title: Scaling and unified characterization of flow instabilities in layered heterogeneous porous media.
abstract: The physics of miscible flow displacements with unfavorable mobility ratios through horizontal layered heterogeneous media is investigated. The flow model is solved numerically, and the effects of various physical parameters such as the injection velocity, diffusion, viscosity, and the heterogeneity length scale and variance are examined. The flow instability is characterized qualitatively through concentration contours as well as quantitatively through the mixing zone length and the breakthrough time. This characterization allowed us to identify four distinct regimes that govern the flow displacement. Furthermore, a scaling of the model resulted in generalized curves of the mixing zone length for any flow scenario in which the first three regimes of diffusion, channeling, and lateral dispersion superpose into a single unifying curve and allowed us to clearly identify the onset of the fourth regime. A critical effective Péclet number w_{c} based on the layers' width is proposed to identify flows where heterogeneity effects are expected to be important and those where the flow can be safely treated as homogeneous. A similar scaling of the breakthrough time was obtained and allowed us to identify two optimal effective Péclet numbers w_{opt} that result in the longest and shortest breakthrough times for any flow displacement.
authors.affiliation: Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, Canada T2N 1N4.
authors.forename: M
authors.initials: M
authors.lastname: Sajjadi
authors.forename: J
authors.initials: J
authors.lastname: Azaiez