On the time scales of nonlinear instability in miscible displacement porous media flow

摘要

In this paper, we analyze the time scales as sociated with instable fingering induced by density con trasts in miscible displacement porous media flow. We perform numerical simulations of a two-dimensional domain with boundaries that are closed to flow and identify the three regimes of the dynamics, namely the development of a stable diffusive boundary layer, the onset and growth of instabilities, and the fully nonlinear dynamics. Special focus is given to the onset of the fully nonlinear regime. The results are generic in the sense that there are no parameters in the non-dimensional model problem. Large ensembles are studied and an error estimate is given based on the combined effect of numerical errors and sampling errors. The nonlinear time scales show a dependence on the size of initial per turbations. We estimate this size for three formations used for CO_2 storage and find that the onset of en hanced convective mixing is considerably delayed com pared with the linear onset time.