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

Abstract

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.

Investigation of concentration‐dependent diffusion on frontal instabilities and mass transfer in homogeneous porous media

“…[26,33] With the same boundary and initial conditions, exactly the same VF structures are obtained for the two codes. However, the time step for the latter code should be as small as Dt ¼ 0.01.…”

“…In addition, it is worth noting that, although the apparent Pe is fixed in computation, the effective Pe may vary significantly depending on the spatial and temporal change of local velocities and the CDDC in the miscible displacement process. [15] Following previous studies, [9,26] the relation between concentration and viscosity is given by Equation (7). This exponential variation can closely characterize the "quarter-power mixing rule" adopted by petroleum engineers.…”

“…It would require a much larger grid size and smaller time step to achieve convergence when solving the governing equations with the previous semi-implicit predictorcorrector time-stepping algorithm. [26,33] More computational resources and a much longer time are needed, which make the simulations too time-consuming.…”

“…This result is similar to that of the previously reported CDC cases. [9,26] However, several differences can be clearly observed when comparing the two scenarios. At the same R, the values of mixing the CDDC case are initially less than its CDC counterpart.…”

Flow instabilities of time‐dependent injection schemes in immiscible displacements

“…This linear profile is defined by specified initial and final radii. [27] With few exceptions, most of the existing studies dealing with time-dependent injections of immiscible displacements have been limited to linear stability analysis. These results were recently tested by Huang and Chen for immiscible, partially miscible, and fully miscible flows in a Hele-Shaw Cell.…”