Investigation of anisotropic mixing in miscible displacements

Dispersion (or local mixing) degrades miscibility in miscible flood displacements by interfering with the transfer of intermediate components that develop miscibility. Dispersion, however, can also 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 mixing in a finite difference compositional simulator at different scales (both fine and coarse scale) using a two-dimensional convection-dispersion model. All simulations were of constant mobility and density, first-contact miscible flow. The model allows for variations of velocity in both directions. We analyzed local (grid-block) concentration profiles for various miscible displacement models with different scales of heterogeneity and permeability autocorrelation lengths. To infer dispersivitiy we fitted an analytical two-dimensional convection dispersion model to the local concentration profile to determine simultaneously local longitudinal and transverse dispersivities. 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 one-dimensional convection dispersion model of dispersion, is significant when the flow direction changes locally as a result of heterogeneity. The computed streamlines, which highlight the variation in flow 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 (homogenized) during upscaling. This paper gives a quantitative and systematic 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.