| Viscous fingering is an undesirable characteristic of many enhanced oil recovery (EOR) displacements, both miscible and immiscible, resulting in poor displacement efficiency. The complexity of the process has limited understanding to frontal stability analyses, experimental studies, simulations which attempt to mimic complex displacement patterns seen in the experiments, and heuristic models which, while oversimplified, do match some experimental data well. For the petroleum engineer to cope with the problem, however, the mechanics of finger growth must be understood.;Like any complex phenomenon, viscous fingering must be understood through studying its separate parts. As viscous forces are the primary driving mechanism in secondary and EOR processes, the purpose of this work is to study viscous fingering using vertical equilibrium (VE) concepts which assume viscous forces dominate all others. With this assumption, an analytic model of the growth of viscous fingers is derived based upon simulations of a single finger.;The single finger is seen to grow more like the heuristic Koval finger model, which assumes mixing, than a model which prohibits mixing. This establishes viscous mixing as an important mechanism in finger growth. In addition, adjusting transverse communication is seen to control finger growth, establishing viscous crossflow as the mechanism which causes the viscous mixing. The analytic model demonstrates that this mixing occurs in the absence of dispersion and diffusion, and can be used to study the sensitivity of viscous fingering to process parameters. Further, the model can match experimental data well, which suggests that the important finger growth mechanisms are represented in this simple model.;The study is extended to include heterogeneous systems to comment on both the effect of heterogeneity on the displacement and the generation of stochastic permeability fields. It is concluded that heterogeneity should include measures of both the variability and spatial arrangement of the values, as the effect of the heterogeneity varies greatly with both. Strong heterogeneity dominates the viscous effects, while weak heterogeneity allows viscous fingers to form and grow. |
