Stability of double-diffusive double-convective miscible displacements in porous media

The present study offers a paradigm on the stability of two-component miscible displacements in a homogeneous porous medium. The components have, in general, different mobility ratios, may diffuse at different rates, and are convected at different speeds. As a result, one of the components may lag behind the other. For the adopted transport models, it is found that the differences in the rates of diffusion and the lag between the two component fronts resulting from the differences in the speeds of convection can modify radically the instability characteristics. In particular, an unstable single-component displacement is always made more unstable by the presence of a second unfavorable component. The instability of the same flow is, on the other hand, attenuated by the presence of a favorable, less diffusive lagging component. However, this same flow instability can actually be enhanced when the favorable lagging second component is more diffusive. Furthermore, the larger the lag between the two components is, the more unstable the flow is when the lagging component is favorable to the displacement. An opposite trend is found when the the lagging component is unfavorable to the displacement. Finally, changes due to the lag between the two components fronts are stronger for a less diffusive lagging component and weaker for a more diffusive one. For illustration, these results are discussed in the special context of a thermal displacement where mass and heat are transported in the porous media.