DISPERSION AND RESERVOIR HETEROGENEITY

This work examines the validity of physical models such as the convection-dispersion (C-D) equation to describe transport and mixing in a miscible displacement through the permeable medium. Dispersivity is a parameter which determines the degree of mixing and the dissipation of the injected slug. In this work dissipation of the fluid is modeled as mixing caused by the spatial variability in permeability.;The degree of autocorrelation in the medium determines whether or not megascopic dispersivity is uniquely defined. Large correlation distances (with respect to the reservoir dimensions) imply a dispersivity that grows with distance travelled. Small correlation distances imply a dispersivity that is eventually stabilized at some constant value. This value is related to the heterogeneity of the medium. Macroscopic dispersivity is smaller than or equal to megascopic dispersivity, and only slightly larger than the laboratory-measured dispersivity.;A simple technique is outlined to determine megascopic dispersivity from statistical and geostatistical parameters. These parameters include the mean, the standard deviation, and the degree of autocorrelation for the flux distribution. This work establishes a connection between Fickian and non-Fickian transport through the permeable medium, and the transition from one to the other is studied. The results from numerical simulations are compared with Taylor's theory of dispersion by continuous movements. This work shows that under certain conditions, Taylor's theory can predict both the Fickian and the non-Fickian transport.;This work examines the time and space dependent behavior of dispersivity at two scales of averaging--macroscopic and megascopic. Macroscopic dispersivity is the mixing, on the scale of several tens of grain diameters, at a point in the permeable medium which is free of boundary effects. Megascopic dispersivity is the one-dimensional dispersivity derived by averaging across an entire cross-section. A systematic study of the variables which determine the behavior of dispersivity in constant mobility displacements at these two scales is undertaken. The most important parameter influencing miscible transport is the magnitude and spatial distribution of rock permeability. Other important variables studied in this work include the shape of the reservoir, degree of molecular diffusion and the degree of anisotropy.