Miscible porous media displacements in the quarter five-spot configuration. Part 3. Non-monotonic viscosity profiles

摘要

The influence of a non-monotonic viscosity-concentration relationship on miscible displacements in porous media is studied for radial source flows and the quarter five-spot configuration. Based on linear stability results, a parametric study is presented that demonstrates the dependence of the dispersion relations on both the Peclet number and the parameters of the viscosity profile. The stability analysis suggests that any displacement can become unstable provided only that the Peclet number is sufficiently high. In contrast to rectilinear flows, for a given end-point viscosity ratio an increase of the maximum viscosity generally has a destabilizing effect on the flow. The physical mechanisms behind this behaviour are examined by inspecting the eigensolutions to the linear stability problem. Nonlinear simulations of quarter five-spot displacements, which for small times correspond to radial source flows, confirm the linear stability results. Surprisingly, displacements characterized by the largest instability growth rates, and consequently by vigorous viscous fingering, lead to the highest breakthrough recoveries, which can even exceed that of a unit mobility ratio flow. It can be concluded that, for non-monotonic viscosity profiles, the interaction of viscous fingers with the base-flow vorticity can result in improved recovery rates.