Dispersive mixing degrades field-scale miscible displacements through dilution of the injected solvent. This paper examines how local mixing owing to pore scale heterogeneity compares with the apparent mixing caused by numerical dispersion in heterogeneous permeable media. The numerical dispersion is associated with the truncation error inevitably introduced in finite difference approximations of the conservation equations.

In this study, the finite difference form of the convection-dispersion equation is derived to determine the numerical dispersion coefficients when flow velocity varies with distance. In addition, a simulation approach is used to evaluate local mixing in heterogeneous permeable media. The simulation models consist of an injector and a producer located at the ends of a two-dimensional grid. The simulations are performed with a fixed total dispersivity and different ratios of numerical to physical dispersivities. The local mixing for each grid block is determined through matching the concentration history to solution of the convection-dispersion equation.

Furthermore, spatial distribution of the local mixing caused by dissimilar sources of dispersivity is examined; geostatistics functions (the autocorrelation coefficient function and the semivariance) are determined for different separation distances. Autocorrelogram and variogram plots illustrate the variation of dispersivity in the longitudinal direction.

It turns out that the off-diagonal elements of the numerical dispersivity tensor are twice as large as in homogeneous reservoirs when the velocity changes with distance. Furthermore, the results indicate that the local mixing and the corresponding spatial distributions are considerably different when dissimilar ratios of numerical to physical are implemented. The different spatial distribution of local mixing explains why the growth of mixing zone is not characterized properly when considerable numerical dispersion is present. In addition, the results suggest that adjusting the size of grid blocks to account for the physical dispersivity is not appropriate in heterogeneous permeable media.

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