Scale-up of dispersion for simulation of miscible displacements
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Dispersion has been shown to degrade miscibility in miscible displacements by lowering the concentration of the injected solute at the displacement fronts. Dispersion can also improve oil recovery by increasing sweep efficiency. Either way, dispersion is an important factor in understanding miscible displacement performance. Conventionally, dispersion is measured in the laboratory by fitting the solution of one-dimensional convection-dispersion equation (CDE) to the effluent concentration from a core flood. However dispersion is anisotropic and mixing occurs in both longitudinal and transverse directions. This dissertation uses the analytical solution of the two-dimensional CDE to simultaneously determine longitudinal and transverse dispersion. The two-dimensional analytical solution for an instantaneous finite volume source is used to investigate anisotropic mixing in miscible displacements. We conclude that transverse mixing becomes significant with large a concentration gradient in the transverse direction and significant local variation in flow directions owing to heterogeneity. We also utilized simulation models similar to Blackwell's (1962) experiments to determine transverse dispersion. This model coupled with the analytical solution for two-dimensional CDE for continuous injection source is used to determine longitudinal and transverse dispersivity for the flow medium. The validated model is used to investigate the effect of heterogeneity and other first contact miscible (FCM) scaling groups on dispersion. We derive the dimensionless scaling groups that affect FCM displacements and determine their impact on dispersion. Experimental design is used to determine the impact and interactions of significant scaling groups and generate a response surface function for dispersion based on the scaling groups. The level of heterogeneity is found to most significantly impact longitudinal dispersion, while transverse dispersion is most significantly impacted by the dispersion number. Finally, a mathematical procedure is developed to use the estimated dispersivities to determine a-priori the maximum grid-block size to maintain an equivalent level of dispersion between fine-scale and upscaled coarse models. Non-uniform coarsening schemes is recommended and validated for reservoir models with sets of different permeability distributions. Comparable sweep and recovery are observed when the procedure was extended to multi-contact miscible (MCM) displacements.