothesize that a formulation along the lines of Young, modified to allow for distinct longitudinal and transverse dispersivities, can use coarse-grid dispersion relationships to represent averaged fine-scale behavior. To study this question, we perform numerical simulations in five-spot geometries, using accurate finite-element methods on very fine grids, and attempt to match the resulting recoveries with coarse simulations employing an appropriate anisotropic dispersion term. We also compare the coarse-grid and fine-grid simulations to published experimental data.

It turns out to be very difficult to analyze the effects of the parameters in Young's model, due to statistical uncertainties in oil recovery. Different realizations of the same statistical properties of permeability can yield very different results. This raises many questions that should be studied further.

Despite the uncertainties, some clear conclusions can be drawn from our data. The anisotropic coarse-grid dispersion model can match experiments and averages of fine-grid realizations very well, while the traditional mixing-parameter model of fingering overestimates sweep efficiency and underestimates displacement efficiency when a comparable grid is used. Anisotropy is important, because it reduces recovery and avoids the optimistic predictions often attributed to convective-dispersion models. At the levels of heterogeneity considered in this study, with one standard deviation of a log-normal distribution representing a permeability increment of up to 50 percent, heterogeneity by itself does not influence recovery as much as fingering does.

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