Inertial effects in cyclic time-dependent displacement flows in homogeneous porous media

Miscible displacements in homogeneous porous media are investigated through numerical simulations for cyclic time-dependent velocities considering inertial effects. It is found that the velocity's models, cycle period, and amplitude have significant impacts on the flow, however the effects greatly depend on whether inertia is considered or not. Generally, cyclic extraction-injection (E/I) processes are always less unstable than constant injection and their injection-extraction (I/E) counterpart, regardless of the strength of inertia. Instabilities of E/I processes are reduced as the velocity period or amplitude increases, and these attenuating effects increase with the Reynolds number. However, in the case of I/E processes, the effects of the period and the amplitude are strongly dependent on inertia. For non-inertial cases, larger periods or amplitudes lead to more unstable flows, while for their inertial counterparts, the effects are found to be non-monotonic. In particular, as the period increases, instabilities first decrease and then increase. A period-stabilizing range is identified in which the displacements of the time-dependent injection velocities are actually less unstable than those of the constant injection flow. When the period is further increased to the period-destabilizing range, the flows tend to become more unstable. Moreover, the velocity amplitude can attenuate or enhance the instabilities depending on whether the period is within the period-stabilizing or period-destabilizing range. Furthermore, stronger inertial effects are found to greatly reduce the instabilities and to expand the period-stabilizing range.