Investigation of anisotropic mixing in miscible displacements

Dispersion (or local mixing) degrades miscibility in miscible- fiood displacements by interfering with the transfer of intermedi ate components that develop miscibility. Dispersion, however, also can improve oil recovery by increasing sweep efficiency. Either way, dispersion is an important factor in understanding miscible-flood performance. This paper investigates longitudinal and transverse local mix ing in a finite-difference compositional simulator at different scales (both fine and coarse scale) using a 2D convection-disper sion model. All simulations were of constant-mobility and -den sity, first-contact miscible How. The model allows for variations of velocity in both directions. We analyzed local (gridblock) con centration profiles for various miscible-displacement models with different scales of heterogeneity and permeability autocorrelation lengths. To infer dispersivity, we fitted an analytical 2D con vection-dispersion model to the local concentration profile to determine local longitudinal and transverse dispersivities simulta neously. Streamlines of simulation models were traced using the algorithm proposed by Pollock (1988). To our knowledge, this is the first systematic attempt to numerically study local transverse dispersivity. The results show that transverse mixing, which is usually neglected in the ID convection-dispersion model of dispersion, is significant when the How direction changes locally as a result of heterogeneity. The computed streamlines, which highlight the variation in How directions, agree with the computed transverse- dispersivity trends. We find that both transverse and longitudinal dispersion can grow with travel distance and that there are several instances in which transverse dispersion is the larger of the two. Often, the variations in the streamlines are suppressed (homog enized) during upscaling. This paper gives a quantitative and sys tematic procedure to estimate the degree of transverse mixing (dispersivity) in any model. We conclude that local mixing, including transverse mixing, should be considered when upscaling a fine-scale model for miscible displacement to ensure proper preservation of fine-scale sweep and displacement efficiency and ultimate oil recovery for miscible-displacement simulations.